Publikacje

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 inter-
preted. 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.

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Analytical Solutions of the 3-DOF Gyroscope Model