SOME PROBLEMS OF THE STABILITY OF A REVERSIBLE SYSTEM WITH A SMALL-PARAMETER

A solution of the problem of the stability of periodic and conditional ly periodic nearly autonomous systems, and a qualitative analysis of s ystems close to resonance are given reversible systems using a single approach. In addition, the problem of the rolling of Chaplygin's nearl y dynamically symmetrical sphere is considered. It is shown that rolli ng along a straight line is formally stable for all values of the para meters. For a nearly homogeneous sphere a main resonance is possible w hich leads to instability.