Constrained integration of rigid body dynamics
In the present paper rigid body dynamics is formulated as mechanical system with holonomic constraints. This approach offers the appealing possibility to deal with finite rotations without employing any specific rotational parameterization. The numerical discretization of the underlying system of differential algebraic equations is treated in detail. The proposed algorithm obeys major conservation laws of the underlying continuous system such as conservation of energy and angular momentum. In addition to that, the constraints on the configuration and momentum level are fulfilled exactly. Two numerical examples are dealt with to assess the performance of the constrained algorithm.
finite rotations differential algebraic equations energymomentum methods multi-body dynamics