Geometric Insight into the Dynamics of a Rigid Body Using the Theory of Screws

The paper begins with a review of screw algebra including dual numbers, unit line vectors, dual vectors, screws, line coordinates, and screw coordinates and summarizes the essential rules of operation for screw algebra. A significant advantage of the algebra is that geometric, kinematic, and dynamic equations of a rigid body can be expressed in a concise and compact form. Several physical quantities, which are important in the study of the dynamics of a rigid body, are shown to be screws. Geometric relationships between the velocity screw and the momentum screw are discussed, and the dual angle between the two screws is shown to provide insight into the kinetics of a rigid body. For the first time in the literature, the centripetal screw is defined, and the significance of the screw is explained. The dual Euler equation, which is the dual form of the Newton-Euler equations of motion, is shown to be a spatial triangle.