Lagrangian and hamiltonian dynamics on SO(3)

Abstract

The configuration manifold is a product of copies of the special orthogonal group SO(3) embedded in R3×3. A Lagrangian function L:T(SO(3)×…×SO(3))→R1 is introduced and variational methods are used to derive Euler-Lagrange equations and Hamilton’s equations. Several rotating rigid body systems are studied to illustrate the developments.