메뉴 건너뛰기




Volumn 102, Issue 1-3, 2008, Pages 149-162

Quaternions for regularizing Celestial Mechanics: The right way

Author keywords

Birkhoff transformation; Joukowsky Birkhoff mapping; Kepler formulas; Kustaanheimo Stiefel transformation; Perturbed Kepler problem; Quaternion algebra; Quaternions; Regularization

Indexed keywords


EID: 54849426680     PISSN: 09232958     EISSN: 15729478     Source Type: Journal    
DOI: 10.1007/s10569-008-9124-y     Document Type: Conference Paper
Times cited : (47)

References (25)
  • 3
    • 0004091009 scopus 로고
    • Reprinted in Dover Publications, New York
    • Reprinted in Collected Mathematical Papers, vol. 1. Dover Publications, New York (1968)
    • (1968) Collected Mathematical Papers , vol.1
  • 7
    • 0348123273 scopus 로고
    • Application of quaternions in the theory of orbital motion of a satellite
    • Chelnokov, Y.N.: Application of quaternions in the theory of orbital motion of a satellite. Kosm. Issled. [Cosmic Res.] 30, 759-770 (1992);
    • (1992) Kosm. Issled. [Cosmic Res.] , vol.30 , pp. 759-770
    • Chelnokov, Y.N.1
  • 9
    • 54849405777 scopus 로고    scopus 로고
    • Application of quaternions in the mechanics of space flight
    • 27
    • Y.N. Chelnokov 1999 Application of quaternions in the mechanics of space flight Gyroscopy Navigation 4 27 47 66
    • (1999) Gyroscopy Navigation , vol.4 , pp. 47-66
    • Chelnokov, Y.N.1
  • 10
    • 0000613202 scopus 로고
    • On quaternions, or a new system of imaginaries in algebra
    • W.R. Hamilton 1844 On quaternions, or a new system of imaginaries in algebra Philos. Mag. 25 489 495
    • (1844) Philos. Mag. , vol.25 , pp. 489-495
    • Hamilton, W.R.1
  • 11
    • 34250967993 scopus 로고
    • Über die Abbildung der dreidimensionalen Sphäre auf die Kugelfläche
    • Hopf, H.: Über die Abbildung der dreidimensionalen Sphäre auf die Kugelfläche. Math. Ann. 104 (1931).
    • (1931) Math. Ann. , vol.104
    • Hopf, H.1
  • 12
    • 33749333312 scopus 로고
    • Reprinted in Springer-Verlag, Berlin
    • Reprinted in Selecta Heinz Hopf, pp. 38-63. Springer-Verlag, Berlin (1964)
    • (1964) Selecta Heinz Hopf , pp. 38-63
  • 13
    • 0002620663 scopus 로고
    • Spinor regularisation of the Kepler motion
    • Publ. Astr. Obs. Helsinki 102
    • Kustaanheimo, P.: Spinor regularisation of the Kepler motion. Ann. Univers. Turkuensis, Ser. A, 73, 1-7 (1964); Publ. Astr. Obs. Helsinki 102
    • (1964) Ann. Univers. Turkuensis, Ser. A , vol.73 , pp. 1-7
    • Kustaanheimo, P.1
  • 14
    • 84936358059 scopus 로고
    • Perturbation theory of Kepler motion based on spinor regularization
    • P. Kustaanheimo E.L. Stiefel 1965 Perturbation theory of Kepler motion based on spinor regularization J. Reine Angew. Math. 218 204 219
    • (1965) J. Reine Angew. Math. , vol.218 , pp. 204-219
    • Kustaanheimo, P.1    Stiefel, E.L.2
  • 15
    • 0002024654 scopus 로고
    • Sur la régularisation du problème des trois corps
    • T. Levi-Civita 1920 Sur la régularisation du problème des trois corps Acta Math. 42 99 144
    • (1920) Acta Math. , vol.42 , pp. 99-144
    • Levi-Civita, T.1
  • 17
    • 33749326293 scopus 로고
    • Généralisation de la régularisation de Birkhoff pour le mouvement du mobile dans l'espace àtrois dimensions
    • E.L. Stiefel J. Waldvogel 1965 Généralisation de la régularisation de Birkhoff pour le mouvement du mobile dans l'espace àtrois dimensions C.R. Acad. Sci. Paris 260 805
    • (1965) C.R. Acad. Sci. Paris , vol.260 , pp. 805
    • Stiefel, E.L.1    Waldvogel, J.2
  • 19
    • 0042699931 scopus 로고
    • The KS transformation in hypercomplex form
    • M.D. Vivarelli 1983 The KS transformation in hypercomplex form Celest. Mech. Dyn. Astron. 29 45 50
    • (1983) Celest. Mech. Dyn. Astron. , vol.29 , pp. 45-50
    • Vivarelli, M.D.1
  • 20
    • 0041698119 scopus 로고
    • Celestial mechanics via quaternions
    • J. Vrbik 1994 Celestial mechanics via quaternions Can. J. Phys. 72 141 146
    • (1994) Can. J. Phys. , vol.72 , pp. 141-146
    • Vrbik, J.1
  • 21
    • 33749349436 scopus 로고
    • Perturbed Kepler problem in quaternionic form
    • J. Vrbik 1995 Perturbed Kepler problem in quaternionic form J. Phys. A 28 193 198
    • (1995) J. Phys. a , vol.28 , pp. 193-198
    • Vrbik, J.1
  • 22
    • 33749329728 scopus 로고
    • Die Verallgemeinerung der Birkhoff-Regularisierung für das räumliche Dreikörperproblem
    • Waldvogel, J.: Die Verallgemeinerung der Birkhoff-Regularisierung für das räumliche Dreikörperproblem. Bulletin Astronomique, Série 3, Tome II, Fasc. 2, 295-341 (1967a)
    • (1967) Bulletin Astronomique, Série 3 , vol.2 , Issue.2 , pp. 295-341
    • Waldvogel, J.1
  • 23
    • 33749325008 scopus 로고
    • The restricted elliptic three-body problem
    • Stiefel E. et al. (eds.) Methods of Regularization for Computing Orbits in Celestial Mechanics
    • Waldvogel, J.: The restricted elliptic three-body problem. In: Stiefel E. et al. (eds.) Methods of Regularization for Computing Orbits in Celestial Mechanics. NASA Contractor Report NASA CR, vol. 769, pp. 88-115 (1967b)
    • (1967) NASA Contractor Report NASA CR , vol.769 , pp. 88-115
    • Waldvogel, J.1
  • 25
    • 33749356512 scopus 로고    scopus 로고
    • Quaternions and the perturbed Kepler problem
    • J. Waldvogel 2006 Quaternions and the perturbed Kepler problem Celest. Mech. Dyn. Astron. 95 201 212
    • (2006) Celest. Mech. Dyn. Astron. , vol.95 , pp. 201-212
    • Waldvogel, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.