Bifurcations from relative equilibria of Hamiltonian systems

Autor:	R. M. Roberts, M E R de Sousa Dias
Rok vydání:	1997
Předmět:	Applied Mathematics Mathematical analysis Rotational symmetry General Physics and Astronomy Motion (geometry) Statistical and Nonlinear Physics Hamiltonian system Momentum Classical mechanics Compact group Slice theorem Mathematical Physics Bifurcation Mathematics Symplectic geometry
Zdroj:	Nonlinearity. 10:1719-1738
ISSN:	1361-6544 0951-7715
DOI:	10.1088/0951-7715/10/6/015
Popis:	A symplectic version of the slice theorem for compact group actions is used to give a general description of the dynamics of a symmetric Hamiltonian system near a relative equilibrium as an interaction between rotational and vibrational motion. This is then used to prove a bifurcation theorem for relative equilibria. The bifurcation theorem is applied to two examples, the classical dynamics of an molecule near a symmetric linear equilibrium, and the dynamics of a system of two coupled identical axisymmetric rigid bodies near an equilibrium for which the two bodies are aligned on top of each other. Slice reduction of these systems is also used to describe other aspects of their dynamics. The results suggest that this will be a useful general technique for describing the dynamics of systems near relative equilibria which are singular points of the associated momentum maps.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::13859e7520e303a1b2c5f77341c7c04d https://doi.org/10.1088/0951-7715/10/6/015 Zobrazit plný text záznamu