Simple pendulum in a rotating reference frame

Describing the harmonic motion of a simple pendulum observed from a rotating reference frame necessitates solving the differential equations governing three-dimensional motion in a non-inertial reference frame, which can be a challenging endeavor for newcomers to this subject. However, in this study, we propose a highly didactic and visually accessible approach by considering the rotating reference frame as a matrix transformation. This approach enables a deeper understanding of the origin of Coriolis and centrifugal accelerations, which are responsible for the curved trajectories exhibited by the simple pendulum in a rotating reference frame.

Keywords:
Harmonic motion; simple pendulum; non-inertial reference frame; foucault pendulum; bravais pendulum