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Mathematical Problems in Engineering
Volume 2012, Article ID 680394, 12 pages
Research Article

On Bounded Satellite Motion under Constant Radial Propulsive Acceleration

1Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
2Departamento de Ingeniería Mecánica, Universidad de La Rioja, 26004 Logroño, Spain
3Columnas de Hercules 1, 11100 San Fernando, Spain

Received 31 October 2011; Accepted 16 February 2012

Academic Editor: Ben T. Nohara

Copyright © 2012 Juan F. San-Juan et al. 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 Hamiltonian formulation of the constant radial propulsive acceleration problem in nondimensional units reveals that the problem does not depend on any physical parameter. The qualitative description of the integrable flow is given in terms of the energy and the angular momentum, showing that the different regimes are the result of a bifurcation phenomenon. The solution via the Hamilton-Jacobi equation demonstrates that the elliptic integrals of the three kinds are intrinsic to the problem.