Higher-Order Kinematics of Rigid Bodies. A Tensors Algebra Approach

Abstract

The problem of determining the tensors and the vector invariants that describe the vector field of the nth order accelerations is generally avoided in rigid body kinematics. This paper extends the discussion from velocities and accelerations to nth order accelerations. Using the tensor calculus and the dual numbers algebra, a computing method for studying the nth order acceleration field properties is proposed for the case of the general motion of the rigid body. This approach uses the isomorphism between the Lie group of the rigid displacements $S{\mathbb{E}}_{3}$ and the Lie group of the orthogonal dual tensors $\underline{{S{\mathbb{O}}}}_{3}$.