Summary The Lagrange-Dirichlet theorem states that the equilibrium position of a discrete,
conservative mechanical system is stable if the potential energy U (q) assumes a minimum …

The existence, stability, and branching of steady motions of an isosceles tetrahedron (a
disphenoid) with a fixed point in the central Newtonian field of forces are studied. The …

Consideration is given to the local structure of energy functions for electric power networks
near points (parameter values) of incipient flutter instability. Previous work by several …

Abstract The author's results/1–3/on the stationary motions in a central Newtonian field of
force when the centre of mass is assumed fixed, of a fixed system of particles of equal mass …

This article describes ways in which constrained variational principles can be used to study
the stability properties of special solutions, eg equilibria, relative equilibria and other special …

The problem of the stability of stationary motions (SM) of mechanical systems admitting of
first integrals and a function that does not grow along the motions is considered. Theorems …

Bifurcation theory for stationary motions was developed by Poincaré [1] and Chetaev [2] for
Lagrangian conservative mechanical systems. This theory is based on the investigation of …

The bifurcations of the equilibria of a gyrostat satellite with a centre of mass moving
uniformly in a circular Kepler orbit around an attracting centre are investigated. It is assumed …

In this paper we discuss problems of stability of stationary motions of conservative and
dissipative mechanical systems with first integrals. General results are illustrated by the …

ui =y - + $ A,yilz + Azyi22 + A,yis2 Page 1 PMM USSR,Vo1.45,pp.360-367 Copyright
Pergamon Press Ltd.1982.Printed in UK 0021-8928/82/j 0360 $7.50/O IJDC 531.35:521.% ON …