Abstract
The paper presents a quaternion approach of giving a closed form solution of the motion in a central force field relative to a rotating reference frame. This new method involves two quaternion operators: the first one transforms the motion from a non-inertial reference frame to a inertial one with a very significant consequence of vanishing all the non-inertial terms (Coriolis and centripetal forces); the second quaternion operator provides the solution of the motion in the noninertial reference frame by applying it to the solution in the inertial reference frame. This process will govern the inverse transformation of the motion and is proved on two particular cases, the Foucault Pendulum and Keplerian motions problems relative to rotating reference frames.
Highlights
The present paper presents a quaternion solution of the motion in a central force field relative to a rotating reference frame
A quaternion operator Fω will be defined in order to determine the solution of the below nonlinear initial value problem which describes the motion in a central force field relative to a rotating reference frame
By using the quaternion operator Fω, the complex problem given by the non-linear initial value problem with variable coefficients described by Equation (3.1) is reduced to the finding the solution of Equation (3.16) which describes the motion in a central force field, with ω being the instantaneous angular velocity of the rotating reference frame
Summary
The present paper presents a quaternion solution of the motion in a central force field relative to a rotating reference frame. It starts from the main Cauchy problem stated below:. How to cite this paper: Ciureanu, I.-A. and Condurache, D. (2015) A Quaternion Solution of the Motion in a Central Force Field Relative to a Rotating Reference Frame.
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