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Volumn 38, Issue 12, 1997, Pages 6367-6381

An approach to the relativistic brachistochrone problem by sub-Riemannian geometry

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EID: 0031481406     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532217     Document Type: Article
Times cited : (11)

References (16)
  • 1
    • 0011598238 scopus 로고
    • Relativistic brachistochrone
    • F. Goldstein and C. M. Bender, "Relativistic brachistochrone," J. Math. Phys. 27, 507-511 (1985).
    • (1985) J. Math. Phys. , vol.27 , pp. 507-511
    • Goldstein, F.1    Bender, C.M.2
  • 2
    • 0011670434 scopus 로고
    • The brachistochrone in almost flat space
    • G. Kamath, "The brachistochrone in almost flat space," J. Math. Phys. 29, 2268-2272 (1988).
    • (1988) J. Math. Phys. , vol.29 , pp. 2268-2272
    • Kamath, G.1
  • 3
    • 0001966558 scopus 로고
    • The brachistochrone problem in a stationary space-time
    • V. Perlick, "The brachistochrone problem in a stationary space-time," J. Math. Phys. 32, 3148-3157 (1991).
    • (1991) J. Math. Phys. , vol.32 , pp. 3148-3157
    • Perlick, V.1
  • 4
    • 0003241547 scopus 로고
    • Shortest paths for sub-Riemannian metrics on rank-2 distribution
    • W. Liu and H. J. Sussman, "Shortest paths for sub-Riemannian metrics on rank-2 distribution," Memoirs AMS 564, 1995, Vol. 118.
    • (1995) Memoirs AMS 564 , vol.118
    • Liu, W.1    Sussman, H.J.2
  • 5
    • 0000674734 scopus 로고
    • Singular extremals on Lie groups
    • R. Montgomery, "Singular extremals on Lie groups," Math. Control Signals 7, 217-234 (1994).
    • (1994) Math. Control Signals , vol.7 , pp. 217-234
    • Montgomery, R.1
  • 9
    • 0001496905 scopus 로고
    • Fermat principle in arbitrary gravitational fields
    • I. Kovner, "Fermat principle in arbitrary gravitational fields," Astrophys. J. 351, 114-120 (1990).
    • (1990) Astrophys. J. , vol.351 , pp. 114-120
    • Kovner, I.1
  • 10
    • 0000320207 scopus 로고    scopus 로고
    • A timelike extension of Fermat's principle in general relativity and applications
    • to appear in
    • F. Giannoni, A. Masiello, and P. Piccione, "A timelike extension of Fermat's principle in general relativity and applications," to appear in Calculus of Variations and PDE.
    • Calculus of Variations and PDE
    • Giannoni, F.1    Masiello, A.2    Piccione, P.3
  • 11
    • 36149035770 scopus 로고
    • On Fermat's principle in ceneral relativity: I. The general case
    • V. Perlick, "On Fermat's principle in ceneral relativity: I. The general case," Class. Quantum Grav. 7, 1319-1331 (1990).
    • (1990) Class. Quantum Grav. , vol.7 , pp. 1319-1331
    • Perlick, V.1
  • 14
    • 34249759036 scopus 로고
    • A survey of singular curves in sub-Riemannian geometry
    • R. Montgomery, "A survey of singular curves in sub-Riemannian geometry," J. Dyn. Controlled Syst. 1, 49-90 (1995).
    • (1995) J. Dyn. Controlled Syst. , vol.1 , pp. 49-90
    • Montgomery, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.