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Volumn 118, Issue 3-4, 1998, Pages 311-342

Dynamics of the Kirchhoff equations I: Coincident centers of gravity and buoyancy

Author keywords

Bifurcation; Global dynamics; Kirchhoff equations; Non integrability; Stability; Underwater vehicle

Indexed keywords

BIFURCATION (MATHEMATICS); BUOYANCY; EQUATIONS OF MOTION; GRAVITATION; PHASE SPACE METHODS; ROTATION;

EID: 0032121965     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(98)00032-3     Document Type: Article
Times cited : (51)

References (27)
  • 3
    • 0000686877 scopus 로고
    • Control of noisy heteroclinic cycles
    • B.D. Coller, P. Holmes, J.L. Lumley, Control of noisy heteroclinic cycles, Physica D 72 (1994) 135-160.
    • (1994) Physica D , vol.72 , pp. 135-160
    • Coller, B.D.1    Holmes, P.2    Lumley, J.L.3
  • 4
    • 0030737327 scopus 로고    scopus 로고
    • Suppression of bursting
    • B.D. Coller, P. Holmes, Suppression of bursting, Automatica 33 (1997) 1-11.
    • (1997) Automatica , vol.33 , pp. 1-11
    • Coller, B.D.1    Holmes, P.2
  • 5
    • 0042349153 scopus 로고
    • Periodic solutions of Kirchhoff's equations for the free motion of a rigid body in a fluid and the extended theory of Lyusternik-Shnirel'man-Morse (LSM). I
    • S.P. Novikov, I. Shmel'tser, Periodic solutions of Kirchhoff's equations for the free motion of a rigid body in a fluid and the extended theory of Lyusternik-Shnirel'man-Morse (LSM). I, Funct. Anal. Appl. 15 (1982) 197-207.
    • (1982) Funct. Anal. Appl. , vol.15 , pp. 197-207
    • Novikov, S.P.1    Shmel'tser, I.2
  • 6
    • 0031084463 scopus 로고    scopus 로고
    • Stability of a bottom-heavy underwater vehicle
    • N.E. Leonard, Stability of a bottom-heavy underwater vehicle, Automatica 33 (3) (1997) 331-346.
    • (1997) Automatica , vol.33 , Issue.3 , pp. 331-346
    • Leonard, N.E.1
  • 7
    • 0004168443 scopus 로고
    • Cambridge University Press, Cambridge, UK; 6th edn., reissued by: Dover, New York
    • H. Lamb, Hydrodynamics, Cambridge University Press, Cambridge, 1932 UK; 6th edn., reissued by: Dover, New York, 1945.
    • (1932) Hydrodynamics
    • Lamb, H.1
  • 8
    • 0007324484 scopus 로고
    • Nonintegrability of Kirchhoff's equations
    • V.V. Kozlov, D.A. Onishchenko, Nonintegrability of Kirchhoff's equations, Soviet Math Dokl. 26 (1983) 495-498.
    • (1983) Soviet Math Dokl. , vol.26 , pp. 495-498
    • Kozlov, V.V.1    Onishchenko, D.A.2
  • 9
    • 0027475275 scopus 로고
    • Chaotic motion of a solid through ideal fluid
    • H. Aref, S.W. Jones, Chaotic motion of a solid through ideal fluid, Phys. Fluids A 5 (1993) 3026-3028.
    • (1993) Phys. Fluids A , vol.5 , pp. 3026-3028
    • Aref, H.1    Jones, S.W.2
  • 10
    • 0024187242 scopus 로고
    • Quadratic integrals of the equations of motion of a rigid body in a liquid
    • V.N. Rubanovskii, Quadratic integrals of the equations of motion of a rigid body in a liquid, J. Appl. Math. Mech. 52 (1988) 312-322.
    • (1988) J. Appl. Math. Mech. , vol.52 , pp. 312-322
    • Rubanovskii, V.N.1
  • 11
    • 0001005627 scopus 로고    scopus 로고
    • Stability and drift of underwater vehicle dynamics: Mechanical systems with rigid motion symmetry
    • N.E. Leonard, J.E. Marsden, Stability and drift of underwater vehicle dynamics: mechanical systems with rigid motion symmetry, Physica D 105 (1997) 130-162.
    • (1997) Physica D , vol.105 , pp. 130-162
    • Leonard, N.E.1    Marsden, J.E.2
  • 12
    • 22244489030 scopus 로고
    • On the stability of motion of a body in a fluid
    • V.N. Rubanovskii, On the stability of motion of a body in a fluid, J. Appl. Math. Mech. 31 (1967) 142-145.
    • (1967) J. Appl. Math. Mech. , vol.31 , pp. 142-145
    • Rubanovskii, V.N.1
  • 13
    • 84914748272 scopus 로고
    • Reversible diffeomorphism and flows
    • R.L. Devaney, Reversible diffeomorphism and flows, Trans. Am. Math. Soc. 218 (1976) 89-113.
    • (1976) Trans. Am. Math. Soc. , vol.218 , pp. 89-113
    • Devaney, R.L.1
  • 14
    • 22244465208 scopus 로고    scopus 로고
    • Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
    • The Warwick Symposium on Reversible Symmetries in Dynamical Systems, to appear
    • A.R. Champneys, Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics, in: The Warwick Symposium on Reversible Symmetries in Dynamical Systems, Physica D, to appear.
    • Physica D
    • Champneys, A.R.1
  • 17
    • 0023817889 scopus 로고
    • Spatially complex equilibria of buckled rods
    • A. Mielke, P. Holmes, Spatially complex equilibria of buckled rods, Arch. Rat. Mech. Anal. 101 (1988) 319-348.
    • (1988) Arch. Rat. Mech. Anal. , vol.101 , pp. 319-348
    • Mielke, A.1    Holmes, P.2
  • 18
    • 0007281538 scopus 로고
    • Integrable Euler equations on Lie algebras arising in problems of mathematical physics
    • O.I. Bogoyavlenskii, Integrable Euler equations on Lie algebras arising in problems of mathematical physics, Math. USSR Izvestiya 25 (1985) 207-257.
    • (1985) Math. USSR Izvestiya , vol.25 , pp. 207-257
    • Bogoyavlenskii, O.I.1
  • 19
    • 22244490320 scopus 로고
    • Some possible motions of a heavy solid in a fluid
    • V.N. Rubanovskii, Some possible motions of a heavy solid in a fluid, J. Appl. Math. Mech. 32 (1968) 794-800.
    • (1968) J. Appl. Math. Mech. , vol.32 , pp. 794-800
    • Rubanovskii, V.N.1
  • 20
    • 0002245635 scopus 로고
    • Nonlinear stability of fluid and plasma equilibria
    • D.D. Holm, J.E. Marsden, T. Ratiu, A. Weinstein, Nonlinear stability of fluid and plasma equilibria, Phys. Rep. 123 (1985) 1-116.
    • (1985) Phys. Rep. , vol.123 , pp. 1-116
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.3    Weinstein, A.4
  • 25
    • 0001764721 scopus 로고
    • Horseshoes and Arnold diffusion for Hamiltonian systems on Lie groups
    • P. Holmes, J.E. Marsden, Horseshoes and Arnold diffusion for Hamiltonian systems on Lie groups, Indiana U. Math. J. 32 (1983) 273-310.
    • (1983) Indiana U. Math. J. , vol.32 , pp. 273-310
    • Holmes, P.1    Marsden, J.E.2
  • 26
    • 43949176143 scopus 로고
    • Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
    • G. Iooss, M.C. Pérouème, Perturbed homoclinic solutions in reversible 1:1 resonance vector fields, J. Diff. Eqs. 102 (1993) 62-88.
    • (1993) J. Diff. Eqs. , vol.102 , pp. 62-88
    • Iooss, G.1    Pérouème, M.C.2
  • 27
    • 0002635502 scopus 로고
    • Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center
    • A. Mielke, P. Holmes, O. O'Reilly, Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center, J. Dyn. Diff. Eqs. 4 (1992) 95-126.
    • (1992) J. Dyn. Diff. Eqs. , vol.4 , pp. 95-126
    • Mielke, A.1    Holmes, P.2    O'Reilly, O.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.