Hill Problem Analytical Theory to the Order Four: Application to the Computation of Frozen Orbits around Planetary Satellites. (30th November 2009)

• Record Type: Journal Article
• Authors: Lara, Martin; Palacián, Jesús F.
• Other Names: Winter Silvia Maria Giuliatti Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2009(2009)
• Publication Date: 2009-11-30
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2009/753653
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Frozen orbits of the Hill problem are determined in the double-averaged problem, where short and long-period terms are removed by means of Lie transforms. Due to the perturbation method we use, the initial conditions of corresponding quasi-periodic solutions in the nonaveraged problem are computed straightforwardly. Moreover, the method provides the explicit equations of the transformation that connects the averaged and nonaveraged models. A fourth-order analytical theory is necessary for the accurate computation of quasi-periodic frozen orbits.