An approximate and an analytical solution to the carousel-pendulum problem

Alexandre Vial
Pôle Physique, Mécanique, Matériaux et Nanotechnologies
Université de technologie de Troyes
12, rue Marie Curie BP-2060 F-10010 TROYES Cedex

Published in Eur. J. Phys. 30(4), September 2009


We show that an improved solution to the carousel-pendulum problem can be easily obtained through a first order Taylor expansion, and its accuracy is determined after the obtention of an unusable analytical exact solution, advantageously replaced by a numerical one. It is shown that the accuracy is unexpectedly high, even when the ratio length of the pendulum to carousel radius approaches the unity.

1 Introduction
2 Poor man solution
3 Improved solutions
 3.1 Approximate solution
 3.2 Exact solution
4 Conclusion