Generalization of Hamilton–Ishlinskii Solid Angle Theorem for Spatial Motion of a Solid Body and its Applications

Abstract

Using the Kotelnikov–Study transference principle, a generalization of the Hamilton–Ishlinskii solid angle theorem for spatial motion of a solid that is a composition of translational and rotational motions and the dual conjugate theorem for the body motion are presented. An example of the studied spatial motion of a solid is considered. Possible applications of the dual solid angle theorem in the theory of spatial mechanisms and the mechanics of robotic manipulators are pointed out. Its application for the inertial navigation problem for determining the orientation and apparent velocity of a moving object is given. In considering the example and application, biquaternionic kinematic equations and their analytical solutions are used for the solid’s spatial motions under consideration. In the present study, the results obtained earlier by the author of the article are developed and generalized.