This is a preview of subscription content, log in via an institution to check access.
REFERENCES
V. I. Arnold, Mathematical Methods of Classical Mechanics [in Russian ], Nauka, Moscow (1974).
N. K. Badalyan, “On the form of the trajectories in the two-xed center roblem, ”Proceedings of All-Union Mathematical congress [in Russian ], Vol. 2, 1937,. 239–241.
V. V. Beletsky, Notes on the Motion of a Cosmic Body [in Russian ], Nauka, Moscow (1972).
A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems, Vols. 1, 2 (1999).
A. V. Bolsinov, P. Rikhter, A. T. Fomenko, “Method of circle molecules and topology of the Ko-valevskaya to, ”Mat. Sb., 191, No. 2, 1–42 (2000).
M. Born Vorlesungen über Atommechanik, Vol. 1, 2, Springer (1925).
K. L. Charlier, Die Mechanic des Himmels, Berlin–Leipzig (1927).
N. A. Chernikov, “The Kepler problem in the Lobachevsky space and its solution, ”Acta Phys. Polon., B23, 115–119 (1992).
G. N. Duboshin, Celestial Mechanics. Analytical and Qualitative Methods [in Russian], Nauka, Moscow (1964).
E. A. Grebennikov, V. G. Demin, and E. P. Aksenov, “The general solution of the problem on the motion of an artificial satellite in the normal field of attraction of Earth, ”In: Artificial Satellites of Earth, No. 8, 64–72 (1961).
P. W. Higgs, “Dynamical symmetries in a spherical geometry. I, ”J. Phys. A: Math. Gen., 12, No. 3, 309–323 (1979).
M. P. Kharlamov, Topological Analysis of Integrable Problems of Rigid Body Dynamics [in Russian ], LGU, Leningrad (1988).
V. V. Kozlov, “On dynamics in spaces of constant curvature, ”Vestn. MGU, Ser. Mat., Mekh., 2, 28–35, (1994).
V. V. Kozlov, Symmetry, Topology, and Resonances in Hamiltonian Mechanics [in Russian ], Udm. Univ. (1995).
V. V. Kozlov and O. A. Harin, “Kepler's problem in spaces of constant curvature, ”Cel. Mech. Dyn. Astr., 54, 393–399 (1992).
E. Schrödinger, “A method for the determination of quantum-mechanical eigenvalues and eigenfunctions, ” In: Selected Works on Quantum Mechanics [Russian transl.], Nauka, Moscow (1976),. 239–247.
A. V. Shepetilov, “Reduction of the two-body roblem with central interaction on sim ly connected spaces of constant sectional curvature, ”J. Phys. A. Math. Gen., 31, 6279–6291 (1998).
S. Smale, “Topology and mechanics, ”Usp. Mat. Nauk, 27, No. 2 (1972).
H. J. Tallqvist, “Ñber die Bewegung eines Punktes, welcher von zwei festen Zentren nach dem New-tonischen Yesetze angezogen wird, ”Acta Soc. Sci. Fenn. A, 1, No. 5 (1927).
T. G. Vozmischeva, “Classiffcation of motions for generalization of the two-center roblem on a sphere, ”Cel. Mech. Dyn. Astr., 77, 37–48 (2000).
T. G. Vozmischeva, “Mathematical aspects in celestial mechanics: The Lobachevskii space, ”Proc. Int. Conf. “Geometry, Integrability and Quantization,” Bulgaria, 1999.
T. G. Vozmischeva, “The classffication of the motion for generalization of the Euler problem to a sphere, ”Math. Collection [in Russian ], Udm. Univ. (1998),. 34–40.
T. G. Vozmischeva and A. A. Oshemkov, “To ological analysis of the two-center roblem on the two-dimensional sphere, ”Mat. Sb., 2001 (in ress).
E. T. Whittaker, Analytical Dynamics (1937).
N. E. Zhukovski, “On the motion of a material seudos herical gure on the surface of a seudo-sphere, ”In: Collection of Works, Vol. 1 (1937),. 490–535.
Rights and permissions
About this article
Cite this article
Vozmishcheva, T.G. Some Integrable Problems in Celestial Mechanics in Spaces of Constant Curvature. Journal of Mathematical Sciences 114, 1025–1066 (2003). https://doi.org/10.1023/A:1021859127738
Issue Date:
DOI: https://doi.org/10.1023/A:1021859127738