A Quaternion Solution of the Motion in a Central Force Field Relative to a Rotating Reference Frame


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.

Share and Cite:

Ciureanu, I. and Condurache, D. (2015) A Quaternion Solution of the Motion in a Central Force Field Relative to a Rotating Reference Frame. World Journal of Mechanics, 5, 71-79. doi: 10.4236/wjm.2015.55008.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Hamilton, W.R. (2000) On Quaternions, or on a New System of Imaginaries in Algebra. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, Vols. xxv-xxxvi, No. 3rd Series, 92 p.
[2] Darboux, G. (1887) Lecons sur la theorie generale des surfaces et les applications geometriques du calcul infinitesimal. Gauthier-Villars, Paris.
[3] Condurache, D. and Martinusi, V. (2010) Quaternionic Exact Solution to the Relative Orbital Motion Problem. Journal of Guidance, Control, and Dynamics, 33, 1035-1047.
[4] Angeles, J. (1988) Rational Kinematics. (Springer Tracts in Natural Philosophy, Vol. 34). Springer-Verlag, New York.
[5] Condurache, D. and Martinusi, V. (2008) Foucault Pendulum-Like Problems: A Tensorial Approach. International Journal of Non-Linear Mechanics, 43, 743-760.
[6] Condurache, D. and Martinusi, V. (2007) Kepler’s Problem in Rotating Reference Frames; Part 1: Prime Integrals, Vectorial Regularization. Journal of Guidance, Control and Dynamics, 30, 192-200.
[7] Condurache, D. and Martinusi, V. (2007) A Complete Closed Form Vectorial Solution to the Kepler Problem. Meccanica, 42, 465-476.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.