Higher-Order Relative Kinematics of Rigid Body Motions: A Dual Lie Algebra Approach

In this paper, using the tensor calculus and the dual numbers algebra, a new computing method for studying the higher-order accelerations field properties is proposed in the case of the general rigid body motion. For the spatial kinematic chains, equations that allow the determination of the nth order accelerations field are given, using a Brockett-like formula specific to the dual algebra. The results are coordinate-free and in a closed form. In particular cases, the properties for velocities, accelerations, jerks and jounces fields are given. This approach uses the isomorphism between the Lie group of the rigid displacements SE3 and the Lie group of the orthogonal dual tensors.