An augmented Lagrangian formulation for the equations of motion of multibody systems subject to equality constraints.

摘要

Some new theoretical and numerical results are presented on the dynamic response of a class of mechanical systems with equal ity motion constraints. At the beginning, the equations of motion of the corresponding unconstrained system are presented, first in strong and then in a weak form. Next, the formulation is extended to systems with holonomic and/or non-holonomic constraints. The formulation is based on a new set of equations of motion, represented by a system of second order ordinary differential equations (ODEs) in both the coordinates and the Lagrange multipliers associated to the motion constraints. Moreover, the position, velocity and momentum type quantities are assumed to be independent, forming a three field set of equations. The weak formulation developed was employed as a basis for producing a suitable time integration scheme for the systems examined. The validity and efficiency of this scheme was tested and illustrated by applying it to a number of characteristic example systems.