On the stability of the system with generalized potential

Veljko A. Vujičić

Theoretical and applied mechanics, Tome 8 (1982) no. 1, p. 139 .

Résumé

The stability of the equilibrium state and stationary movements of mechanical systems under the influence of forces that have a general potential $V=V_\alpha(q,t)\dot q^\alpha+\Pi(q,t)$. Starting from criterion (1), it is shown that when the potential $\Pi$ is a positive definite function and when $V(q,\dot q,t)\leq V(q,\dot q,t_0)$, the equilibrium position is stable. It is also shown that when the Lagrange function $L=T-V(q,\dot q)$ does not explicitly depend on time and when the potential is a positive definite function, the equilibrium position and also the stationary motion for which there are cyclic coordinates are stable.