Euler-Poisson equations of a dancing spinning top, integrability and examples of analytical solutions

Autor:	Deriglazov, Alexei A.
Rok vydání:	2023
Předmět:	Mathematical Physics Astrophysics - Solar and Stellar Astrophysics High Energy Physics - Theory Nonlinear Sciences - Exactly Solvable and Integrable Systems Physics - Classical Physics
Zdroj:	Communications in Nonlinear Science and Numerical Simulation, 127 (2023) 107579
Druh dokumentu:	Working Paper
DOI:	10.1016/j.cnsns.2023.107579
Popis:	Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point, immersed in a fictitious gravity field. Using this analogy, we have found examples of analytical solutions for the case of a heavy symmetrical dancing top. They describe the motions with center of mass keeping its height fixed above the supporting plane. General solution to equations of a dancing top in terms of exponential of Hamiltonian field is given. An extra constraint, that take into account the reaction of supporting plane, leads to modification of the canonical Poisson structure and therefore the integrability according to Liouville is under the question. Comment: 12 pages, typos fixed
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2307.12201 View this record from Arxiv