Mises Derivatives of Motors and Motor Tensors

Abstract

In the present paper it will be shown that the correct time derivatives of a motor or a motor tensor up to any degree are motors or motor tensors again. The correct time derivative of a motor is the “motor-derivative” which R.von Mises (1925) defined in his two great papers. As this derivation substantially deviates from the usual derivation of a vector or tensor — where all components are derived in the same way — we call it Mises derivative. It is shown that the “spatial derivative”, which was introduced by Featherstone (1987) for “spatial vectors” (six dimensional affine vectors representing motors), actually gives the same results as the Mises derivation of motors. Furthermore the question is briefly discussed as to whether a “true” acceleration motor or a “true” jerk motor exists. Although this question is of less importance, it has recently caused some confusion. Finally it is shown how the two fundamental dynamic equations for the rigid body (Newton-Euler) amalgamate into one single dynamic motor equation, and how advantageously Mises derivations can be applied to the inverse kinematics of the Gough-Stewart platform.