Variational Equations on the Möbius Strip

• Autorzy: Zbynek Urban , Jana Volna
• Języki publikacji: EN

Abstrakty

EN

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. (original abstract)

Słowa kluczowe

EN

Lagrange multiplier; Differential equations; Mechanics

PL

Mnożniki Lagrange'a; Równania różniczkowe; Mechanika

• Czasopismo: Systems Supporting Production Engineering
• Rocznik: 2017
• Numer: 6(4) Cross-Border Exchange of Experience in Production Engineering Using Principles of Mathematics
• Strony: 325--333

Twórcy

autor

Zbynek Urban

• VŠB - Technical University of Ostrava, Czech Republic

autor

Jana Volna

• VŠB - Technical University of Ostrava, Czech Republic

Bibliografia

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• D. Krupka, D. Saunders (Eds.). Handbook of Global Analysis, Elsevier, Amsterdam, 2008.
• D. Krupka, Z. Urban, J. Volná. "Variational submanifolds of Euclidean spaces", submitted, 2017.
• J.M. Lee. Introduction to Smooth Manifolds, 2nd Edition, Springer-Verlag, New York, 2012.
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• F.Takens. "A global version of the inverse problem of the calculus of variations", J. Diff. Geom., Vol. 14, 1979, p. 543-562.
• 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.
• F.W. Warner. Foundations of Differentiable Manifolds and Lie Groups, 2nd Ed., Springer, New York, 1983.