ON THE INSTABILITY OF EQUILIBRIUM OF NONHOLONOMIC SYSTEMS WITH A NONANALYTIC POTENTIAL

We have proved the theorem on the instability of equilibrium of non-ho lonomic systems in the field of conservative forces under the followin g assumptions: the equilibrium position is the critical point of the p otential; the potential is non-analytical and can be expressed in the form of the sum of the homogeneous function of a positive homogeneity degree and an infinitesimally small function in comparison with the ho mogeneous function when the latter tends to zero; in the subspace whic h is orthogonal to the vectors of the non-holonomic constraints comput ed in the equilibrium position, the homogeneous part of the potential has negative values. The suggested theorem is a generalization of the results from [V. V. Kozlov, Soviet Math. Dokl. 33, 654-656 (1986) repr inted by the American Mathematical Society (1987)]. Copyright (C) 1996 Elsevier Science Ltd.