## 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

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.