The General Problem of Motion of a Rigid Body Acted upon by a Coaxial Combination of Potential and Gyroscopic Forces

Abstract

In the last chapter, we have seen that the problem of motion of a body in a liquid or, more precisely, the alternative problem of motion of a body about a fixed point, while acted by magnetic, electric and Lorentz forces, lies on the top of a hierarchy of problems, each of which generalizes the one below it. In this chapter, we extend this hierarchy upwards, by allowing general axi-symmetric potential and gyroscopic forces to act on the body. The fact that problems on that level of complication were not treated in the literature in no way means that such problems have little physical significance. A natural reason is that the grave theoretical difficulties met in as simple as the classical problem gave the impression that difficulties will grow with the degree of complication of forces applied to the body. Fortunately, it turned out that certain symmetries grow with the complication, opening wide chances to achieve far-reaching results.