Time dependent forces and stability of equilibrium for holonomic systems (Q1309408)

The paper revisits some results given by \textit{L. Salvadori} and \textit{F. Visentin} [Rend. Semin. Mat. Univ. Padova 68, 129-147 (1982; Zbl 0524.34046)] concerning the Lyapunov stability of the equilibrium positions of an holonomic mechanical system subject to a (generalized) force of the type \({\mathcal F}(t,q)=-\lambda (t) \nabla \Pi (q)\) and to a dissipative force \({\mathcal R}(t,q,v)\). Here \(q\) is a system of Lagrangian coordinates, \(v\) is the Lagrangian velocity, and \(\lambda(t)\) is a scalar function with \(\lambda(0) \neq 0\). The case of an unbounded \(\lambda\) is also considered.