Exact Closed-Form Solutions of the Motion in Non-Inertial Reference Frames, Using the Properties of Lie Groups SO3 and SE3

What is it about?

The paper presents a new general method for studying motion in a non-inertial reference frame, using the properties of the Lie groups SO3 and SE3. This method is based on proper orthogonal and skew-symmetric tensor valued functions, introduced by the Poisson-Darboux equation and an appropriately defined differentiation operator, as a function of the instantaneous angular velocity of the non-inertial reference frame. Three applications are presented: the motion in a gravitational force field with respect to a rotating reference frame, the motion of a charged particle in non-stationary electric and magnetic fields, and the exact solution of the rigid body motion in the non-inertial reference frame. The results are closed-form and coordinate-free.

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