Poincaré-Chetaev equations in the Dirac's formalism of constrained systems

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 Poincaré-Chetaev equations. The general solution to these equations is written in terms of exponential of the Hamiltonian vector field.

arXiv comment6 pages, Typos fixed, references added

References in corpus (9)

• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Geometric Origin of the Tennis Racket Effect
• Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system
• Massless polarized particle and Faraday rotation of light in the Schwarzschild spacetime
• Nonminimal spin-field interaction of the classical electron and quantization of spin
• Basic notions of Poisson and symplectic geometry in local coordinates, with applications to Hamiltonian systems
• Geodesic motion on the symplectic leaf of $SO(3)$ with distorted $e(3)$ algebra and Liouville integrability of a free rigid body
• The Relativistic Spherical Top as a Massive Twistor
• Coulomb problem for classical spinning particle

Cited by in corpus (4)

• Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system
• Has the problem of the motion of a heavy symmetric top been solved in quadratures?
• Lagrange top: integrability according to Liouville and examples of analytic solutions
• An alternative interpretation of the Grioli gyroscope suspension points