S. Sorokin
Russia,
195251,
St.-Petersburg,
Politechnicheskaya Street 29,
St.-Petersburg State Technical University,
Department of Theoretical Mechanics,
P. Zhilin
Russia,
199178,
St.-Petersburg,
V.O., Bolshoi 61,
Institute of the mechanical engineering Problems,
Russian Academy of Sciences,
The present paper develops a new model named rigid body oscillator. This model plays the same role in the Euler mechanics as a model of nonlinear oscillator in the Newton mechanics. Many scientists pointed out the importance of introduction of a rigid body oscillator model (a rigid body on the elastic base of the general form). However, the problem is not formalized up to now. In the paper we are interested in studying a gyrostat, i. e. rigid body with one or many built-in rotors, on the elastic base. All concepts necessary for mathematical description are introduced. Some of these concepts (e. g. the concept of a potential moment) are new. The equations of motions are represented in the form that is unusual for the rigid body dynamics. On the one hand, these equations have a simple structure clearly expressed and, on the other hand, contain a nonlinearity of a complicated type. These equations are of specific interest for the theory of nonlinear differential equations for they have a very typical and poorly studied structure and a very large area of applications. Some problems related to the rigid body oscillator are solved in the paper.