2 - Kinematics and dynamics of rigid bodies

Abstract

This chapter focuses on kinematics and dynamics of rigid bodies. The application of a modern multibody systems computer program requires a good understanding of the underlying theory involved in the formulation and solution of the equations of motion. It is necessary to examine the use of vectors for static analysis in multibody systems (MBS) to understand development of the equations of motion associated with large displacement rigid body dynamic motion. In multibody dynamics, bodies may undergo motion which involves rotation about all three axes of a given reference frame. An understanding that large rotations are not a vector is an important aspect of multibody systems analysis. In multibody systems analysis, it is often necessary to transform the components of a vector measured parallel to the axis of one reference frame to those measured parallel to a second reference frame. These operations should not be confused with vector rotation. If a rigid body comprises rigidly attached combinations of regular shapes, the overall inertial properties of the body can be found using the parallel axis theorem. It is possible to formulate six equations of motion corresponding with the six degrees of freedom resulting from unconstrained motion. In addition to the derivation of the equations of motion based on the direct application of Newton's laws, variational methods, including, Lagranges equations, provide an elegant alternative and are often employed in MBS formulations.