Geodesic motion on the symplectic leaf of with distorted e(3) algebra and Liouville integrability of a free rigid body
Depto. de Matemática, ICE, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, Brazil
Accepted: 19 March 2023
Published online: 30 March 2023
The solutions to the Euler–Poisson equations are geodesic lines of SO(3) manifold with the metric determined by inertia tensor. However, the Poisson structure on the corresponding symplectic leaf does not depend on the inertia tensor. We calculate its explicit form and confirm that it differs from the algebra e(3). The obtained Poisson brackets are used to demonstrate the Liouville integrability of a free rigid body. The general solution to the Euler–Poisson equations is written in terms of exponential of the Hamiltonian vector field.
© The Author(s) 2023
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