TABLE OF CONTENTS The dynamics of multibody systems consisting of interconnected rigid and deformable bodies can be described by the coupled set of differential and algebraic equations given by Eqs. 155 and 158. Many techniques are available in the literature for the numerical solution of a mixed set of differential and algebraic equations. In this section, however, we outline the technique proposed by Wehage (1980) and discuss the use of Wehage s algorithm for solving the dynamic equations of multibody systems consisting of interconnected rigid and deformable bodies.
In the preceding section, we outlined a method for obtaining the acceleration vector. As pointed out earlier, the acceleration vector is a vector function of the system generalized coordinates, velocities, and time. This functional relationship represents n second-order differential equations, where n is the number of system generalized coordinates. The solutions of these equations, however, are not independent because of the kinematic constraints that describe mechanical joints as well as specified trajectories. One has to identify a set of independent coordinates and the associated set of differential equations that can be integrated forward in time in order to define the independent variables. Dependent coordinates (variables) can then be determined by using the kinematic relations.
For a virtual change ? q in the system generalized coordinates, Eq. 155 yields
| (5.176) |  |
The Jacobian matrix C q is an n c n matrix where n c < n. Since the constraint...
