Zastosowanie równania Hamiltona-Jacobiego do stabilizacji układów mechanicznych

The method of stabilization of mechanical systems is presented in the paper. The method consists in using the Hamilton-Jacobi equation for the proper selection of such forces which, when applied to the system, ensure the asymptotic stability of the equilibrium position. This selection follows from the minimalization condition of the given functional. The minimalization conditions are obtained from the Euler-Lagrange equations. The method described is applied to the case when the optimization condition is the derivative of the kinetic energy of the system. This procedure is explained in an example.