A complete closed form vectorial solution to the Kepler problem

Meccanica

Volumn 42, Issue 5, 2007, Pages 465-476

  Condurache, Daniel ^a   Martinuşi, Vladimir ^a  

^a GHEORGHE ASACHI TECHNICAL UNIVERSITY OF IASI   (Romania)

Author keywords

Classical Mechanics; Kepler problem; Sundman transformation; Vectorial regularization

Indexed keywords

COMPUTATION THEORY; MATHEMATICAL TRANSFORMATIONS; MOTION ESTIMATION; PROBLEM SOLVING;

CLASSICAL MECHANICS; KEPLER PROBLEMS; SUNDMAN TRANSFORMATION; VECTORIAL REGULARIZATION;

VECTORS;

EID: 35148829831     PISSN: 00256455     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11012-007-9065-7     Document Type: Article

References (22)

1. Anosov DV (2002) A note on the Kepler problem. J Dyn Control Syst 8(3):413-442, AAS/AIAA Space flight mechanics meeting, San Antonio, Texas (2002)
2. Burdet CA (1967). Regularization of the two body problem. Z Angew Math Phys 18: 434-438
3. Condurache D and Martinuşi V (2007). Kepler's Problem in rotating reference frames. Part I: Prime integrals, Vectorial regularization. J Guidance, Control Dyn 30(1): 192-200
4. Deprit A, Elipe A and Ferrer S (1994). Linearization: Laplace versus Stiefel. Celestial Mech Dyn Astron 58: 1510-201
5. Goldstein H (1976). More on the prehistory of the Laplace or Runge-Lenz vector. Am J Phys 44: 1123-1124
6. Goldstein H, Poole CHP, Sakfko JP (2002) Classical mechanics, 3rd edn. Addison Wesley
7. Kustaanheimo PE (1964). Spinor regularization of Kepler motion. Ann Univ Turkuens A, I, 73, fasc1, Publ Astron Obs Helsinki 102: 3-7
8. Kustaanheimo PE and Stiefel E (1965). Perturbation theory of Kepler motion based on spinor regularization. J Reine Angew Math 218: 204-219
9. Landau L, Lifchitz E (1981) Mécanique Ed. Mir, Moscow
10. Laplace PS (1969) Celestial Mechanics, vol I. Chelsea, NY
11. Levi-Civita T, Amaldi U (1922-1926) Lezioni di mecanica razionale. Nicola Zanichelli, editore
12. Levi-Civita T (1920). Sur la régularisation du problème des trois corps. Acta Math 42: 99-144
13. Roy AE (2005) Orbital Motion. Institute of Physics Publishing, Bristol and Philadelphia
14. Stumpff P (1987). The general Kepler equation and its solutions. Celestial Mech Dyn Astron 43(1-4): 211-222
15. Sundman KF (1912). Mémoire sur le problème des trois corps. Acta Mathematica 36: 105-179
16. Vivarelli MD (1994). The Kepler problem: a unifying view. Celestial Mech Dyn Astron 60: 291-395
17. Vivarelli MD (1997). The Levi-Civita time transformation and a Killing vector for the Kepler problem. Meccanica 32: 135-142
18. Vivarelli MD (2000). The sum vector S and the fictitious time s in the Kepler problem. Meccanica 35: 55-67
19. Vivarelli MD (2005). The amazing S-code of the conic sections and the Kepler problem. Polipress, Politecnico di Milano
20. Vrbik J (2003). A novel solution to Kepler's problem. Eur J Phys 24: 575-583
21. Vrbik J New methods of celestial mechanics http://spartan.ac.brocku.ca/ ~jvrbik/RESEARCH/revised.pdf
22. Waldvogel J (2006). Quaternions and the perturbed Kepler problem. Celestial Mech Dyn Astron 95(1-4): 201-212