Integration of the primer vector in a central force field
This paper examines the primer vector which governs optimal solutions for orbital transfer when the central force field has a more general form than the usual inverse-square-force law. Along a null-thrust are that connects two successive impulses, the two sets of state and adjoint equations are decoupled. This allows the reduction of the problem to the integration of a linear first-order differential equation, and hence the solution of the optimal coasting are in the most general central force field can be obtained by simple quadratures. Immediate applications of the results can be seen in solving problems of escape in the equatorial plane of an oblate planet, satellite swing by, or station keeping around Lagrangian points in the three-body problem.
KeywordsDifferential Equation Force Field Equatorial Plane Adjoint Equation Central Force
Unable to display preview. Download preview PDF.
- 1.Lawden, D. F.,Optimal Trajectories for Space Navigation, Butterworths Publishers, London, England, 1963.Google Scholar
- 2.Vinh, N. X.,Exact Relations of Optimum Switching in the Problem of Impulsive Transfer, Journal of the Astronautical Sciences, Vol. 17, No. 6, 1970.Google Scholar
- 3.Brookes, C. J., andSmith, J.,Optimum Rocket Trajectories in a General Force-Field, Astronautica Acta, Vol. 15, No. 3, 1970.Google Scholar
- 4.Marchal, C.,Généralisation Tridimensionnelle et Étude de l'Optimalité des Arcs à Poussée Intermédiaire de Lawden (Dans un Champ Newtonien), La Recherche Aérospatiale, No. 123, 1968.Google Scholar
- 5.Vinh, N. X., andMarchal, C.,The Lawden's Singular Arcs in a Newtonian Force Field, Paper presented at the 21st International Astronautical Congress, Constance, Germany, 1970.Google Scholar
- 6.Pines, S.,Constants of the Motion for Optimum Thrust Trajectories in a Central Force Field, AIAA Journal, Vol. 2, No. 11, 1964.Google Scholar
- 7.Marec, J. P.,Transferts Optimaux Entre Orbites Elliptiques Proches, ONERA, Report No. 121, 1967.Google Scholar