The Dynamics of Two Coupled Rigid Bodies,
Abstract
In this paper we derive a Poisson bracket on the phase space so(3) x so(3) x SO(3) such that the dynamics of two three dimensional rigid bodies coupled by a ball and socket joint can be written as a Hamiltonian system. This paper we introduce a Poisson bracket on the phase space. SO(3) is the dual of the Lie algebra of SO(3), so that the dynamics of two rigid bodies coupled by a ball and socket joint can be written as the Hamilitonian system H = (F,H). This sets the stage so that the stability and asymptotics of the system can be studied using the energy Casimir method as in Holm, Marsden, Ratiu and Weinstein 1985 and Krishnaprasad 1985; so that chaotic solutions can be found using the Melnikov method such as in Holmes and Marsden 1983; so that bifurcations of the system can be described using the techniques in Golubitsky and Stewart 1986 and Lewis, Marsden and Ratiu 1986; and so that control issues can be studied, as in Sanchez de Alvarez 1986.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1987
- Accession Number
- ADA187592
Entities
People
- Jerrold E. Marsden
- P.S.Krishnaprasad
- R. Grossman
Organizations
- University of Maryland