Non-standard Lagrangians in rotational dynamics and the modified Navier–Stokes equation

Abstract

We report some of the implications of non-standard Lagrangians in rotational dynamics. After deriving a new form of the Euler–Lagrange equation from the variational principle for the case of a particle moving in a non-inertial frame and subject to a velocity constraint, we deduce the modified Coriolis force, the modified centrifugal force and the modified transverse force. We then discuss the modified equation of motion relative to Earth, the free-fall problem and the Foucault pendulum issue. We show that the modified dynamics results on a modified Navier–Stokes equation where some features were raised and discussed accordingly.