메뉴 건너뛰기




Volumn 157, Issue 1, 1999, Pages 120-149

The inverted pendulum: A singularity theory approach

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033196198     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3623     Document Type: Article
Times cited : (24)

References (29)
  • 1
    • 0003319234 scopus 로고
    • Mathematical Methods of Classical Mechanics
    • New York/Berlin: Springer-Verlag
    • Arnol'd V. I. Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics. 60:1980;Springer-Verlag, New York/Berlin.
    • (1980) Graduate Texts in Mathematics , vol.60
    • Arnol'd V., I.1
  • 3
    • 0002761467 scopus 로고
    • Formal Normal Form Theorems for Vector Fields and some Consequences for Bifurcations in the Volume Preserving Case
    • New York/Berlin: Springer-Verlag
    • Broer H. W. Formal Normal Form Theorems for Vector Fields and some Consequences for Bifurcations in the Volume Preserving Case. Lecture Notes in Mathematics. 898:1981;Springer-Verlag, New York/Berlin.
    • (1981) Lecture Notes in Mathematics , vol.898
    • Broer H., W.1
  • 5
    • 0003002106 scopus 로고
    • The Hamiltonian double-zero eigenvalue
    • "Normal Forms and Homoclinic Chaos, Proceedings, Workshop, Fields Institute for Research in Mathematical Sciences, Waterloo, Ontario, November 13-16, 1992" (W. F. Langford, & W. Nagata, Eds.) Providence: Amer. Math. Soc.
    • Broer H. W., Chow S.-N., Kim Y.-I., Vegter G. The Hamiltonian double-zero eigenvalue. Langford W. F., Nagata W. Normal Forms and Homoclinic Chaos, Proceedings, Workshop, Fields Institute for Research in Mathematical Sciences, Waterloo, Ontario, November 13-16, 1992. Fields Institute Communications. 4:1995;1-19 Amer. Math. Soc. Providence.
    • (1995) Fields Institute Communications , vol.4 , pp. 1-19
    • Broer H., W.1    Chow, S.-N.2    Kim, Y.-I.3    Vegter, G.4
  • 6
    • 0002610598 scopus 로고    scopus 로고
    • Resonances in a spring-pendulum: Algorithms for equivariant singularity theory
    • Broer H. W., Hoveijn I., Lunter G. A., Vegter G. Resonances in a spring-pendulum: algorithms for equivariant singularity theory. Nonlinearity. 11:1998;1569-1605.
    • (1998) Nonlinearity , vol.11 , pp. 1569-1605
    • Broer H., W.1    Hoveijn, I.2    Lunter G., A.3    Vegter, G.4
  • 7
    • 0002954939 scopus 로고    scopus 로고
    • A reversible bifurcation analysis of the inverted pendulum
    • Broer H. W., Hoveijn I., van Noort M. A reversible bifurcation analysis of the inverted pendulum. Phys. D. 112:1998;50-63.
    • (1998) Phys. D. , vol.112 , pp. 50-63
    • Broer H., W.1    Hoveijn, I.2    Van Noort, M.3
  • 8
    • 21844486186 scopus 로고
    • Geometrical aspects of stability theory for Hill's equations
    • Broer H. W., Levi M. Geometrical aspects of stability theory for Hill's equations. Arch. Rational Mech. Anal. 131:1995.
    • (1995) Arch. Rational Mech. Anal. , vol.131
    • Broer H., W.1    Levi, M.2
  • 9
    • 22244480073 scopus 로고    scopus 로고
    • Equivariant singularity theory with distinguished parameters: Two case studies of resonant Hamiltonian systems
    • Broer H. W., Lunter G. A., Vegter G. Equivariant singularity theory with distinguished parameters: Two case studies of resonant Hamiltonian systems. Phys. D. 112:1998;64-80.
    • (1998) Phys. D. , vol.112 , pp. 64-80
    • Broer H., W.1    Lunter G., A.2    Vegter, G.3
  • 11
    • 0002700073 scopus 로고
    • Formally symmetric normal forms and genericity
    • Broer H. W., Takens F. Formally symmetric normal forms and genericity. Dynamic. Report. 2:1989;39-59.
    • (1989) Dynamic. Report. , vol.2 , pp. 39-59
    • Broer H., W.1    Takens, F.2
  • 12
    • 0002208766 scopus 로고
    • Bifurcational aspects of parameteric resonance
    • Broer H. W., Vegter G. Bifurcational aspects of parameteric resonance. Dynamic. Report. (N.S.). 1:1992;1-53.
    • (1992) Dynamic. Report. (N.S.) , vol.1 , pp. 1-53
    • Broer H., W.1    Vegter, G.2
  • 13
    • 0000789656 scopus 로고
    • Equivalence and decomposition of vector fields about an elementary critical point
    • Chen K. T. Equivalence and decomposition of vector fields about an elementary critical point. Amer. J. Math. 85:1963;693-722.
    • (1963) Amer. J. Math. , vol.85 , pp. 693-722
    • Chen K., T.1
  • 15
    • 0003270068 scopus 로고
    • Singularities and Groups in Bifurcation Theory, I
    • New York/Berlin: Springer-Verlag
    • Golubitsky M., Schaeffer D. G. Singularities and Groups in Bifurcation Theory, I. Applied Mathematical Sciences. 51:1985;Springer-Verlag, New York/Berlin.
    • (1985) Applied Mathematical Sciences , vol.51
    • Golubitsky, M.1    Schaeffer D., G.2
  • 16
    • 0003285244 scopus 로고
    • Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
    • New York/Berlin: Springer-Verlag
    • Guckenheimer J., Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. 42:1983;Springer-Verlag, New York/Berlin.
    • (1983) Applied Mathematical Sciences , vol.42
    • Guckenheimer, J.1    Holmes, P.2
  • 17
    • 0001209620 scopus 로고
    • On constructing formal integrals of a Hamiltonian system near an equilibrium point
    • Gustavson F. G. On constructing formal integrals of a Hamiltonian system near an equilibrium point. Astron. J. 71:1966;670-686.
    • (1966) Astron. J. , vol.71 , pp. 670-686
    • Gustavson F., G.1
  • 20
    • 0024127333 scopus 로고
    • Stability of the inverted pendulum - A topological explanation
    • Levi M. Stability of the inverted pendulum - A topological explanation. SIAM Rev. 30:1988;639-644.
    • (1988) SIAM Rev. , vol.30 , pp. 639-644
    • Levi, M.1
  • 21
    • 0003275295 scopus 로고
    • Singularities of Smooth Functions and Maps
    • Cambridge: Cambridge Univ. Press
    • Martinet J. Singularities of Smooth Functions and Maps. London Mathematical Society Lecture Notes Series. 58:1982;Cambridge Univ. Press, Cambridge.
    • (1982) London Mathematical Society Lecture Notes Series , vol.58
    • Martinet, J.1
  • 22
    • 0003349147 scopus 로고
    • The Hamiltonian Hopf Bifurcation
    • New York/Berlin: Springer-Verlag
    • van der Meer J. C. The Hamiltonian Hopf Bifurcation. Lecture Notes in Mathematics. 1160:1985;Springer-Verlag, New York/Berlin.
    • (1985) Lecture Notes in Mathematics , vol.1160
    • Van der Meer J., C.1
  • 24
    • 0001865471 scopus 로고
    • Generic bifurcations in Hamiltonian systems
    • "Dynamical Systems - Warwick 1974" (A. Manning, Ed.) Springer-Verlag, New York/Berlin
    • Meyer K. Generic bifurcations in Hamiltonian systems. Manning A. Dynamical Systems - Warwick 1974. Lecture Notes in Mathematics. 468:1975;62-69 Springer-Verlag, New York/Berlin.
    • (1975) Lecture Notes in Mathematics , vol.468 , pp. 62-69
    • Meyer, K.1
  • 25
  • 26
    • 0041658514 scopus 로고
    • ∞ en présence de symétrie
    • New York/Berlin: Springer-Verlag
    • ∞ en présence de symétrie. Lecture Notes in Mathematics. 510:1976;Springer-Verlag, New York/Berlin.
    • (1976) Lecture Notes in Mathematics , vol.510
    • Poénaru, V.1
  • 28
    • 0003229603 scopus 로고
    • Averaging Methods in Nonlinear Dynamical Systems
    • New York/Berlin: Springer-Verlag
    • Sanders J. A., Verhulst F. Averaging Methods in Nonlinear Dynamical Systems. Applied Mathematical Sciences. 59:1985;Springer-Verlag, New York/Berlin.
    • (1985) Applied Mathematical Sciences , vol.59
    • Sanders J., A.1    Verhulst, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.