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arXiv · 2302.12423

Poincar\'e-Chetaev equations in the Dirac's formalism of constrained systems

Alexei A. Deriglazov
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Abstract

We single out a class of Lagrangians on a group manifold, for which one can introduce non-canonical coordinates in the phase space, which simplify the construction of the Poisson structure without explicitly calculating the Dirac bracket. In the case of $SO(3)$\,- manifold, the application of this formalism leads to the Poincar\'e-Chetaev equations. The general solution to these equations is written in terms of exponential of the Hamiltonian vector field.

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BibTeXRIS

Alexei A. Deriglazov. 2023-02-24. Poincar\'e-Chetaev equations in the Dirac's formalism of constrained systems. https://doi.org/10.3390/particles6040059

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