On the motion of a gyro in the presence of a Newtonian force field and applied moments

This work focuses on the motion of a dynamical model that consists of a symmetric rigid body (gyro) that rotates about a fixed point similar to Lagrange’s gyroscope. This body is acted upon by external forces represented by a Newtonian force field, gyro torques about the principal axes of inertia of the gyro and perturbing moments acting on the same axes. Assuming that, the gyro initially has a high angular velocity about the dynamic axis of symmetry. The averaging technique is used to obtain a more appropriate averaging system for the governing system of equations of motion in terms of a small parameter. Therefore, the analytical solutions of this system for two applications, depending on different forms of perturbing moments, are presented. These solutions are represented graphically to clarify the effectiveness of the different parameters of the body on the motion.

The Routh theorem for mechanical systems with unknown first integrals

In this paper we discuss problems of stability of stationary motions of conservative and dissipative mechanical systems with first integrals. General results are illustrated by the problem of motion of a rotationally symmetric rigid body on a perfectly rough plane.