Averaging method for the stability analysis of strongly nonlinear mechanical systems

A mechanical system under strongly nonlinear potential and dissipative forces, with nonstationary perturbations having zero mean values, is studied. Proposing a special construction of Lyapunov function, the conditions are found, which do not influence asymptotic stability trivial equilibrium position system. These include requirements on disturbance-free relations nonlinearity orders between forces. The developed approach extended to problem monoaxial stabilization rigid body.