On the Foucault pendulum

Abstract

Abstract The Foucault pendulum is a physical apparatus that shows the Earth’s rotation through the variation of the plane of oscillation over time. The main physical agent responsible for this phenomenon is the non-inertial Coriolis force, which couples the coordinates in the equation of motion. Although the Foucault pendulum is more than 170 years old, its theoretical description still lacks completeness, as there is no exact vector solution to the problem or even a decoupled equation of motion. Furthermore, the main prediction about the Foucault pendulum, the dependence of the pendulum’s plane of oscillation rotation on the latitude, needs to be revised as such dependence is more complex than is shown in the literature, once it depends essentially on the initial conditions. Here all these points raised are successfully answered.

Keywords

• Foucault pendulum
• high-order differential equations
• exact solution