Sciweavers

Share
FOCM
2008

Optimal Control and Geodesics on Quadratic Matrix Lie Groups

9 years 1 months ago
Optimal Control and Geodesics on Quadratic Matrix Lie Groups
In this paper, we consider some matrix subgroups of the general linear group and in particular the special linear group that are defined by a quadratic matrix identity. The Lie algebras corresponding to these matrix groups include several classical semisimple matrix Lie algebras. We describe an optimal control problem on these groups which gives rise to geodesic flows with respect to a positive definite metric. These geodesic flows generalize the Euler equations and the symmetric representation of the geodesic flow for the n-dimensional rigid body (given earlier by Bloch, Crouch, Marsden and Ratiu), to these matrix groups. A discretization of these flows is given which gives a numerical algorithm for computation of the flow dynamics. Contents
Anthony M. Bloch, Peter E. Crouch, Jerrold E. Mars
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where FOCM
Authors Anthony M. Bloch, Peter E. Crouch, Jerrold E. Marsden, Amit K. Sanyal
Comments (0)
books