Solving a Problem of Rotary Motion for a Heavy Solid Using the Large Parameter Method

Abstract

The small parameter method was applied for solving many rotational motions of heavy solids, rigid bodies, and gyroscopes for different problems which classify them according to certain initial conditions on moments of inertia and initial angular velocity components. For achieving the small parameter method, the authors have assumed that the initial angular velocity is sufficiently large. In this work, it is assumed that the initial angular velocity is sufficiently small to achieve the large parameter instead of the small one. In this manner, a lot of energy used for making the motion initially is saved. The obtained analytical periodic solutions are represented graphically using a computer program to show the geometric periodicity of the obtained solutions in some interval of time. In the end, the geometric interpretation of the stability of a motion is given.