Parametrization of finite rotations in computational dynamics: A review

Finite rotations are traditionnally regarded as geometric operations on vectors. By adopting an algebraic point of view, they many also be regarded as linear transformations with invariance properties. They can thus be described in terms of a minimal set of parameters, the choice of which is very wide. The objective of the paper is to make a general presentation of finite and differential motion kinematics in algebraic form and to discuss different methods of parametrization. The proposed concepts are then applied to develop an energy conserving time integration strategy to compute the long term response of a spinning top in a gravity field.