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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Projective Dynamics and First Integrals
Alain Albouy IMCCE-CNRS-UMR, Observatoire de Paris, 77, avenue Denfert-Rochereau, 75014 Paris, France
Аннотация:
We present the theory of tensors with Young tableau symmetry as an efficient computational tool in dealing with the polynomial first integrals of a natural system in classical mechanics. We relate a special kind of such first integrals, already studied by Lundmark, to Beltrami’s theorem about projectively flat Riemannian manifolds. We set the ground for a new and simple theory of the integrable systems having only quadratic first integrals. This theory begins with two centered quadrics related by central projection, each quadric being a model of a space of constant curvature. Finally, we present an extension of these models to the case of degenerate quadratic forms.
Ключевые слова:
bi-hamiltonian, Beltrami’s theorem, Young tableau symmetry, free motion, force field, decomposability preserving.
Поступила в редакцию: 02.02.2015
Образец цитирования:
Alain Albouy, “Projective Dynamics and First Integrals”, Regul. Chaotic Dyn., 20:3 (2015), 247–276
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd42 https://www.mathnet.ru/rus/rcd/v20/i3/p247
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Страница аннотации: | 193 | Список литературы: | 41 |
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