ON THE ANALYTICAL METHODS APPROXIMATING THE TIME PERIOD OF THE NONLINEAR PHYSICAL PENDULUM

Abstract

This paper gives a survey on the computation of the time period of the nonlinear physical pendulum. The analytical methods, based on the third-order normal forms and on Krylov´s asymptotic technique are compared to each other. It is shown that these procedures can yield the same result. Though in case of Krylov´s technique, it depends on the power series expansion of the angular eigenfrequency. Finally, the analytical formulas are compared to the results of numerical computations.