ISSN:
1572-9222
Keywords:
Geometric mechanics
;
reduction
;
stability
;
chaos
;
rigid body dynamics
;
periodic orbits
;
58F
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01053929