메뉴 건너뛰기




Volumn 454, Issue 1970, 1998, Pages 543-585

Bifurcations in gyroscopic systems with an application to rotating shafts

Author keywords

Bifurcations; Dissipative and symmetry breaking perturbations; Gyroscopic systems; Nonlinear dynamics; Normal forms

Indexed keywords


EID: 0000815588     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1998.0174     Document Type: Article
Times cited : (25)

References (31)
  • 1
    • 0022734596 scopus 로고
    • Periodically perturbed nonlinear gyroscopic systems
    • Ariaratnam, S. T. & Sri Namachchivaya, N. 1986 Periodically perturbed nonlinear gyroscopic systems. J. Struct. Mech. 14, 153-175.
    • (1986) J. Struct. Mech. , vol.14 , pp. 153-175
    • Ariaratnam, S.T.1    Sri Namachchivaya, N.2
  • 6
    • 85020761765 scopus 로고
    • Rotordynamics
    • (ed. W. H. Kliemann & N. Sri Namachchivaya). Boca Raton, FL: Chemical Rubber Company
    • Crandall, S. H. 1995 Rotordynamics. In Nonlinear dynamics and stochastic dynamics (ed. W. H. Kliemann & N. Sri Namachchivaya). Boca Raton, FL: Chemical Rubber Company.
    • (1995) Nonlinear Dynamics and Stochastic Dynamics
    • Crandall, S.H.1
  • 7
    • 0000894149 scopus 로고
    • Generic bifurcation of Hamiltonian vector fields with symmetry
    • Dellnitz, M., Melbourne, I. & Marsden, J. E. 1992 Generic bifurcation of Hamiltonian vector fields with symmetry. Nonlinearity 5, 979-996.
    • (1992) Nonlinearity , vol.5 , pp. 979-996
    • Dellnitz, M.1    Melbourne, I.2    Marsden, J.E.3
  • 8
    • 0000025015 scopus 로고
    • Homoclinic bifurcations with non-hyperbolic equilibria
    • Deng, B. 1990 Homoclinic bifurcations with non-hyperbolic equilibria. SIAM Jl Math. Analysis 21, 693-720.
    • (1990) SIAM Jl Math. Analysis , vol.21 , pp. 693-720
    • Deng, B.1
  • 9
    • 0000717287 scopus 로고
    • Canonical transformations depending on a small parameter
    • Deprit, A. 1969 Canonical transformations depending on a small parameter. Celest. Mech. 1, 12-30.
    • (1969) Celest. Mech. , vol.1 , pp. 12-30
    • Deprit, A.1
  • 13
    • 0002867258 scopus 로고
    • Versal deformation of linear Hamiltonian systems
    • Galin, D. M. 1982 Versal deformation of linear Hamiltonian systems. Am. Math. Soc. Transl. 118, 1-12.
    • (1982) Am. Math. Soc. Transl. , vol.118 , pp. 1-12
    • Galin, D.M.1
  • 14
    • 33746783684 scopus 로고
    • On the bifurcations of the equilibrium states of a Hamiltonian system with two degrees of freedom
    • Garvrilov, N. K. & Šil'nikov 1991 On the bifurcations of the equilibrium states of a Hamiltonian system with two degrees of freedom. Selecta Math. Sov. 10, 61-68.
    • (1991) Selecta Math. Sov. , vol.10 , pp. 61-68
    • Garvrilov, N.K.1    Šil'nikov2
  • 15
    • 0001454797 scopus 로고
    • Generic bifurcation of Hamiltonian systems with symmetry
    • Golubitsky, M. & Stewart, I. 1987 Generic bifurcation of Hamiltonian systems with symmetry. Physica D 24, 391-405.
    • (1987) Physica D , vol.24 , pp. 391-405
    • Golubitsky, M.1    Stewart, I.2
  • 17
    • 0001413716 scopus 로고
    • Instability induced by symmetry reduction
    • Guckenheimer, J. & Mahalov, A. 1992 Instability induced by symmetry reduction. Phys. Rev. Lett. 68, 2257-2260.
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 2257-2260
    • Guckenheimer, J.1    Mahalov, A.2
  • 18
    • 0001123379 scopus 로고
    • A generalization of several investigations of A. M. Lyapunov on linear differential equations with periodic coefficients
    • Krein, M. G. 1950 A generalization of several investigations of A. M. Lyapunov on linear differential equations with periodic coefficients. Dokl. Akad. Nauk. SSSR 73, 445-448.
    • (1950) Dokl. Akad. Nauk. SSSR , vol.73 , pp. 445-448
    • Krein, M.G.1
  • 21
    • 0030752785 scopus 로고    scopus 로고
    • Global bifurcations in periodically perturbed gyroscopic systems with application to rotating shafts
    • McDonald, R. & Sri Namachchivaya, N. 1997 Global bifurcations in periodically perturbed gyroscopic systems with application to rotating shafts. Chaos Solitons Fractals 8, 613-636.
    • (1997) Chaos Solitons Fractals , vol.8 , pp. 613-636
    • McDonald, R.1    Sri Namachchivaya, N.2
  • 22
    • 1842583188 scopus 로고
    • Combination resonances in mechanical systems under harmonic excitation
    • Academia
    • Mettler, E. 1968 Combination resonances in mechanical systems under harmonic excitation. In Proc. 4th Conf. on Nonlinear Oscillations, Prague 1968, pp. 51-70. Academia.
    • (1968) Proc. 4th Conf. on Nonlinear Oscillations, Prague 1968 , pp. 51-70
    • Mettler, E.1
  • 23
    • 0000457036 scopus 로고
    • Normal forms for the general equilibrium
    • Meyer, K. R. 1984 Normal forms for the general equilibrium. Funkcialaj Ekvacioj 27, 261-271.
    • (1984) Funkcialaj Ekvacioj , vol.27 , pp. 261-271
    • Meyer, K.R.1
  • 25
    • 0024701378 scopus 로고
    • Instabilities and bifurcations in a rotating shaft
    • Shaw, J. & Shaw, S. W. 1989 Instabilities and bifurcations in a rotating shaft. J. Sound. Vib. 132, 227-244.
    • (1989) J. Sound. Vib. , vol.132 , pp. 227-244
    • Shaw, J.1    Shaw, S.W.2
  • 26
    • 0026172611 scopus 로고
    • Nonlinear resonance of an unbalanced rotating shaft with internal damping
    • Shaw, J. & Shaw, S. W. 1991 Nonlinear resonance of an unbalanced rotating shaft with internal damping. J. Sound. Vib. 147, 435-451.
    • (1991) J. Sound. Vib. , vol.147 , pp. 435-451
    • Shaw, J.1    Shaw, S.W.2
  • 27
    • 0016216299 scopus 로고
    • On the stability of an autonomous Hamiltonian system
    • Sokolskii, A. 1978 On the stability of an autonomous Hamiltonian system. J. Appl. Math. Mech. 38, 741-749.
    • (1978) J. Appl. Math. Mech. , vol.38 , pp. 741-749
    • Sokolskii, A.1
  • 30
    • 0003349147 scopus 로고
    • The Hamiltonian Hopf bifurcation
    • Berlin: Springer
    • van der Meer, J.-C. 1985 The Hamiltonian Hopf bifurcation. In Lecture Notes in Mathematics, vol 1160. Berlin: Springer.
    • (1985) Lecture Notes in Mathematics , vol.1160
    • Van Der Meer, J.-C.1
  • 31
    • 0001316020 scopus 로고
    • On an algebraic problem concerning the normal forms of linear dynamical systems
    • Williamson, J. 1936 On an algebraic problem concerning the normal forms of linear dynamical systems. Am. J. Math. 58, 141-163
    • (1936) Am. J. Math. , vol.58 , pp. 141-163
    • Williamson, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.