Kinetic Energy and Complementary Kinetic Energy in Gyrodynamics

Abstract

The concepts of kinetic energy and complementary kinetic energy permit to distinguish between two different formulations of what happens to be the same quantity in Newtonian mechanics. These formulations turn out to play a significant role in gyrodynamics in that they can be used very effectively to establish fundamental equations. It is relatively straightforward to establish a complementary kinetic energy expression. The establishment of the kinetic energy expression is, in spite of its unambiguous definition, more complicated, and a way is presented how to obtain it without too much difficulty. Equations are presented for the more common angle systems, i.e., for Euler angles of the first kind, Cardan angles of the first kind, both because of their fundamental importance, and Cardan angles of the fifth kind because of its prevalence in aeronautics.