ALTERNATIVE APPROACHES TO MELNIKOV ANALYSIS FOR FORCED OSCILLATORS

Abstract A method is presented based on energy balance to derive the Melnikov criterion for a forced oscillator with one degree of freedom. An integration scheme is also discussed for numerically calculating the criterion when the integrals involved cannot be evaluated analytically. The example of the forced pendulum with constant torque is considered and results from a numerical Melnikov are compared with those obtained by other methods, including homoclinic tangency following.