ADIABATIC INVARIANTS OF DYNAMICAL-SYSTEMS WITH 2 DEGREES OF FREEDOM

In this paper the adiabatic invariants of dynamic systems with two degrees of freedom are obtained. The method (Dj. S. Djukic, Int. J. Non-linear Mech. 16, 489-498, 1981) developed for dynamic systems with one degree of freedom is extended for the system with two degrees of freedom. The method is based on Noether's theory and the use of the Krylov-Bogolubov-Mitropolski asymptotic technique. The equations of motion of a rotor with hydrodynamic force are approximately solved using four independent adiabatic invariants for the problem.