메뉴 건너뛰기




Volumn 8, Issue 3, 2002, Pages 413-442

A note on the Kepler problem

Author keywords

Circle net; Excentric anomaly; Geodesic flow; Hodograph; Kepler problem; Runge Lenz vector; Stereographic map; Trajectory space

Indexed keywords

DIFFERENTIAL EQUATIONS; GEOMETRY; HAMILTONIANS; LINEAR ALGEBRA; VECTORS;

EID: 0036657092     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016386605889     Document Type: Article
Times cited : (12)

References (16)
  • 1
    • 4243624490 scopus 로고    scopus 로고
    • On the history of deducing of Kepler laws from the laws of mechanics
    • Russian
    • D. V. Anosov, On the history of deducing of Kepler laws from the laws of mechanics. (Russian) Historical-mathematical studies, ser. 2 40 (2000), No. 5, 9-25.
    • (2000) Historical-mathematical studies, ser. 2 , vol.40 , Issue.5 , pp. 9-25
    • Anosov, D.V.1
  • 4
    • 0003183377 scopus 로고
    • The hodograph, or a new method of expressing in symbolic language the Newtonian law of attraction
    • Reprinted in: The mathematical papers of sir William Rowen Hamilton, v. II, Dynamics, 287-292. Cambridge: At the University press
    • W. Hamilton, The hodograph, or a new method of expressing in symbolic language the Newtonian law of attraction. Proc. Roy. Irish Acad., 1845-47, v. III, 344-353. Reprinted in: The mathematical papers of sir William Rowen Hamilton, v. II, Dynamics, 287-292. Cambridge: At the University press, 1940.
    • (1940) Proc. Roy. Irish Acad. 1845-47 , vol.3 , pp. 344-353
    • Hamilton, W.1
  • 6
    • 84980148530 scopus 로고
    • Regularization of Kepler's problem and the averaging method on a manifold
    • J. Moser, Regularization of Kepler's problem and the averaging method on a manifold. Comm. Pure Appl. Math. 23 (1970), No. 4, 609-636.
    • (1970) Comm. Pure Appl. Math. , vol.23 , Issue.4 , pp. 609-636
    • Moser, J.1
  • 7
    • 0010481775 scopus 로고
    • Geometric interpretation of Kepler problem
    • Yu. S. Osipov, Geometric interpretation of Kepler problem. Uspekhi Mat. Nauk 24 (1972), No. 2, p. 161.
    • (1972) Uspekhi Mat. Nauk , vol.24 , Issue.2 , pp. 161
    • Osipov, Yu.S.1
  • 8
    • 0010445510 scopus 로고
    • Structural stability of noncompact Anosov flows and hyperbolic motions in Kepler's problem
    • _, Structural stability of noncompact Anosov flows and hyperbolic motions in Kepler's problem. Soviet Math. Dokl. 17 (1976), No. 5, 1389-1393.
    • (1976) Soviet Math. Dokl. , vol.17 , Issue.5 , pp. 1389-1393
  • 9
    • 0010440368 scopus 로고    scopus 로고
    • Lectures on celestial mechanics
    • (Russian) Moscow
    • Lectures on celestial mechanics. (Russian) Moscow (Ed. of the journal Regular and chaotic dynamics) (1999).
    • (1999) Journal Regular and chaotic dynamics
  • 10
    • 84953678168 scopus 로고
    • Prehistory of the "Runge-Lenz" vector
    • H. Goldstein, Prehistory of the "Runge-Lenz" vector. Amer. J. Phys. 43 (1975), No. 8, 737-738.
    • (1975) Amer. J. Phys. , vol.43 , Issue.8 , pp. 737-738
    • Goldstein, H.1
  • 11
    • 84927884764 scopus 로고
    • More on the prehistory of the Laplace or Runge-Lenz vector
    • _, More on the prehistory of the Laplace or Runge-Lenz vector. Amer. J. Phys. 44 (1976), No. 11, 1123-1124.
    • (1976) Amer. J. Phys. , vol.44 , Issue.11 , pp. 1123-1124
  • 12
    • 0003183377 scopus 로고
    • On the application of the method of quaternions to some dynamical questions
    • Appendix, Reprinted in: The mathematical papers of sir William Rowen Hamilton, v. III, Algebra, 441-448. Cambridge, At the University press, 1967
    • W. R. Hamilton, On the application of the method of quaternions to some dynamical questions. Proc. Roy. Irish Acad, 1847, vol. III. Appendix, pp. XXXVI - L. Reprinted in: The mathematical papers of sir William Rowen Hamilton, v. III, Algebra, 441-448. Cambridge, At the University press, 1967.
    • (1847) Proc. Roy. Irish Acad , vol.3
    • Hamilton, W.R.1
  • 13
    • 0010485045 scopus 로고
    • Théorie des variations séculaires des éléments des planètes
    • Paris, Gauthier-Villars
    • J. Lagrange, Théorie des variations séculaires des éléments des planètes. Oeuvres, vol. 5, 125-207. Paris, Gauthier-Villars, 1870.
    • (1870) Oeuvres , vol.5 , pp. 125-207
    • Lagrange, J.1
  • 14
    • 33748531184 scopus 로고
    • Sur la résolution qualitative du problème restreint des trois corps
    • Reprinted in: T. Levi-Civita, Opere matematiche. Vol. 2 (1901)-(1907), 419-439. (Bologna: Nicola Zanichelli, ed.), 1956.
    • T. Levi-Civita. Sur la résolution qualitative du problème restreint des trois corps. Acta Math. 30 (1906), 306-327. Reprinted in: T. Levi-Civita, Opere matematiche. Vol. 2 (1901)-(1907), 419-439. (Bologna: Nicola Zanichelli, ed.), 1956.
    • (1906) Acta Math. , vol.30 , pp. 306-327
    • Levi-Civita, T.1
  • 15
    • 0041911713 scopus 로고
    • The Kepler problem and geodesic flows in spaces of constant curvature
    • Yu. S. Osipov, The Kepler problem and geodesic flows in spaces of constant curvature. Celestial mechanics 16 (1977), 191-208.
    • (1977) Celestial mechanics , vol.16 , pp. 191-208
    • Osipov, Yu.S.1
  • 16
    • 0000785009 scopus 로고
    • On the geometry of the Kepler problem
    • J. Milnor, On the geometry of the Kepler problem. Amer. Math. Monthly 90 (1983), 353-365.
    • (1983) Amer. Math. Monthly , vol.90 , pp. 353-365
    • Milnor, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.