GMC Notes, Number 1 (2012)

Leonardo Colombo and Fernando Jiménez

Continuous and discrete mechanics for the attitude dynamics of a rigid

body on SO(3)

based on a course of Dr. Taeyoung Lee

Abstract. This review is devoted to the obtaining of the continuous and discrete Euler-Lagrange equations for the attitude dynam- ics of a rigid body in SO(3). On that purpose, we introduce basics about Lagrangian mechanics, Hamilton’s principle, Lie groups, Lie algebras, discrete Mechanics, geometric integration, Variational In- tegratos and some of its geometric properties. We present, quite exhaustively, the development of both continuous and discrete Euler- Lagrange equations for Lie group systems and, as particular cases, that ones concerning the rigid body and SO(3).