ransgression Effect in weakly nonholonomic systems with small degrees of freedom

Аuthors

Vidov N. M.^*, Kuleshov A. S.^*

Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russia

*e-mail: nikitavidov98@gmail.com

Abstract

In the late 1980s Ya. V. Tatarinov laid the foundations for the theory of so-called weakly nonholonomic systems. Mechanical systems with nonholonomic constraints depending on a small parameter are considered. First of all, it is assumed, that for zero value of this parameter the constraints of such a system become integrable; i.e., in this case, we have a family of holonomic systems depending on several arbitrary integration constants. Secondly, it is assumed, that these holonomic systems are completely integrable Hamiltonian systems. 
When the small parameter is not zero, the behavior of such a system can be represented as a transgression: a combination of the motion of a slightly modified holonomic system with slowly varying previous integration constants. The behavior of conservative nonholonomic systems near the equilibrium manifold is also described within the framework of the theory of weakly nonholonomic systems. This paper presents two examples of mechanical systems whose motion can be described using the theory of weakly nonholonomic systems.    

Keywords:

weakly nonholonomic system; equilibrium manifold; transgression effect

References

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