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

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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.

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  1. College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641112, Sichuan, China

    Rami Ahmad El-Nabulsi

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  1. Rami Ahmad El-Nabulsi
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El-Nabulsi, R.A. Non-standard Lagrangians in rotational dynamics and the modified Navier–Stokes equation. Nonlinear Dyn 79, 2055–2068 (2015). https://doi.org/10.1007/s11071-014-1794-2

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