Variational methods in the theory of motion rigidity. (Q1584125)

The note treats a holonomic mechanical system with \(n\) degrees of freedom. Under certain assumptions there exists a smooth Hamilton function \(H(p,q,t)\). The author denotes \(\,H_0(q,t)=H(0,q,t)\,\) and assumes that \(\,H_0(0,t)=0\). It is proved that if in the neighborhood \(\,q=0\,\) the condition \(\,H_0(q,t,\alpha)\leq 0\,\) is satisfied, \(\,\alpha = (\alpha_1,\dots,\alpha_m)\,\) is the vector of system parameters, then the state \(\,q=0\,\) is not stiff in the sense of Skimel' [see \textit{V. ~N.~Skimel'}, ``Some problems of stiffness for mechanical systems depending on a parameter'', Doctor dissertation, Kazan' (1979)].