An application of the plane curve's standard basis to a certain class of problems from classical mechanics

It is shown that the moving basis of a curve in polar coordinates can always be considered as a right-handed reference frame moving with acceleration. A system of differential equations is obtained that describes the trajectory of a freely falling body in a non-inertial reference frame coinciding with the standard basis of the curve. Finally, they were solved numerically using the Archimedean spiral, the three-petal rose and the cardioid as examples.