A GENERAL METHOD TO STUDY THE MOTION IN A NON-INERTIAL REFERENCE FRAME

Abstract

The paper offers a general method to study the motion of a mass particle with respect to a non-inertial reference frame. By using an adequate tensor instrument, we obtain a simplified form of the initial value problem that models the non-inertial motion. The study of the motion in a non-inertial reference frame in a central positional force field is then reduced to the study of the classic motion in a central force field. The applications to this method are in solving Kepler’s problem in non-inertial reference frames, solving the relative orbital motion problem and deriving the explicit solution to a classic Theoretical Mechanics problem: The Foucault Pendulum. The advantage of using this method in the study of the motion in a non-inertial reference frames is that is significantly reduces the amount of computations and it offers, in some important particular cases, closed form analytical solutions.