Abstract

The forces on a rigid body can always be expressed as the sum of a sliding vector and a rotation. This paper shows how the sum of any set of forces acting on a rigid body can be described by a bivalent alternating holor, and can be decomposed into a single sliding vector plus a single rotation. This problem was first studied by Study (Geometrie der Dynamen, Leipzig, 1901). The holor representation of rigid body motion was developed after tensor calculus had been developed by this author [?Geometric Figures in Affine Space?, J. Math. Phys. 23, 1 (1944) and ?The Tensor Interpretation of the Figures of Study's ?Geometrie der Dynamen?, J. Math Phys 23, 103 (1944)], and is now included in the recent text Theory of Holors by Moon and Spencer (Cambridge University Press, 1986, paperback 2005).