engleski

Lie Group Modeling and Forward Dynamics Simulation of Multibody Systems. Part 2 : Dynamics and Time Integration

By formulating kinematics of multibody systems using the Lie group concepts, the Lagrangian equations of motion of a MBS with a tree structure with and without additional constraints are presented in the paper. In the case of multibody systems with additional constraints, it is shown that the Lagrangian equations of motion projected to the constraint manifold yield the equations of Woronetz. The issue of time integration of a constrained MBS, whose mathematical models are shaped as DAE systems, is addressed in the sequel. Since the DAE formulation of index 1 yields numerical constraint violation at the generalized position and velocity level, the stabilized time-integration procedure, whose constraint stabilization step is based on the projection of integration results to the underlying constraint manifold via post-integration correction of selected coordinates, is discussed. The geometric properties of the algorithm are analysed and optimally partitioned coordinates for generally constrained MBSs are discussed.

multibody systems; Lagrange equations; Lie groups; Riemannian manifolds; Woronetz equations; numerical integration; constraint violation stabilization; CAD; ODE on manifolds; DAE systems

nije evidentirano