Dual numbers representation of rigid body dynamics

A three-dimensional representation of rigid body dynamic equations becomes possible by introducing the dual inertia operator. This paper generalizes t his result and by using motor transformation rules and the dual inertia ope rator, gives a general expression for the three-dimensional dynamic equatio n of a rigid body with respect to an arbitrary point. Then, the dual Lagrange equation is formulated by developing derivative rul es of a real function with respect to dual variables. It is shown that the same rules hold for derivatives of a real function with respect to both rea l and dual variables. The analogy between rigid body spherical dynamics and the dual three-dimens ional spatial one is discussed and summarized. (C) 1998 Elsevier Science Lt d, All rights reserved.