Identyfikatory
Warianty tytułu
Variační rovnice na Möbiově pásce
Języki publikacji
Abstrakty
In this paper, systems of second-order ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by the canonical embedding of the two-dimensional Möbius strip into the Euclidean space, are considered in the class of variational equations. For a given non-variational system, the conditions assuring variationality (Helmholtz conditions) for the induced system on the Möbius strip are formulated. The theory contributes to variational foundations of geometric mechanics.
V tomto clánku je studována variacnost systému obycejných diferenciálních rovnic (dynamických forem v geometrické mechanice) druhého rádu, kterou indukuje kanonické vložení dvojrozmerné Möbiovy pásky do Euklidova prostoru. Pro daný nevariacní systém rovnic jsou formulovány nutné a postacující podmínky variacnosti (Helmholtzovy podmínky). Práce je príspevkem k variacním základum geometrické mechaniky na Möbiove pásce.
Wydawca
Czasopismo
Rocznik
Tom
Strony
325--333
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- VŠB – Technical University of Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33, Ostrava, Czech Republic, tel.: +420 597 324 152
autor
- VŠB – Technical University of Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33, Ostrava, Czech Republic, tel.: +420 597 324 152
Bibliografia
- 1. D. Krupka. “On the local structure of the Euler–Lagrange mapping of the calculus of variations”, in: Proc. Conf. Diff. Geom. Appl., Charles University, Prague, 1981, p. 181–188; arXiv:math-ph/0203034.
- 2. D.Krupka. “Variational sequences in mechanics”, Calc. Var., Vol. 5, 1997, p. 557–583.
- 3. D. Krupka, D. Saunders (Eds.). Handbook of Global Analysis, Elsevier, Amsterdam, 2008.
- 4. D. Krupka, Z. Urban, J. Volná. “Variational submanifolds of Euclidean spaces”, submitted, 2017.
- 5. J.M. Lee. Introduction to Smooth Manifolds, 2nd Edition, Springer-Verlag, New York, 2012.
- 6. W. Sarlet. “The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics”, J. Phys. A: Math. Gen., Vol. 15, 1982, p. 1503–1517.
- 7. F.Takens. “A global version of the inverse problem of the calculus of variations”, J. Diff. Geom., Vol. 14, 1979, p. 543–562.
- 8. J. Volná, Z. Urban. “First-order Variational Sequences in Field Theory”, in: D. Zenkov (Ed.), The Inverse Problem of the Calculus of Variations, Local and Global Theory, Atlantis Press, Amsterdam–Beijing–Paris, 2015, p. 215–284.
- 9. F.W. Warner. Foundations of Differentiable Manifolds and Lie Groups, 2nd Ed., Springer, New York, 1983.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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