The simple pendulum: a relativistic revisit

Abstract

The equation of motion of the simple pendulum is derived in the framework ofspecial relativity. The relativistic effect on the motion of the simplependulum is investigated through numerical simulation. We present adiscussion of the relativistic effects on the pendulum's period and on thedynamics of the phase space. We find that, although negligibly small, thereexist calculable differences between the periods of the relativistic andnon-relativistic pendulum if one implements a high-order precision during theevaluation. Furthermore, the discrepancy increases, first nonlinearly andthen linearly, with the amplitude. The period for the non-relativistic caseisalways shorter than that for the relativistic case. While the generalcharacteristicsof the relativistic phase space remain the same as for the non-relativisticcase,constant-energy-level curves conform to the relativistic limit.