Counter-Balanced Pendulum

摘要

To simulate zero-gravity in ground-testing, one may analyze a system of counter-balanced pendulums made up of two identical bobs which are tied to the ends of an inextensible string and are suspended from two pulleys separated by a certain distance. With this diskette you will explore the dynamics of counter-balanced pendulums when only one bob is swung, while the other is allowed to move vertically. There are two basic modules. One is the in-situ integration by the fourth-order Runge-Kutta scheme with a tolerance check. Although there is a restriction on the choice of initial angles, you may integrate the motion as long as you please. The other module is a theoretical analysis for small and large times to deduce qualitative dynamical behavior. We have discovered an asymptotic invariant of motion which is defined analogous to the action of standard pendulum.