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Mathematical Problems in Engineering
Volume 2015, Article ID 980652, 9 pages
Research Article

Efficient Formulation of the Periodic Corrections in Brouwer’s Gravity Solution

Instituto de Ciencia y Technologia, Universidade Federal de São Paulo, Rua Talim 330, 12231-280 São José dos Campos, SP, Brazil

Received 16 March 2015; Accepted 10 August 2015

Academic Editor: Stefan Balint

Copyright © 2015 Martin Lara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The periodic terms of Brouwer’s gravity solution are reconstructed in a nonsingular set of variables which are derived from the well-known polar-nodal variables. This change does not affect the essence of the solution, which still keeps all the benefits of the action-angle variables approach and yields two major improvements. Namely, the periodic corrections of Brouwer’s solution are now valid for any eccentricity below one and any inclination except the critical inclination and, besides, are significantly simpler than the nonsingular corrections in Lyddane’s reformulation of Brouwer’s theory.