Application of hyper-dual numbers to rigid bodies equations of motion

Abstract

This paper formulates the equations of motion of a rigid body in a hyper-dual number form. By introducing the hyper-dual Jacobian matrix, hyper-dual velocity, hyper-dual momentum and the hyper dual inertia operator, while taking advantage of the “automatic differentiation” feature of the dual numbers, rigid body equations of motion are derived in a compact form with no need for further time differentiation. An open kinematic chain robot manipulator is presented as an exemplary application of the hyper-dual scheme to multi-body system dynamics.