On Construction of the Effective Potential in Singular Cases

It is known that the problem of an investigation of invariant sets (in particular stationary motions) of mechanical systems with symmetries can be reduced to the problem of the analysis of the effective potential [1-11]. The effective potential represents the minimum of the total mechanical energy with respect to quasivelocities on fixed levels of Noether's integrals corresponding to symmetries of the system. The effective potential is a function in the configuration space depending on constants of Noether's integrals. This function is defined in such points of the configuration space where Noether's integrals independent and can have singularities at some points where these integrals are dependent.