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Volumn 1, Issue 2, 2001, Pages 143-182

A restricted four-body model for the dynamics near the lagrangian points of the sun-jupiter system

Author keywords

First integrals; Invariant tori; Normal forms; Trojan asteroids

Indexed keywords


EID: 0009825666     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2001.1.143     Document Type: Article
Times cited : (39)

References (50)
  • 3
    • 0002764805 scopus 로고
    • Proof of A.N. Kolmogorov's theorem on the preservation of quasi-periodic motions under small perturbations of the Hamiltonian
    • V.I. Arnold. Proof of A.N. Kolmogorov's theorem on the preservation of quasi-periodic motions under small perturbations of the Hamiltonian. Russian Math. Surveys, 18(5):9-36, 1963.
    • (1963) Russian Math. Surveys , vol.18 , Issue.5 , pp. 9-36
    • Arnold, V.I.1
  • 4
    • 0000877933 scopus 로고
    • Instability of dynamical systems with several degrees of freedom
    • V.I. Arnold. Instability of dynamical systems with several degrees of freedom. Soviet Math. Dokl., 5:581-585, 1964.
    • (1964) Soviet Math. Dokl. , vol.5 , pp. 581-585
    • Arnold, V.I.1
  • 6
    • 54649083612 scopus 로고    scopus 로고
    • Nekhoroshev-stability of L and £5 in the spatial Restricted Three-Body Problem
    • G. Benettin, F. Fassö, and M. Guzzo. Nekhoroshev-stability of L and £5 in the spatial Restricted Three-Body Problem. Regul. Chaotic Dyn., 3(3):56-72, 1998.
    • (1998) Regul. Chaotic Dyn. , vol.3 , Issue.3 , pp. 56-72
    • Benettin, G.1    Fassö, F.2    Guzzo, M.3
  • 9
    • 0040845842 scopus 로고    scopus 로고
    • On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem
    • E. Castellà and A. Jorba. On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mech., 76(l):35-54, 2000.
    • (2000) Celestial Mech. , vol.76 , Issue.50 , pp. 35-54
    • Castellà, E.1    Jorba, A.2
  • 10
    • 34249917727 scopus 로고
    • On the stability of the Lagrangian points in the spatial Restricted Three Body Problem
    • A. Celletti and A. Giorgilli. On the stability of the Lagrangian points in the spatial Restricted Three Body Problem. Celestial Mech., 50(l):31-58, 1991
    • (1991) Celestial Mech. , vol.50 , Issue.50 , pp. 31-58
    • Celletti, A.1    Giorgilli, A.2
  • 12
    • 0040251437 scopus 로고
    • Some periodic solutions of a four-body problem
    • J. Cronin, P.B. Richards, and L.H. Russell. Some periodic solutions of a four-body problem. Icarus, 3:423-428, 1964.
    • (1964) Icarus , vol.3 , pp. 423-428
    • Cronin, J.1    Richards, P.B.2    Russell, L.H.3
  • 13
    • 0001350331 scopus 로고
    • Stability of the triangular points in the elliptic restricted problem of three bodies
    • J.M.A. Danby. Stability of the triangular points in the elliptic restricted problem of three bodies. Astron. J., 69:165-172, 1964.
    • (1964) Astron. J. , vol.69 , pp. 165-172
    • Danby, J.M.A.1
  • 14
    • 0000467293 scopus 로고
    • Stability of the triangular Lagrangian points
    • A. Deprit and A. Deprit-Bartolome. Stability of the triangular Lagrangian points. Astron. J., 75(2):173-179, 1967.
    • (1967) Astron. J. , vol.75 , Issue.2 , pp. 173-179
    • Deprit, A.1    Deprit-Bartolome, A.2
  • 15
    • 34249922199 scopus 로고
    • A dynamical equivalent to the equilateral libration points of the real Earth-Moon system
    • C. Diez, A. Jorba, and C. Simö. A dynamical equivalent to the equilateral libration points of the real Earth-Moon system. Celestial Mech., 50(l):13-29, 1991.
    • (1991) Celestial Mech. , vol.50 , Issue.50 , pp. 13-29
    • Diez, C.1    Jorba, A.2    Simö, C.3
  • 16
    • 0002484921 scopus 로고
    • Stabilité ou instabilité des points fixes elliptiques
    • R. Douady. Stabilité ou instabilité des points fixes elliptiques. Ann. Sci. École Norm. Sup. (4), 21:1-46, 1988.
    • (1988) Ann. Sci. École Norm. Sup. , vol.4 , Issue.21 , pp. 1-46
    • Douady, R.1
  • 17
    • 0035644955 scopus 로고    scopus 로고
    • Arnold diffusion in perturbations of analytic integrable Hamiltonian systems
    • E. Fontich and P. Martin. Arnold diffusion in perturbations of analytic integrable Hamiltonian systems. Discrete Contin. Dynam. Systems, 7(l):61-84, 2001.
    • (2001) Discrete Contin. Dynam. Systems , vol.7 , Issue.50 , pp. 61-84
    • Fontich, E.1    Martin, P.2
  • 18
    • 0009101129 scopus 로고
    • Rigorous results on the power expansions for the integrals of a Hamiltonian system near an elliptic equilibrium point
    • A. Giorgilli. Rigorous results on the power expansions for the integrals of a Hamiltonian system near an elliptic equilibrium point. Ann. Inst. If. Poincaré Phys. Théor., 48(4):423-439, 1988.
    • (1988) Ann. Inst. If. Poincaré Phys. Théor. , vol.48 , Issue.4 , pp. 423-439
    • Giorgilli, A.1
  • 19
    • 0000163515 scopus 로고
    • Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem
    • A. Giorgilli, A. Delshams, E. Fontich, L. Galgani, and C. Simö. Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem. J. Differential Equations, 77:167-198, 1989.
    • (1989) J. Differential Equations , vol.77 , pp. 167-198
    • Giorgilli, A.1    Delshams, A.2    Fontich, E.3    Galgani, L.4    Simö, C.5
  • 20
    • 0000330285 scopus 로고
    • Formal integrals for an autonomous Hamiltonian system near an equilibrium point
    • A. Giorgilli and L. Galgani. Formal integrals for an autonomous Hamiltonian system near an equilibrium point. Celestial Mech., 17:267-280, 1978.
    • (1978) Celestial Mech. , vol.17 , pp. 267-280
    • Giorgilli, A.1    Galgani, L.2
  • 21
    • 0000744245 scopus 로고    scopus 로고
    • On the stability of the Trojan asteroids
    • A. Giorgilli and C. Skokos. On the stability of the Trojan asteroids. Astron. Astrophys., 317:254-261, 1997.
    • (1997) Astron. Astrophys. , vol.317 , pp. 254-261
    • Giorgilli, A.1    Skokos, C.2
  • 23
    • 0041162895 scopus 로고
    • A quasiperiodicsolution as asubstitute of/4 in the Earth-Moon system. in
    • ESTEC, Noordwijk, Holand, ESA Publications Division.
    • G. Gömez, A. Jorba, J. Masdemont, and C. Simô. A quasiperiodicsolution as asubstitute of/4 in the Earth-Moon system. In Proceedings of the 3rd International Sysmposium on Spacecraft Flight Dynamics, pages 35-41, ESTEC, Noordwijk, Holand, 1991. ESA Publications Division.
    • (1991) Proceedings of the , vol.3
    • Gömez, G.1    Jorba, A.2    Masdemont, J.3    Simô, C.4
  • 27
    • 0033243813 scopus 로고    scopus 로고
    • A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems
    • A. Jorba. A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems. Exp. Math., 8(2):155-195, 1999.
    • (1999) Exp. Math. , vol.8 , Issue.2 , pp. 155-195
    • Jorba, A.1
  • 28
    • 0009825667 scopus 로고    scopus 로고
    • A numerical study on the existence of stable motions near the triangular points of the real Earth-Moon system
    • A. Jorba. A numerical study on the existence of stable motions near the triangular points of the real Earth-Moon system. Astron. Astrophys., 3G4(l):327-338, 2000.
    • (2000) Astron. Astrophys. , vol.3 , Issue.50 , pp. 327-338
    • Jorba, A.1
  • 29
    • 85037291820 scopus 로고    scopus 로고
    • On practical stability regions for the motion of a small particle close to the equilateral points of the real Earth-Moon system. Proceedings of the
    • Pàtzcuaro (Mexico), December 7-11, 1998. World Scientific (to appear)
    • A. Jorba. On practical stability regions for the motion of a small particle close to the equilateral points of the real Earth-Moon system. Proceedings of the /// International Symposium HAMSYS-98. Geometrical Methods in Hamiltonian Systems and Celestial Mechanics. Pàtzcuaro (Mexico), December 7-11, 1998. World Scientific (to appear), 2000.
    • (2000) International Symposium HAMSYS-98. Geometrical Methods in Hamiltonian Systems and Celestial Mechanics.
    • Jorba, A.1
  • 31
    • 0030520995 scopus 로고    scopus 로고
    • On quasiperiodic perturbations of elliptic equilibrium points
    • A. Jorba and C. Simö. On quasiperiodic perturbations of elliptic equilibrium points. SIAM J. Math. Anal., 27(6):1704-1737, 1996.
    • (1996) SIAM J. Math. Anal. , vol.27 , Issue.6 , pp. 1704-1737
    • Jorba, A.1    Simö, C.2
  • 32
    • 0040507795 scopus 로고    scopus 로고
    • On the normal behaviour of partially elliptic lower dimensional tori of Hamiltonian systems
    • A. Jorba and J. Villanueva. On the normal behaviour of partially elliptic lower dimensional tori of Hamiltonian systems. Nonlinearity, 10:783-822, 1997.
    • (1997) Nonlinearity , vol.10 , pp. 783-822
    • Jorba, A.1    Villanueva, J.2
  • 33
    • 0000500437 scopus 로고    scopus 로고
    • On the persistence of lower dimensional invariant tori under quasi-periodic perturbations
    • A. Jorba and J. Villanueva. On the persistence of lower dimensional invariant tori under quasi-periodic perturbations. J. Nonlinear Set., 7:427-473, 1997.
    • (1997) J. Nonlinear Set. , vol.7 , pp. 427-473
    • Jorba, A.1    Villanueva, J.2
  • 34
    • 0001686403 scopus 로고    scopus 로고
    • Numerical computation of normal forms around some periodic orbits of the Restricted Three Body Problem
    • A. Jorba and J. Villanueva. Numerical computation of normal forms around some periodic orbits of the Restricted Three Body Problem. Phys. D, 114:197-229, 1998.
    • (1998) Phys. D , vol.114 , pp. 197-229
    • Jorba, A.1    Villanueva, J.2
  • 36
    • 85037318887 scopus 로고    scopus 로고
    • http://ssd.jpl.nasa.gov/horizons .htnl.
    • http://ssd.jpl.nasa.gov/horizons .htnl.
  • 37
    • 0001246972 scopus 로고
    • On the persistence of conditionally periodic motions under a small change of the Hamilton function
    • A.N. Kolmogorov. On the persistence of conditionally periodic motions under a small change of the Hamilton function. Dokl. Acad. Nauk. SSSR, 98(4):527-530, 1954.
    • (1954) Dokl. Acad. Nauk. SSSR , vol.98 , Issue.4 , pp. 527-530
    • Kolmogorov, A.N.1
  • 38
    • 0041595135 scopus 로고
    • On the stability of the Lagrange periodic solutions of the restricted problem of three bodies
    • A.M. Leontovich. On the stability of the Lagrange periodic solutions of the restricted problem of three bodies. Soviet Math. Dokl., 3:425-428, 1962.
    • (1962) Soviet Math. Dokl. , vol.3 , pp. 425-428
    • Leontovich, A.M.1
  • 39
    • 0009431334 scopus 로고
    • The quasi integrals
    • C. Marchai. The quasi integrals. Celestial Mech., 21:183-191, 1980.
    • (1980) Celestial Mech. , vol.21 , pp. 183-191
    • Marchai, C.1
  • 41
    • 21244444580 scopus 로고
    • Stability of the triangular Lagrangian solutions of the restricted three-body problem in the three-dimensional circular case
    • A.P. Markeev. Stability of the triangular Lagrangian solutions of the restricted three-body problem in the three-dimensional circular case. Soviet Astronom. AJ, 15:682-686, 1971.
    • (1971) Soviet Astronom. AJ , vol.15 , pp. 682-686
    • Markeev, A.P.1
  • 42
    • 21244481271 scopus 로고
    • On the stability problem for the Lagrange solutions of the restricted three-body problem
    • A.P. Markeev. On the stability problem for the Lagrange solutions of the restricted three-body problem. J. Appl. Math. Mech., 37:713-717, 1973.
    • (1973) J. Appl. Math. Mech. , vol.37 , pp. 713-717
    • Markeev, A.P.1
  • 44
    • 0001410062 scopus 로고
    • The stability of the Lagrange triangular point and a theorem of Arnold
    • K. R. Meyer and D. S. Schmidt. The stability of the Lagrange triangular point and a theorem of Arnold. J. Differential Equations, 62(2):222-236, 1986.
    • (1986) J. Differential Equations , vol.62 , Issue.2 , pp. 222-236
    • Meyer, K.R.1    Schmidt, D.S.2
  • 45
    • 0001851184 scopus 로고
    • On invariant curves of area-preserving mappings of an annulus
    • J. Moser. On invariant curves of area-preserving mappings of an annulus. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 2:1-20, 1962.
    • (1962) Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II , vol.2 , pp. 1-20
    • Moser, J.1
  • 46
    • 84908024292 scopus 로고
    • An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems
    • N.N. Nckhoroshcv. An exponential estimate of the time of stability of nearly-integrable Hamiltonian systems. Russian Math. Surveys, 32:1-65, 1977.
    • (1977) Russian Math. Surveys , vol.32 , pp. 1-65
    • Nckhoroshcv, N.N.1
  • 47
    • 0013207330 scopus 로고    scopus 로고
    • Stability over exponentially long times in the planetary problem
    • L. Niederman. Stability over exponentially long times in the planetary problem. Nonlinearity, 9(1):1703-1751, 1996.
    • (1996) Nonlinearity , vol.9 , Issue.1 , pp. 1703-1751
    • Niederman, L.1
  • 48
    • 0003369366 scopus 로고
    • C. Simo. Estabilitat de sistemes Hamiltonians. Mem. Real Acad. Cienc. Artes Barcelona, 48(7):303-348, 1989.
    • (1989) Mem. Real Acad. Cienc. Artes Barcelona , vol.48 , Issue.7 , pp. 303-348
  • 49
    • 0000879938 scopus 로고
    • The Bicircular model near the triangular libration points of the RTBP. in A.E. Roy and B.A. Steves, editors, from
    • New York, Plenum Press.
    • C. Simö, G. Gomez, A. Jorba, and J. Masdemont. The Bicircular model near the triangular libration points of the RTBP. In A.E. Roy and B.A. Steves, editors, From Newton to Chaos, pages 343-370, New York, 1995. Plenum Press.
    • (1995) Newton to Chaos, Pages , pp. 343-370
    • Simö, C.1    Gomez, G.2    Jorba, A.3    Masdemont, J.4


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