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SEO Keyword summary for en.wikipedia.org/wiki/hamilton%e2%80%93jacobi_theory
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle mathbf frac |
long Tail Keywords (2 words) mathbf q hamiltonjacobi equation partial spartial q mathbf mathbf p |
long Tail Keywords (3 words) mathbf dot q frac partial spartial omega xi 1 qdisplaystyle mathbf q mathbf q 0 hamiltons principal function q mathbf p |
en.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a en.wikipedia.org/wiki/hamilton%e2%80%93jacobi_theory page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
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hamiltonndashjacobi equation wikipedia
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
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Headings
Heading distribution
Heading normalisation
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Emphasis (bold and italic)
Emphasis SEO impact
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Mobile SEO en.wikipedia.org/wiki/hamilton%e2%80%93jacobi_theory
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SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
hamilton found in path !
jacobi found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistics
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Item | Factor | Pointers | |
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PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 43% | A title should reflect the contents of a site. This site has a 33 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 43 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
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Number of internal links | 30% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 424 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 6 folders above or in the first level of navigation. | |
Headings | 25% | Headers should reflect the contents of a site. This site has a 11 % match | |
Links | 8% | Link anchors should to some degree reflect the contents of a site. This site has a 4 % match | |
Image alt tags | 20% | Image alt tags should to some degree reflect the contents of a site. This site has a 7 % match | |
Bold and italic | 24% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 8 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
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WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 7415 words | |
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Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 671 inline style declarations ( <a style="color:green">) with a size of 24748 bytes | |
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Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
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Css | 30% | We detected too much (2) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 40% | We dit not font a normalized heading structure. A heading 2 (h2) for example should be followed by a heading of an equal level (h2), a child heading (h3) or even a aprent heading (h1). |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/667211b683b48896651f4bc24dd3995e489b37ef height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {v} \,{\stackrel {\text{def}}{=}}\,{\dot {\gamma }}(\tau ;t,t_{0},\mathbf {q} ,\mathbf {q} _{0})|_{\tau =t}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ba6aa2ea316658897f600fce7c6444dea46d90d4 height: height attribute not set width: width attribute not set description: {\displaystyle \tau =t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1181ac575661863a8c3c4f61f7f089f093880b9d height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\partial s}{\partial q^{i}}}=\left.{\frac {\partial {\cal {l}}}{\partial {\dot {q}}^{i}}}\right|_{\mathbf {\dot {q}} =\mathbf {v} }\!\!\!\!\!\!\!,\quad i=1,\ldots ,n.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d7035fcb9fe3ebecc6bc9f372f82d0352202c8bf height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {r} ^{n},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/27962ddb2d082ea88e141807e88ee5afdfbfaa67 height: height attribute not set width: width attribute not set description: {\displaystyle {\cal {s}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5cdfa2d22d859ddc69a6950ab5f6faa4a1ee72e4 height: height attribute not set width: width attribute not set description: {\displaystyle \xi =\xi (t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/227d0b68ccae2a48b4ef96c85a864a6575ccb3cf height: height attribute not set width: width attribute not set description: {\displaystyle \delta \xi =\delta \xi (t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b461aaf61091abd5d2c808931c48b8ff9647db height: height attribute not set width: width attribute not set description: {\displaystyle \xi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4ea3ad87830a1055c7b85c04cf940cfd3b847ae6 height: height attribute not set width: width attribute not set description: {\displaystyle t,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6d488b922983fe0297a866544d5a65209eeb8108 height: height attribute not set width: width attribute not set description: {\displaystyle \delta \xi (t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d14b0b0146f7196ff6234dd7fc36608035da5b3a height: height attribute not set width: width attribute not set description: {\displaystyle \xi (t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5925bb75ac2527ebec817fa292ef461324b12d2b height: height attribute not set width: width attribute not set description: {\displaystyle \delta {\cal {s}}_{\delta \xi }[\gamma ,t_{1},t_{0}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/719c0fa3ca0c6c21d2609a6b8e3017919b4a0c25 height: height attribute not set width: width attribute not set description: {\displaystyle \delta \xi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3c7d21084e5f41892a45563e97683f4f205ded9e height: height attribute not set width: width attribute not set description: {\displaystyle \delta {\cal {s}}_{\delta \xi }[\xi ,t_{1},t_{0}]=\int _{t_{0}}^{t_{1}}\left({\frac {\partial {\cal {l}}}{\partial \mathbf {q} }}-{\frac {d}{dt}}{\frac {\partial {\cal {l}}}{\partial \mathbf {\dot {q}} }}\right)\delta \xi \,dt+{\frac {\partial {\cal {l}}}{\partial \mathbf {\dot {q}} }}\,\delta \xi {\biggl |}_{t_{0}}^{t_{1}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/36d27c66f01c5bc434a10d21658f78d9882e7cac height: height attribute not set width: width attribute not set description: {\displaystyle q^{i}=\xi ^{i}(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a375d012b650295d7435977d4ab87ef5e91e4b37 height: height attribute not set width: width attribute not set description: {\displaystyle {\dot {q}}^{i}={\dot {\xi }}^{i}(t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d2e3c2914268bf399cea9484ce9ddd63d0c6b7e7 height: height attribute not set width: width attribute not set description: {\displaystyle \delta \xi (t_{0})=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aa70b09d9f637c3eb8da5dbb7f7f0570e295e85c height: height attribute not set width: width attribute not set description: {\displaystyle \delta {\cal {s}}_{\delta \xi }[\xi ,t;t_{0}]=\left.{\frac {\partial {\cal {l}}}{\partial \mathbf {\dot {q}} }}\right|_{\mathbf {\dot {q}} ={\dot {\xi }}(t)}^{\mathbf {q} =\xi (t)}\,\delta \xi (t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6ef1d1c228bee2610c7380fd713361bd0be2ef6a height: height attribute not set width: width attribute not set description: {\displaystyle \gamma =\gamma (\tau ;\mathbf {q} ,\mathbf {q} _{0},t,t_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f303b0227e8951945f669bf33432f7d3ab824980 height: height attribute not set width: width attribute not set description: {\displaystyle \delta \gamma =\delta \gamma (\tau )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e0e69b347b17068b0ddc3ff4626f10a4d1e8dc94 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dadf7bbc4e0f696ed3ab7b81002bf43dc828ff0c height: height attribute not set width: width attribute not set description: {\displaystyle \gamma _{\varepsilon }=\gamma _{\varepsilon }(\tau ;\mathbf {q} _{\varepsilon },\mathbf {q} _{0},t,t_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a223c880b0ce3da8f64ee33c4f0010beee400b1a height: height attribute not set width: width attribute not set description: {\displaystyle \gamma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/10183b579f930de36b9193eb077081df594dc088 height: height attribute not set width: width attribute not set description: {\displaystyle \delta \gamma .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e68812db1b3db25af338ce3804e61a530d1f6e8a height: height attribute not set width: width attribute not set description: {\displaystyle \gamma _{\varepsilon }|_{\varepsilon =0}=\gamma ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e60b490aba99cc6e81d371549f4e1d425ef8e422 height: height attribute not set width: width attribute not set description: {\displaystyle {\dot {\gamma }}_{\varepsilon }|_{\varepsilon =0}=\delta \gamma ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ae592b41a596a0299bd06d9ec20a3b7ed1a0086e height: height attribute not set width: width attribute not set description: {\displaystyle \gamma _{\varepsilon }|_{\tau =t_{0}}=\gamma |_{\tau =t_{0}}=\mathbf {q} _{0}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5ac37e83ad61a3ed68e813e829cfc91acc0584d2 height: height attribute not set width: width attribute not set description: {\displaystyle \delta {\cal {s}}_{\delta \gamma }[\gamma ,t]{\overset {\text{def}}{{}={}}}\left.{\frac {d{\cal {s}}[\gamma _{\varepsilon },t]}{d\varepsilon }}\right|_{\varepsilon =0}=\left.{\frac {ds(\gamma _{\varepsilon }(t),t)}{d\varepsilon }}\right|_{\varepsilon =0}={\frac {\partial s}{\mathbf {\partial q} }}\,\delta \gamma (t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8058bc95987be560c199554f331e5ce77acfbc2d height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {q} =\gamma (t;\mathbf {q} ,\mathbf {q} _{0},t,t_{0})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fa3e545cc3b60263f544c5c6774d29ff59140359 height: height attribute not set width: width attribute not set description: {\displaystyle \xi =\gamma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9434cb09aa85a9bf2a8720bb70b2f9b1e624124c height: height attribute not set width: width attribute not set description: {\displaystyle \delta \xi =\delta \gamma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bf64c7c89fb15ff0e0510833c3230577076a58ca height: height attribute not set width: width attribute not set description: {\displaystyle \delta {\cal {s}}_{\delta \xi }[\xi ,t;t_{0}]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cc6292a466a15c81d962b16c3c5545fa736f47b1 height: height attribute not set width: width attribute not set description: {\displaystyle t>t_{0},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8fbef1ae179942d66721f1ad240f04364001fa91 height: height attribute not set width: width attribute not set description: {\displaystyle \delta \gamma } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d7407579244856095966c24674e1192ed0da225 height: height attribute not set width: width attribute not set description: {\displaystyle h(\mathbf {q} ,\mathbf {p} ,t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7d145e27f5f1b89833b4e82e7601f3764630e7b0 height: height attribute not set width: width attribute not set description: {\displaystyle -{\frac {\partial s}{\partial t}}=h\left(\mathbf {q} ,{\frac {\partial s}{\partial \mathbf {q} }},t\right).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c9ed2749efda21bfb47b51bf6738cee88116d65f height: height attribute not set width: width attribute not set description: {\displaystyle \xi =\xi (t;t_{0},\mathbf {q} _{0},\mathbf {v} _{0}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5649a86ffb9947b1a7e492b0849cc97f03cb5281 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {v} _{0}={\dot {\xi }}|_{t=t_{0}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c00f09f39fab9e4db886ebaa5b04dc0671b39bb8 height: height attribute not set width: width attribute not set description: {\displaystyle {\cal {l}}(\xi (t),{\dot {\xi }}(t),t)={\frac {ds(\xi (t),t)}{dt}}=\left[{\frac {\partial s}{\partial \mathbf {q} }}\mathbf {\dot {q}} +{\frac {\partial s}{\partial t}}\right]_{\mathbf {\dot {q}} ={\dot {\xi }}(t)}^{\mathbf {q} =\xi (t)}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/042c4e6d5e9bb137d4f9b5dd6d8f3eaef9462433 height: height attribute not set width: width attribute not set description: {\displaystyle p_{i}=p_{i}(\mathbf {q} ,t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e5c75522ff730946798fd49e6083ff70d1e3c362 height: height attribute not set width: width attribute not set description: {\displaystyle h(\mathbf {q} ,\mathbf {p} ,t)=\mathbf {p} \mathbf {\dot {q}} -{\cal {l}}(\mathbf {q} ,\mathbf {\dot {q}} ,t),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ab792bb7df5db1dcfcdc4f1c5f1aa6a9486313d1 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {\dot {q}} (\mathbf {p} ,\mathbf {q} ,t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7d140e3a82a87719aef960bab07b6556894f736c height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {\dot {q}} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/858a4c4b8b2d81604dff9cd7b63d99537919f6c0 height: height attribute not set width: width attribute not set description: {\textstyle \mathbf {p} ={\frac {\partial {\cal {l}}(\mathbf {q} ,\mathbf {\dot {q}} ,t)}{\partial \mathbf {\dot {q}} }},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a5d9db7bf0e23603e7a46bad5b35770ea15c9797 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\partial s}{\partial t}}={\cal {l}}(\mathbf {q} ,\mathbf {\dot {q}} ,t)-{\frac {\partial s}{\mathbf {\partial q} }}\mathbf {\dot {q}} =-h\left(\mathbf {q} ,{\frac {\partial s}{\partial \mathbf {q} }},t\right),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6ca11e9391a8c06a086acfbcaf3d0f456856292f height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {q} =\xi (t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c669da7d1591a829b5b9acfa9858805261a4b1f1 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {\dot {q}} ={\dot {\xi }}(t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8b4478fa70425f7b47eff68fbdacc0c90ad377b1 height: height attribute not set width: width attribute not set description: {\displaystyle h=h(q_{1},q_{2},\ldots ,q_{n};p_{1},p_{2},\ldots ,p_{n};t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e288621e7bd58c1acc803576d425f3d471394a80 height: height attribute not set width: width attribute not set description: {\displaystyle p_{k}={\frac {\partial s}{\partial q_{k}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf2b9cbfe9051fd4e7b50c8028866d497eac35b height: height attribute not set width: width attribute not set description: {\displaystyle n+1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d1ae98dbb11e36796effcf09a7709fe2266db8df height: height attribute not set width: width attribute not set description: {\displaystyle \alpha _{1},\,\alpha _{2},\dots ,\alpha _{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6a86a7028f8f61d7fd1a423520fca9c6513246f3 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\partial s}{\partial t}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dd73e3862cb92b016721b8c492eadb4e8a577527 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {p} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f18349f87ad2f6c8df573ad4635e4667ea6a5972 height: height attribute not set width: width attribute not set description: {\displaystyle \beta _{k}={\frac {\partial s}{\partial \alpha _{k}}},\quad k=1,2,\ldots ,n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3 height: height attribute not set width: width attribute not set description: {\displaystyle \alpha } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8 height: height attribute not set width: width attribute not set description: {\displaystyle \beta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4ba38e283972ad72a7fd04ba4fee5d47aa336265 height: height attribute not set width: width attribute not set description: {\displaystyle q_{1},\,q_{2},\dots ,q_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aa1dbb3992b89a794fa5318b4fc22d20e24a1293 height: height attribute not set width: width attribute not set description: {\displaystyle p_{1},\,p_{2},\dots ,p_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/50819c971fc99497cddb2e5898d2d97debbe6f83 height: height attribute not set width: width attribute not set description: {\displaystyle g_{2}(\mathbf {q} ,\mathbf {p} ,t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/90952ca48f6687b5002b9fd29fe245ef400b2c64 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {p} ={\partial g_{2} \over \partial \mathbf {q} },\quad \mathbf {q} ={\partial g_{2} \over \partial \mathbf {p} },\quad k(\mathbf {q} ,\mathbf {p} ,t)=h(\mathbf {q} ,\mathbf {p} ,t)+{\partial g_{2} \over \partial t}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/815401783baf18eaee29066a6dd79529ea87770d height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {p} ,\,\mathbf {q} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2b76fce82a62ed5461908f0dc8f037de4e3686b0 height: height attribute not set width: width attribute not set description: {\displaystyle k} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/99f682eceb3e3a28452cbb67ac7b2cddda1f43b2 height: height attribute not set width: width attribute not set description: {\displaystyle {\dot {\mathbf {p} }}=-{\partial k \over \partial \mathbf {q} },\quad {\dot {\mathbf {q} }}=+{\partial k \over \partial \mathbf {p} }.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a4bd07ee8bd3acd19e5313c5b5ac0c81baaf2f60 height: height attribute not set width: width attribute not set description: {\displaystyle k=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/24213d609d50c9e399e1b4b6f32405d1ef60ff57 height: height attribute not set width: width attribute not set description: {\displaystyle {\dot {\mathbf {p} }}={\dot {\mathbf {q} }}=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c0c250ef2a112c86b93c637dfa288c6d7f34ac3f height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {p} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a261664834458407fc6c7def1e787d1a71bf6d83 height: height attribute not set width: width attribute not set description: {\displaystyle p_{m}=\alpha _{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/132d0144479d6f47c30ad82a65d458966ccbe928 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {q} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8be25f8fef093ea5f8df8d3537f54ea433d8f775 height: height attribute not set width: width attribute not set description: {\displaystyle \beta _{1},\,\beta _{2},\dots ,\beta _{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c7b808c646cb9ee62975f958dc904701b4bda551 height: height attribute not set width: width attribute not set description: {\displaystyle q_{m}=\beta _{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3 height: height attribute not set width: width attribute not set description: {\displaystyle a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2de1fad3e7c5dcc174d9bd252be16b20bf24d685 height: height attribute not set width: width attribute not set description: {\displaystyle g_{2}(\mathbf {q} ,{\boldsymbol {\alpha }},t)=s(\mathbf {q} ,t)+a,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a946c706059fc281fa9491328985ae6d2c81ff2d height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {p} ={\frac {\partial g_{2}}{\partial \mathbf {q} }}={\frac {\partial s}{\partial \mathbf {q} }}\,\rightarrow \,h(\mathbf {q} ,\mathbf {p} ,t)+{\partial g_{2} \over \partial t}=0\,\rightarrow \,h\left(\mathbf {q} ,{\frac {\partial s}{\partial \mathbf {q} }},t\right)+{\partial s \over \partial t}=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2b7ca338c19fe8e7bea784483c8401aefec6a745 height: height attribute not set width: width attribute not set description: {\displaystyle s(\mathbf {q} ,{\boldsymbol {\alpha }},t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0dcef16590b1b3cdd0148950ec30fb0098b8556e height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {q} ={\boldsymbol {\beta }}={\partial s \over \partial {\boldsymbol {\alpha }}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9b5b797db22ebf06404b71bfceabfb46877ce00d height: height attribute not set width: width attribute not set description: {\displaystyle q_{m}=\beta _{m}={\frac {\partial s(\mathbf {q} ,{\boldsymbol {\alpha }},t)}{\partial \alpha _{m}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/acebdc7dc039d7a856c8cb426e8ee2983e0ff7ec height: height attribute not set width: width attribute not set description: {\displaystyle {\boldsymbol {\alpha }},\,{\boldsymbol {\beta }},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a0498edd5c4b575183e87051fd991a9deded7d48 height: height attribute not set width: width attribute not set description: {\displaystyle -e} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a50e7694ee54d9601deadcc97b0d203237d261cc height: height attribute not set width: width attribute not set description: {\displaystyle s=w(q_{1},q_{2},\ldots ,q_{n})-et} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9069f5fd8503ff3490057dcd02be54c5b05e99e7 height: height attribute not set width: width attribute not set description: {\displaystyle w(\mathbf {q} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ebe0ac45a38c4437bd2689a14ec434cd499e7e49 height: height attribute not set width: width attribute not set description: {\displaystyle s_{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/86d4d0c58dc49cd567d24211b8677df41d4ea22a height: height attribute not set width: width attribute not set description: {\displaystyle h\left(\mathbf {q} ,{\frac {\partial s}{\partial \mathbf {q} }}\right)=e.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f27215e46abcad60f100434d2c8003310580af95 height: height attribute not set width: width attribute not set description: {\displaystyle q_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/090c2b646e2d494dea3e8197d848e512613ecb5b height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\partial s}{\partial q_{k}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4dc21a83162c3b15e9f635a0db57c82102b906da height: height attribute not set width: width attribute not set description: {\displaystyle \psi \left(q_{k},{\frac {\partial s}{\partial q_{k}}}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cc8582c58e3631bda65f2b0306cf7e9b78619fcb height: height attribute not set width: width attribute not set description: {\displaystyle h=h(q_{1},q_{2},\ldots ,q_{k-1},q_{k+1},\ldots ,q_{n};p_{1},p_{2},\ldots ,p_{k-1},p_{k+1},\ldots ,p_{n};\psi ;t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0f0009534b4ca611053485e9afdae41514c26f2e height: height attribute not set width: width attribute not set description: {\displaystyle s=s_{k}(q_{k})+s_{\text{rem}}(q_{1},\ldots ,q_{k-1},q_{k+1},\ldots ,q_{n},t).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ffb3cb973b6a2204708bcf5c2cde41b8bc3ebdce height: height attribute not set width: width attribute not set description: {\displaystyle \gamma _{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ac082c0e95621a9635c406e86569ba0525c3081 height: height attribute not set width: width attribute not set description: {\displaystyle s_{k}(q_{k}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/01d6bc33dae1935e1c790c09aeda4479d4e04809 height: height attribute not set width: width attribute not set description: {\displaystyle \psi \left(q_{k},{\frac {ds_{k}}{dq_{k}}}\right)=\gamma _{k}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cee223e1ee48b3d3d1176476100947e292f2b01e height: height attribute not set width: width attribute not set description: {\displaystyle s_{m}(q_{m}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de12609abac0edcd401a5def44ebd9197abbfba7 height: height attribute not set width: width attribute not set description: {\displaystyle s=s_{1}(q_{1})+s_{2}(q_{2})+\cdots +s_{n}(q_{n})-et.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1d84f2cba2231029bc99e6c3bcaeb5de497e9874 height: height attribute not set width: width attribute not set description: {\displaystyle h={\frac {1}{2m}}\left[p_{r}^{2}+{\frac {p_{\theta }^{2}}{r^{2}}}+{\frac {p_{\phi }^{2}}{r^{2}\sin ^{2}\theta }}\right]+u(r,\theta ,\phi ).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d2b67400395a83af416082a9b1b38c8e3ad891c height: height attribute not set width: width attribute not set description: {\displaystyle u_{r}(r),u_{\theta }(\theta ),u_{\phi }(\phi )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/458a728f53b9a0274f059cd695e067c430956025 height: height attribute not set width: width attribute not set description: {\displaystyle u} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/23f9ff4beec1102d8c9ec652ac5ce7602f43234e height: height attribute not set width: width attribute not set description: {\displaystyle u(r,\theta ,\phi )=u_{r}(r)+{\frac {u_{\theta }(\theta )}{r^{2}}}+{\frac {u_{\phi }(\phi )}{r^{2}\sin ^{2}\theta }}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e534b4e0546a6b5e24af8be805c3df1935f8f177 height: height attribute not set width: width attribute not set description: {\displaystyle s=s_{r}(r)+s_{\theta }(\theta )+s_{\phi }(\phi )-et} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ca9dad5ab4db3a31800c366190e9494f070890d7 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2m}}\left({\frac {ds_{r}}{dr}}\right)^{2}+u_{r}(r)+{\frac {1}{2mr^{2}}}\left[\left({\frac {ds_{\theta }}{d\theta }}\right)^{2}+2mu_{\theta }(\theta )\right]+{\frac {1}{2mr^{2}\sin ^{2}\theta }}\left[\left({\frac {ds_{\phi }}{d\phi }}\right)^{2}+2mu_{\phi }(\phi )\right]=e.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4 height: height attribute not set width: width attribute not set description: {\displaystyle \phi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1fa2bdef5d278a717d268d5b0999165a1bd11ed7 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {ds_{\phi }}{d\phi }}\right)^{2}+2mu_{\phi }(\phi )=\gamma _{\phi }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f27b8f59be3f92ea2a82f2bf8ef7708fa6fb5dd5 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma _{\phi }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/20ea3b4c9e47946cd9627dc6a28bd629f07e1509 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2m}}\left({\frac {ds_{r}}{dr}}\right)^{2}+u_{r}(r)+{\frac {1}{2mr^{2}}}\left[\left({\frac {ds_{\theta }}{d\theta }}\right)^{2}+2mu_{\theta }(\theta )+{\frac {\gamma _{\phi }}{\sin ^{2}\theta }}\right]=e.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af height: height attribute not set width: width attribute not set description: {\displaystyle \theta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/db7cdf509bc7075310bc3b7ceccf2d57786fe727 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {ds_{\theta }}{d\theta }}\right)^{2}+2mu_{\theta }(\theta )+{\frac {\gamma _{\phi }}{\sin ^{2}\theta }}=\gamma _{\theta }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/55a328bcb0366e512357b01395fc59094aaaaf51 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma _{\theta }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3a0a744a2d705f0d8e360bfb816074cc2cf92455 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2m}}\left({\frac {ds_{r}}{dr}}\right)^{2}+u_{r}(r)+{\frac {\gamma _{\theta }}{2mr^{2}}}=e} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6383853d22c244004b7ce6d11d50f23921ad81c1 height: height attribute not set width: width attribute not set description: {\displaystyle h={\frac {p_{\mu }^{2}+p_{\nu }^{2}}{2ma^{2}\left(\sinh ^{2}\mu +\sin ^{2}\nu \right)}}+{\frac {p_{z}^{2}}{2m}}+u(\mu ,\nu ,z)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/781f67e2fb92a5b7043b0fec0a48b1506a36a69c height: height attribute not set width: width attribute not set description: {\displaystyle \pm a} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4 height: height attribute not set width: width attribute not set description: {\displaystyle x} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7c4137ff616a53546690819cc6047c1b03d977aa height: height attribute not set width: width attribute not set description: {\displaystyle u(\mu ,\nu ,z)={\frac {u_{\mu }(\mu )+u_{\nu }(\nu )}{\sinh ^{2}\mu +\sin ^{2}\nu }}+u_{z}(z)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5e8171b4e3ef2367244bf3247443a75f834c6f54 height: height attribute not set width: width attribute not set description: {\displaystyle u_{\mu }(\mu )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/abba9d1ef0daae0d1226f68e1503f68001135f53 height: height attribute not set width: width attribute not set description: {\displaystyle u_{\nu }(\nu )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3f01d9bd6e9723d2d9aa85a9fd85c9735eaa8f97 height: height attribute not set width: width attribute not set description: {\displaystyle u_{z}(z)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ba784207be7263cf708d40e8f9a53aa435866f8b height: height attribute not set width: width attribute not set description: {\displaystyle s=s_{\mu }(\mu )+s_{\nu }(\nu )+s_{z}(z)-et} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ac87cd9d6f1069ef4944847c2adfe17d7ff9ef30 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2m}}\left({\frac {ds_{z}}{dz}}\right)^{2}+u_{z}(z)+{\frac {1}{2ma^{2}\left(\sinh ^{2}\mu +\sin ^{2}\nu \right)}}\left[\left({\frac {ds_{\mu }}{d\mu }}\right)^{2}+\left({\frac {ds_{\nu }}{d\nu }}\right)^{2}+2ma^{2}u_{\mu }(\mu )+2ma^{2}u_{\nu }(\nu )\right]=e.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f9f87268f63881c3adc885da5e195c2b8e891fb3 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2m}}\left({\frac {ds_{z}}{dz}}\right)^{2}+u_{z}(z)=\gamma _{z}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d97cf48fc54c500d6b7739d5696992e2ea03e9ed height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {ds_{\mu }}{d\mu }}\right)^{2}+\left({\frac {ds_{\nu }}{d\nu }}\right)^{2}+2ma^{2}u_{\mu }(\mu )+2ma^{2}u_{\nu }(\nu )=2ma^{2}\left(\sinh ^{2}\mu +\sin ^{2}\nu \right)\left(e-\gamma _{z}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/acd4dd9a511087ccb6c61ecb91d50731deace329 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {ds_{\mu }}{d\mu }}\right)^{2}+2ma^{2}u_{\mu }(\mu )+2ma^{2}\left(\gamma _{z}-e\right)\sinh ^{2}\mu =\gamma _{\mu }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3c1ea1faeeb7e5de152bd2d5a0be764151130637 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {ds_{\nu }}{d\nu }}\right)^{2}+2ma^{2}u_{\nu }(\nu )+2ma^{2}\left(\gamma _{z}-e\right)\sin ^{2}\nu =\gamma _{\nu }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/15257a0b84d102deb56c66cad0525a82068a2fb7 height: height attribute not set width: width attribute not set description: {\displaystyle h={\frac {p_{\sigma }^{2}+p_{\tau }^{2}}{2m\left(\sigma ^{2}+\tau ^{2}\right)}}+{\frac {p_{z}^{2}}{2m}}+u(\sigma ,\tau ,z).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dd8e13d3c8410bb4b8fb0b06276aef0f810a7bf3 height: height attribute not set width: width attribute not set description: {\displaystyle u(\sigma ,\tau ,z)={\frac {u_{\sigma }(\sigma )+u_{\tau }(\tau )}{\sigma ^{2}+\tau ^{2}}}+u_{z}(z)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/034ecd597bccd5db023afa8efdda5225ad32323c height: height attribute not set width: width attribute not set description: {\displaystyle u_{\sigma }(\sigma )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4193a14947c1109b7d36f387bb504aab0eb11fab height: height attribute not set width: width attribute not set description: {\displaystyle u_{\tau }(\tau )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/036b875f6e37e17a903bd69f488c43a51b08c417 height: height attribute not set width: width attribute not set description: {\displaystyle s=s_{\sigma }(\sigma )+s_{\tau }(\tau )+s_{z}(z)-et+{\text{constant}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2c8bffbfef87ccf88604581a38e5143e245074c2 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2m}}\left({\frac {ds_{z}}{dz}}\right)^{2}+u_{z}(z)+{\frac {1}{2m\left(\sigma ^{2}+\tau ^{2}\right)}}\left[\left({\frac {ds_{\sigma }}{d\sigma }}\right)^{2}+\left({\frac {ds_{\tau }}{d\tau }}\right)^{2}+2mu_{\sigma }(\sigma )+2mu_{\tau }(\tau )\right]=e.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fa8c2a4646c6baadb51fdbf08f2fb54907b4a712 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {ds_{\sigma }}{d\sigma }}\right)^{2}+\left({\frac {ds_{\tau }}{d\tau }}\right)^{2}+2mu_{\sigma }(\sigma )+2mu_{\tau }(\tau )=2m\left(\sigma ^{2}+\tau ^{2}\right)\left(e-\gamma _{z}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dea657a77790ad28d8e8bcfd296a8e9d6c1fdc9c height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {ds_{\sigma }}{d\sigma }}\right)^{2}+2mu_{\sigma }(\sigma )+2m\sigma ^{2}\left(\gamma _{z}-e\right)=\gamma _{\sigma }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1006a1954e446bcf824883f48f86ccfc09f9db96 height: height attribute not set width: width attribute not set description: {\displaystyle \left({\frac {ds_{\tau }}{d\tau }}\right)^{2}+2mu_{\tau }(\tau )+2m\tau ^{2}\left(\gamma _{z}-e\right)=\gamma _{\tau }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/590df57dd01bc80460902d980162fb9f746f902f height: height attribute not set width: width attribute not set description: {\textstyle {\cal {c}}_{t}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bd7fae9c72e84282de6cf66b6381e224eb33852c height: height attribute not set width: width attribute not set description: {\textstyle t=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b2bc926f90178739fccd01a96c6fa778ab3535d6 height: height attribute not set width: width attribute not set description: {\textstyle t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/db299e88e5485f250f4ba15530469c8c6080a8cb height: height attribute not set width: width attribute not set description: {\textstyle t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ccfaad8c8e8a8fe33a54be7812042bc2b83db781 height: height attribute not set width: width attribute not set description: {\displaystyle t={\frac {1}{c}}\int _{a}^{b}n\,ds} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cc6e1f880981346a604257ebcacdef24c0aca2d6 height: height attribute not set width: width attribute not set description: {\textstyle n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/22d0224b72c638d0d873d9b9fcb645aae1af26ac height: height attribute not set width: width attribute not set description: {\textstyle ds} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0cbed7054c016658a5418e797bb30ec4c7269cc0 height: height attribute not set width: width attribute not set description: {\textstyle \mathbf {q} _{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e8c3b38adca34fe0acce62b16498d8553864caa4 height: height attribute not set width: width attribute not set description: {\textstyle t_{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/13fc9c3c79597a6202e57600e32594b3f089ef47 height: height attribute not set width: width attribute not set description: {\textstyle \mathbf {q} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a88d7cb5a06e6c276663e99027205987a2ba3aa height: height attribute not set width: width attribute not set description: {\textstyle s(\mathbf {q} ,t)={\text{const}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7e1d77872b04eff43d2a20957a7bfb56b948273d height: height attribute not set width: width attribute not set description: {\textstyle s(\mathbf {q} ,t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ad42c1d5da8c7ff8dd12946e8760518e86c6fbed height: height attribute not set width: width attribute not set description: {\displaystyle \mathbf {p} ={\frac {\partial s}{\partial \mathbf {q} }}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3ef21723f61dcb9c3b63847706a000987e06cab6 height: height attribute not set width: width attribute not set description: {\textstyle \mathbf {p} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1474aa17e8005b900c58d7dbb297424e86b42e81 height: height attribute not set width: width attribute not set description: {\textstyle {\dot {\mathbf {q} }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/76414de54ed259f1af3c4b58ef16f0f34d62dc7e height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\partial {\cal {l}}}{\partial {\dot {\mathbf {q} }}}}={\boldsymbol {p}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/00f585163a02b24bbc793d7feca35e2a0797f527 height: height attribute not set width: width attribute not set description: {\textstyle {\cal {l}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3a9798e69ae297664214c3045d8bd0b1c0208d5 height: height attribute not set width: width attribute not set description: {\displaystyle s(\mathbf {q} ,t)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2731a7d6c11b2f4c4185185affd5dc5e51e72e72 height: height attribute not set width: width attribute not set description: {\displaystyle \psi =\psi _{0}e^{is/\hbar }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de68de3a92517953436c93b5a76461d49160cc41 height: height attribute not set width: width attribute not set description: {\displaystyle \hbar } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9131ca2e9513ad0d37a73eacdb478c43eb2d7c76 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi -u\psi ={\frac {\hbar }{i}}{\frac {\partial \psi }{\partial t}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a height: height attribute not set width: width attribute not set description: {\displaystyle \psi } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/221e6a4e8e5b861379836ab70b86c9c6fe4c4844 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2m}}\left(\nabla s\right)^{2}+u+{\frac {\partial s}{\partial t}}={\frac {i\hbar }{2m}}\nabla ^{2}s.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cf00388b93a754b255edf3d102b97121f59c65de height: height attribute not set width: width attribute not set description: {\displaystyle \hbar \rightarrow 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e5836d1dc04d698e1f5913326ca4f55fe61f8a3e height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2m}}\left(\nabla s\right)^{2}+u+{\frac {\partial s}{\partial t}}=0.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c99c643fb51c8a9e02068f68fc938094bf191a80 height: height attribute not set width: width attribute not set description: {\displaystyle g^{\alpha \beta }p_{\alpha }p_{\beta }-(mc)^{2}=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc height: height attribute not set width: width attribute not set description: {\displaystyle m} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d8c85e5354c5370a72b45ecaa3f33065d755b37d height: height attribute not set width: width attribute not set description: {\displaystyle g^{\alpha \beta }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455 height: height attribute not set width: width attribute not set description: {\displaystyle c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ee2e7716a05197800e320d8e78c21de1594cd88 height: height attribute not set width: width attribute not set description: {\displaystyle p_{\alpha }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b161bd6f4dd6b6f809f3a4fc4945b77af7a3550f height: height attribute not set width: width attribute not set description: {\displaystyle p_{\alpha }=-{\frac {\partial s}{\partial x^{\alpha }}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77 height: height attribute not set width: width attribute not set description: {\displaystyle g} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1d04cd8d1cdc4c3abbc171f30fd52cd12c4b42f6 height: height attribute not set width: width attribute not set description: {\displaystyle g^{\alpha \beta }{\frac {\partial s}{\partial x^{\alpha }}}{\frac {\partial s}{\partial x^{\beta }}}-(mc)^{2}=0,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467 height: height attribute not set width: width attribute not set description: {\displaystyle e} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bc2f22481d7bd432705a6956ba822699189e1c26 height: height attribute not set width: width attribute not set description: {\displaystyle a_{i}=(\phi ,\mathrm {a} )} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4d1bf2affbb6a03b8c34b99978742f776c7db39e height: height attribute not set width: width attribute not set description: {\displaystyle g^{ik}=g_{ik}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/593d8d5891a72cf181330b7efa6825b3f702e17e height: height attribute not set width: width attribute not set description: {\displaystyle g^{ik}\left({\frac {\partial s}{\partial x^{i}}}+{\frac {e}{c}}a_{i}\right)\left({\frac {\partial s}{\partial x^{k}}}+{\frac {e}{c}}a_{k}\right)=m^{2}c^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a1d12923841ad7a504eab1909149a953a8ea11f height: height attribute not set width: width attribute not set description: {\displaystyle x=-{\frac {e}{c\gamma }}\int a_{z}\,d\xi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6359c1b076b09e04e558ed7a6e3347a346102521 height: height attribute not set width: width attribute not set description: {\displaystyle y=-{\frac {e}{c\gamma }}\int a_{y}\,d\xi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2df9f173f06226755702f130abe81b2e50247244 height: height attribute not set width: width attribute not set description: {\displaystyle z=-{\frac {e^{2}}{2c^{2}\gamma ^{2}}}\int (\mathrm {a} ^{2}-{\overline {\mathrm {a} ^{2}}})\,d\xi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5ed984cbbef7b7df6752a94e79a43772ddb099b3 height: height attribute not set width: width attribute not set description: {\displaystyle \xi =ct-{\frac {e^{2}}{2\gamma ^{2}c^{2}}}\int (\mathrm {a} ^{2}-{\overline {\mathrm {a} ^{2}}})\,d\xi ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dfcc3f2f24545c2577251eba775890dc63d04d9b height: height attribute not set width: width attribute not set description: {\displaystyle p_{x}=-{\frac {e}{c}}a_{x},\quad p_{y}=-{\frac {e}{c}}a_{y},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2aced878bfc8d9c991d90f713e1390909ae77054 height: height attribute not set width: width attribute not set description: {\displaystyle p_{z}={\frac {e^{2}}{2\gamma c}}(\mathrm {a} ^{2}-{\overline {\mathrm {a} ^{2}}}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2d0e108cca14494c3d0515f5c969bc67ecda133d height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {e}}=c\gamma +{\frac {e^{2}}{2\gamma c}}(\mathrm {a} ^{2}-{\overline {\mathrm {a} ^{2}}}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d13aa5cce07b7f362948363bff1497a172627437 height: height attribute not set width: width attribute not set description: {\displaystyle \xi =ct-z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/94e4cd49870797ffd01c026f4faf755b7b4e27c1 height: height attribute not set width: width attribute not set description: {\displaystyle \gamma ^{2}=m^{2}c^{2}+{\frac {e^{2}}{c^{2}}}{\overline {a}}^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c24d529c2e40beedb1a18706438f44aec995cc05 height: height attribute not set width: width attribute not set description: {\displaystyle {\overline {\mathbf {a} }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2a6c8230b50ff18b98b32212af9313463a27e83d height: height attribute not set width: width attribute not set description: {\displaystyle e_{x}=e_{0}\sin \omega \xi _{1},\quad e_{y}=e_{0}\cos \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/54e7422c687819898372166fc01a0f77988c9602 height: height attribute not set width: width attribute not set description: {\displaystyle a_{x}={\frac {ce_{0}}{\omega }}\cos \omega \xi _{1},\quad a_{y}=-{\frac {ce_{0}}{\omega }}\sin \omega \xi _{1}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e29d7e315d83b3ff82d2e1f5dded4c63741e90c2 height: height attribute not set width: width attribute not set description: {\displaystyle x=-{\frac {ece_{0}}{\omega }}\sin \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6f4f59720760d27f24cc723ffdade60de65f9203 height: height attribute not set width: width attribute not set description: {\displaystyle y=-{\frac {ece_{0}}{\omega }}\cos \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b0615e01525f67206c2e231e7bf15cf4267ace8d height: height attribute not set width: width attribute not set description: {\displaystyle p_{x}=-{\frac {ee_{0}}{\omega }}\cos \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/98be8045fdd0501677b0d89a35697366b057fcfd height: height attribute not set width: width attribute not set description: {\displaystyle p_{y}={\frac {ee_{0}}{\omega }}\sin \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/adb2a07ce1bebcf88e8192b5952b89e4064dd36d height: height attribute not set width: width attribute not set description: {\displaystyle \xi _{1}=\xi /c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/568cdcaec2950eefe8c4e85553830f84f16bab77 height: height attribute not set width: width attribute not set description: {\displaystyle ece_{0}/\gamma \omega ^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/43db3ba14f56690f6824e88e2910f85f4dd96c34 height: height attribute not set width: width attribute not set description: {\displaystyle ee_{0}/\omega ^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b height: height attribute not set width: width attribute not set description: {\displaystyle e} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d height: height attribute not set width: width attribute not set description: {\displaystyle y} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a6d2269bd528c3cef53c8836b606e726407f79e5 height: height attribute not set width: width attribute not set description: {\displaystyle e_{y}=e_{0}\cos \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a6106443ff2a23e714e2542e7d178db72567c114 height: height attribute not set width: width attribute not set description: {\displaystyle a_{y}=-{\frac {ce_{0}}{\omega }}\sin \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/99b6598a90d53957091842abd76d5665b43eb8b6 height: height attribute not set width: width attribute not set description: {\displaystyle x={\text{const}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/47f8b7eff2e8663572364fb38737728b41fe6f21 height: height attribute not set width: width attribute not set description: {\displaystyle y_{0}=-{\frac {ece_{0}}{\gamma \omega ^{2}}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/35616b850e50a0cc48ab82eea6153850d64cb7e2 height: height attribute not set width: width attribute not set description: {\displaystyle y=y_{0}\cos \omega \xi _{1},\quad z=c_{z}y_{0}\sin 2\omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2161005619740a64c609695314ce1568da71b21f height: height attribute not set width: width attribute not set description: {\displaystyle c_{z}={\frac {ee_{0}}{8\gamma \omega }},\quad \gamma ^{2}=m^{2}c^{2}+{\frac {e^{2}e_{0}^{2}}{2\omega ^{2}}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/758ea96d9636e7dd58faedde41e79f0996848e69 height: height attribute not set width: width attribute not set description: {\displaystyle p_{x}=0,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f5d9d107649b921d25e38c19f521c145c9f7941 height: height attribute not set width: width attribute not set description: {\displaystyle p_{y,0}={\frac {ee_{0}}{\omega }},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e4c6b13c261bcd0eddf408589ae9b4495d46644c height: height attribute not set width: width attribute not set description: {\displaystyle p_{y}=p_{y,0}\sin \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/036bfc3cd450484945a090f916508d52819cdf59 height: height attribute not set width: width attribute not set description: {\displaystyle p_{z}=-2c_{z}p_{y,0}\cos 2\omega \xi _{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9b648677954973d9184a11b58371fb3b6f56e931 height: height attribute not set width: width attribute not set description: {\displaystyle e=e_{\phi }={\frac {\omega \rho _{0}}{c}}b_{0}\cos \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4ff64087b282cbb99e8d0166a91673193e75ff63 height: height attribute not set width: width attribute not set description: {\displaystyle a_{\phi }=-\rho _{0}b_{0}\sin \omega \xi _{1}=-{\frac {l_{s}}{\pi \rho _{0}n_{s}}}i_{0}\sin \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6fe3365f506788be98b6694dd8baf5a8534bb0a6 height: height attribute not set width: width attribute not set description: {\displaystyle x={\text{constant}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e311bf66504dabce7108939dafb61a32042c29c2 height: height attribute not set width: width attribute not set description: {\displaystyle y_{0}=-{\frac {e\rho _{0}b_{0}}{\gamma \omega }},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/964635f8a3b19c0ba2b080302b100631e15d48d4 height: height attribute not set width: width attribute not set description: {\displaystyle y=y_{0}\cos \omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a2de1bcccbd6ab526435a1c9e3bfc3f7871b3a1b height: height attribute not set width: width attribute not set description: {\displaystyle z=c_{z}y_{0}\sin 2\omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5da1462608d96f0cdae451df614be108a74bc1a2 height: height attribute not set width: width attribute not set description: {\displaystyle c_{z}={\frac {e\rho _{0}b_{0}}{8c\gamma }},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9ab8b316ea8a1be49713907a967aea24c55eea8f height: height attribute not set width: width attribute not set description: {\displaystyle \gamma ^{2}=m^{2}c^{2}+{\frac {e^{2}\rho _{0}^{2}b_{0}^{2}}{2c^{2}}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d697a68fb44babfd46717f6ae9d035aedbd71f86 height: height attribute not set width: width attribute not set description: {\displaystyle p_{y,0}={\frac {e\rho _{0}b_{0}}{c}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/08d41650456ea6f89e6c8319c2490285fa648ab6 height: height attribute not set width: width attribute not set description: {\displaystyle p_{z}=-2c_{z}p_{y,0}\cos 2\omega \xi _{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/03a3f39a56ba486e7c6ec89b99f5ae2a21fa75b6 height: height attribute not set width: width attribute not set description: {\displaystyle b_{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d9c04a9d26b86af8c6205ba2a6287fd655b6b714 height: height attribute not set width: width attribute not set description: {\displaystyle \rho _{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/22f2969037546092e72a12968c4f8c7689cc8401 height: height attribute not set width: width attribute not set description: {\displaystyle l_{s}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6ac3a27c668f576235f61db580f73580f726a358 height: height attribute not set width: width attribute not set description: {\displaystyle n_{s}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/893d08e90ea73781dc133414d661529d0651ca80 height: height attribute not set width: width attribute not set description: {\displaystyle i_{0}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a9c7cbe4344a9d72acfc98a97e2b3ec44bb48d1f height: height attribute not set width: width attribute not set description: {\displaystyle yz} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e height: height attribute not set width: width attribute not set description: {\displaystyle \varphi } |
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http://en.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
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http://en.wikipedia.org/w/resources/assets/poweredby_mediawiki.svg height: 31 width: 88 description: powered by mediawiki |
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