Motor Tensor Calculus

This paper reviews the motor calculus as it was presented by Richard von Mises [1] and extends it to a general motor tensor calculus on the basis of unit motors. R. v. Mises defined a scalar and a motorial product of two motors without using Clifford’s duality unit e (e2 = 0) and introduced motor dyads. In complete analogy to the common tensor analysis, we define motor tensors of any order and show how the motorial product of two motors can be converted into a product of a motor multiplied by second order motor tensor, the cross motor tensor. With this motor tensor, whose matrix is a special function of the motor elements, and the unit motor dyad, the transfer of motor equations into matrix equations, or the decomposition of a motor equation into its six scalar equations, becomes a simple and straightforward procedure. A consistent notation for motor and motor dyads, which are used in the forthcoming English translation of v. Mises motor calculus [2], facilitates the algebra.