On the passive stabilization of the equilibrium state of Lagrangian systems

The idea of passive stabilization of a dynamical system whose motion-is not asymptotically stable was advanced for the first time in the monograph [1] by introducing supplementary degrees of freedom. Based on this idea, Savch enko [2] discussed the stabilization of Hamiltonian systems by a nonlinear method (namely the method of passive stabilization by defreezing parameters ). The authors of this paper investigate the effectiveness of its applicati on to a Lagrangian system by a mechanical model which has independent scien tific meaning. A comparison is also made between this model and another sim ilar mechanical model. The problem of optimal passive stabilization is solv ed at the end of the paper. It is shown that this problem is closely connec ted with the resonance situations.