An Almost Poisson Structure for the Generalized Rigid Body Equations

An Almost Poisson Structure for the Generalized Rigid Body Equations

In this paper we introduce almost Poisson structures on Lie groups which generalize Poisson structures based on the use of the classical Yang-Baxter identity. Almost Poisson structures fail to be Poisson structures in the sense that they do not satisfy the Jacobi identity. In the case of cross products of Lie groups, we show that an almost Poisson structure can be used to derive a system which ...

Relative Equilibria for the Generalized Rigid Body

This paper gives necessary and sufficient conditions for the (n-dimensional) generalized free rigid body to be in a state of relative equilibrium. The conditions generalize those for the case of the three-dimensional free rigid body, namely that the body is in relative equilibrium if and only if its angular velocity and angular momentum align, that is, if the body rotates about one of its princ...

Euler-Poisson equations on Lie algebras and the N-dimensional heavy rigid body.

The classical Euler-Poisson equations describing the motion of a heavy rigid body about a fixed point are generalized to arbitrary Lie algebras as Hamiltonian systems on coad-joint orbits of a tangent bundle Lie group. the N-dimensional Lagrange and symmetric heavy top are thereby shown to be completely integrable.

Almost-global tracking for a rigid body with internal rotors

Almost-global orientation trajectory tracking for a rigid body with external actuation has been well studied in the literature, and in the geometric setting as well. The tracking control law relies on the fact that a rigid body is a simple mechanical system (SMS) on the 3−dimensional group of special orthogonal matrices. However, the problem of designing feedback control laws for tracking using...

Almost Everywhere Convergence of Poisson Integrals on Generalized Half-planes