Abstract
Recently a new class of numerical integration methods — “mixed variable symplectic integrators” — has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of magnitude faster than conventional ODE integration methods. Here we present a simple modification of this method to include small non-gravitational forces. The new scheme provides a similar advantage of computational speed for a larger class of problems in Solar System dynamics.
Similar content being viewed by others
References
Adachi, I., Hayashi, C. and Nakazawa, K.: 1976,Prog. Theor. Phys. 56, 6, 1756–1771.
Battin, R. H.: 1987,An Introduction to the Mathematics and Methods of Astrodynamics, American Institute of Aeronautics and Astronautics, N.Y.
Danby, J. M. A.: 1988,Fundamentals of Celestial Mechanics, Willmann-Bell, Inc., VA.
Holmand, M. and Wisdom, J.: 1993,Astron. J. 105, 1987–1999.
Kinoshita, H., Yoshida, H. and Nakai, H.: 1991,Cel. Mech. & Dyn. Astron. 50, 59–71.
Landau, L. D. and Lifshitz, E. M. L.: 1976,Mechanics, Pergamon Press, New York.
Levison, H. and Duncan, M.: 1993,Astrophys. J. 406, L35–8.
Malhotra, R.: 1994,Physica D, Special Issue on “Modelling the Forces of Nature” (in press).
Nobili, A., Milani, A. and Carpino, M.: 1989,Astron. & Astrophys. 210, 313–36.
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T.: 1989,Numerical Recipes, Cambridge Univ. Press.
Quinlan, G.D. and Tremaine, S.: 1992,MNRAS 259, 505–18.
Saha, P.: 1992,Icarus 100, 434–9.
Saha, P. and Tremaine, S.: 1992,Astron. J. 104, 1633–40.
Sussman, G. J. and Wisdom, J.: 1988,Science 241, 433.
Sussman, G. J. and Wisdom, J.: 1992,Science 257, 56.
Weidenschilling, S. J. and Cuzzi, J. N.: 1993, in E. H. Levy and J. I. Lumine (eds.),Protostars and Planets III, The University of Arizona Press, Tucson, Arizona.
Wisdom, J. and Holman, M.: 1991,Astron. J. 102, 1528–38.
Wisdom, J. and Holman, M.: 1992,Astron. J. 104, 2022–9.
Yoshida, H.: 1990,Phys. Lett. A 150, 262–8.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Malhotra, R. A mapping method for the gravitational few-body problem with dissipation. Celestial Mech Dyn Astr 60, 373–385 (1994). https://doi.org/10.1007/BF00691903
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00691903