STUDY OF PARTICLE MOTION IN NONINERTIAL NUMERAL SYSTEMS BASED ON LAGRANGIAN FORMALISM

Abstract

The motion of a particle in non-inertial reference frames is investigated within the Lagrangian formalism. Starting from the Lagrangian of an inertial frame, the general Lagrangian of a frame that is both accelerating and rotating is derived, and the translational, centrifugal, Coriolis and Euler inertial forces follow from the Euler–Lagrange equations. For a uniformly rotating frame, the equations of motion in polar coordinates, the conserved generalized momentum and the Jacobi integral are analyzed, and numerical estimates for the Earth are given.