ON the stability of the equilibrium in the non-potential forces field

Veljko V. Vujičić, V. V. Kozlov

On the basis of the second Liapunov’s method, the sufficient conditions of asymptotical stability and non-stability of the equilibrium of system in the nonpotential field of forces are obtained. The case when the generalized forces depend on the position of system is investigated in detail. The sufficiency of conditions of non-stability of those systems is based on the use of factorisation of solutions of equations of motion in the lines with special form. Those results develop and spread the ideas of the first Liapunov’s method. The constructive method for solution of Liapunov’s tasks of stability of equilibrium in ratio to some functions of coordinates and velocity is suggested. As an example of using of general characterized results, the task of stability of equilibrium in the “quasi-potential” field of forces is investigated.