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

作者：El Nabulsi Rami Ahmad^*

来源：Nonlinear Dynamics, 2015, 79(3): 2055-2068.

DOI：10.1007/s11071-014-1794-2

• Non-standard Lagrangians
• Modified Euler-Lagrange equation
• Earth dynamics
• Coriolis force
• Foucault's pendulum
• Navier-Stokes equation
• Bernoulli's theorem

We report some of the implications of nonstandard 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.

• 出版日期2015-2
• 单位内江师范学院