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rdf:type
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Description
| - Jedním z výsledků teorie variačních posloupností týkajících se inverzního variačního problému je teorém, že dynamická forma $\varepsilon$, reprezentující systém parciálních diferenciálních rovnic je lokálně variační tehdy a jen tehdy, když její Helmholtzova forma $H(\varepsilon)$ je nulová. V článku je studován vztah mezi Lieovými derivacemi forem $\varepsilon$ a $H(\varepsilon)$. Je ukázáno, že invariance Helmholtzovy formy $H(\varepsilon)$ vzhledem k vektorovému poli $Z$, které zachovává kontaktní formy, je ekvivalentní s lokální variačností Lieovy derivace formy $\varepsilon$ vzhledem k poli $Z$. (cs)
- One of the results of the variational sequence theory, related to the inverse problem of the calculus of variations, states that a dynamical form $\varepsilon$, representing a system of partial differential equations, is locally variational if and only if the Helmholtz form $H(\varepsilon)$ vanishes. In this paper, a relationship between the Lie derivatives of $\varepsilon$ and $H(\varepsilon)$ is studied. It is shown that invariance of the Helmholtz form $H(\varepsilon)$ with respect to a vector field $Z$ preserving contact forms is equivalent with local variationality of the Lie derivative of $\varepsilon$ by $Z$.
- One of the results of the variational sequence theory, related to the inverse problem of the calculus of variations, states that a dynamical form $\varepsilon$, representing a system of partial differential equations, is locally variational if and only if the Helmholtz form $H(\varepsilon)$ vanishes. In this paper, a relationship between the Lie derivatives of $\varepsilon$ and $H(\varepsilon)$ is studied. It is shown that invariance of the Helmholtz form $H(\varepsilon)$ with respect to a vector field $Z$ preserving contact forms is equivalent with local variationality of the Lie derivative of $\varepsilon$ by $Z$. (en)
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Title
| - Contact symmetries and variational sequences
- Contact symmetries and variational sequences (en)
- Kontaktní symetrie a variační posloupnosti (cs)
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skos:prefLabel
| - Contact symmetries and variational sequences
- Contact symmetries and variational sequences (en)
- Kontaktní symetrie a variační posloupnosti (cs)
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skos:notation
| - RIV/61989592:15310/05:00001833!RIV06-MSM-15310___
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/03/0512), Z(MSM 153100011), Z(MSM6198959214)
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/61989592:15310/05:00001833
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Fibered manifold; Lagrangian; variational sequence; contact form; contact symmetry; Helmholtz form (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...ontrolniKodProRIV
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http://linked.open...v/mistoKonaniAkce
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http://linked.open...i/riv/mistoVydani
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http://linked.open...i/riv/nazevZdroje
| - Differential Geometry and its Applications
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...iv/tvurceVysledku
| - Krupková, Olga
- Krupka, Demeter
- Prince, G.
- Sarlet, W.
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http://linked.open...vavai/riv/typAkce
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http://linked.open.../riv/zahajeniAkce
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http://linked.open...n/vavai/riv/zamer
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number of pages
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http://purl.org/ne...btex#hasPublisher
| - Univerzita Karlova v Praze
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https://schema.org/isbn
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http://localhost/t...ganizacniJednotka
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