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 this result and by using motor transformation rules and the dual inertia operator, gives a general expression for the three-dimensional dynamic equation of a rigid body with respect to an arbitrary point. Then, the dual Lagrange equation is formulated by developing derivative rules 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 real and dual variables. The analogy between rigid body spherical dynamics and the dual three-dimensional spatial one is discussed and summarized.