Use of Principal Axes as the Floating Reference Frame for a Moving Deformable Body

In this paper a method to adopt the principal axes of a deformable body as its body-attached frame is presented. The deformable body in a multibody setting is allowed to deform while it undergoes rigid-body motion. The fundamental concepts of imposing the principal axes as a moving reference frame are that the origin of the frame must remain at the instantaneous mass center and that the three products of inertia must remain zero as the body deforms. These conditions require the construction of several auxiliary matrices that are used in the constraint equations at the position, velocity, and acceleration levels. These auxiliary matrices are constructed only once and remain unchanged through the motion of the deformable body. The presented formulation does not depend on the type of finite element and multibody formulations or any associated assumptions.