Analytical Solutions of the 3-DOF Gyroscope Model

Abstract

The motion of a rigid body (a gyroscope) is one of the key issues in classical mechanics. It remains a significant challenge, as evidenced by its extensive practical implementations in various scientific disciplines and engineering operations. It is important to obtain analytical solutions, as they provide solutions that depend directly on the system’s parameters, which can be definitively interpreted. The coupling of numerical and analytical solutions allows for a more precise representation of the real phenomenon. The main objective of the article was to formulate analytical solutions for the motion of a Cardan suspension gyroscope subjected to controlling torque moments. Analytical solutions for the proposed mathematical model were developed using the Laplace transform and Green’s function. Subsequently, they were validated by numerical tests. The obtained analytical solutions are universally applicable, regardless of the type of controlling moments.