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arXiv · 1608.03197

Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics

Roman Ya. Matsyuk
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Abstract

Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry principles and the inverse variational problem considerations in terms of vector-valued differential forms. In three-dimensional space-time we obtain a unique (covector) third-order Poincar\'e-invariant variational equation, which then is identified with the motion of a free relativistic top in flat three-dimensional space-time.

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Roman Ya. Matsyuk. 2016-08-04. Inverse Variational Problem and Symmetry in Action: The Relativistic Third Order Dynamics. https://arxiv.org/abs/1608.03197

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