Long-term analysis of a swing using the two-timing method

Abstract

We analyse the motion of a swing which is an interesting physical system. Due to the limitation of the conventional method using the Taylor series, an alternative method called the 'two-timing method' is used in order to explore its stability nature (i.e., long-term behaviour) properly. It is shown by the numerical work that the two-timing method supplies a good analytic approximation whose amplitude has an exponential dependence on time. By the two-timing method, the exponent is expressed in terms of the pumping and the frictional force. And we discuss the dependence on the pumping manner of the swing's motion.