Stability of equilibriumbranching points
Abstract
The paper investigates the problem of the stability of equilibriumbranching points of finitedimensional conservative systems, whose potential energy depends on a real parameter. The stability problem involves difficulties associated with degeneracy at the branching points of the second differential of potential energy. It is shown that in most cases the stability or instability of the point can be determined on the basis of the equilibrium curve near the point. This assertion is proved using geometrical considerations which do not depend on the rank of the Hessian of potential energy; this independence makes the proof valid for systems which do not satisfy Poincare conditions.
 Publication:

Prikladnaia Matematika i Mekhanika
 Pub Date:
 April 1978
 Bibcode:
 1978PriMM..42..259V
 Keywords:

 Branching (Mathematics);
 Potential Energy;
 Systems Stability;
 Motion Stability;
 Set Theory;
 Topology;
 Physics (General)