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Volumn 11, Issue 1, 1994, Pages 37-90

Dissipation Induced Instabilities

Author keywords

Mechanics; stability

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV FUNCTIONS; MECHANICS; MOMENTUM; QUANTUM THEORY; RIGID ROTORS;

EID: 85012295353     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(16)30196-2     Document Type: Article
Times cited : (123)

References (51)
  • 2
    • 0004282301 scopus 로고
    • Foundations of Mechanics
    • second edition Addison-Wesley Publishing, Co., Reading, Mass.
    • Abraham, R., Marsden, J.E., Foundations of Mechanics. second edition, 1978, Addison-Wesley Publishing, Co., Reading, Mass.
    • (1978)
    • Abraham, R.1    Marsden, J.E.2
  • 3
    • 0003478133 scopus 로고
    • Manifolds, Tensor Analysis and Applications
    • second edition Springer-Verlag New York
    • Abraham, R., Marsden, J.E., Ratiu, T.S., Manifolds, Tensor Analysis and Applications. second edition, 1988, Springer-Verlag, New York.
    • (1988)
    • Abraham, R.1    Marsden, J.E.2    Ratiu, T.S.3
  • 4
    • 85012295889 scopus 로고
    • Encyclopedia of Mathematics
    • Springer-Verlag
    • Arnold, V., Encyclopedia of Mathematics. Dynamical Systems III, 1987, Springer-Verlag.
    • (1987) Dynamical Systems III
    • Arnold, V.1
  • 5
    • 0023383117 scopus 로고
    • Rotational Elastic Dynamics
    • Baillieul, J., Levi, M., Rotational Elastic Dynamics. Physica, Vol. D 27, 1987, 43–62.
    • (1987) Physica , vol.Vol. D 27 , pp. 43-62
    • Baillieul, J.1    Levi, M.2
  • 6
    • 0001289149 scopus 로고
    • Constrained Relative Motions in Rotational Mechanics
    • Baillieul, J., Levi, M., Constrained Relative Motions in Rotational Mechanics. Arch. Rat. Mech. An Vol. 115 (1991), 101–135.
    • (1991) Arch. Rat. Mech. An , vol.115 , pp. 101-135
    • Baillieul, J.1    Levi, M.2
  • 7
    • 0004185542 scopus 로고
    • Matrix Analysis
    • Academic Press New York
    • Bellman, R., Matrix Analysis. 1963, Academic Press, New York.
    • (1963)
    • Bellman, R.1
  • 10
    • 0003427140 scopus 로고
    • Finite Dimensional Linear Systems
    • Wiley
    • Brockett, R., Finite Dimensional Linear Systems. 1970, Wiley.
    • (1970)
    • Brockett, R.1
  • 11
    • 0003868242 scopus 로고
    • Ellipsoidal Figures of Equilibrium
    • Dover
    • Chandrasekhar, K., Ellipsoidal Figures of Equilibrium. 1977, Dover.
    • (1977)
    • Chandrasekhar, K.1
  • 12
    • 0004293343 scopus 로고
    • The Stability of Motion
    • Trans, by M. Nadler Pergamon Press New York
    • Chetaev, N.G., The Stability of Motion. Trans, by M. Nadler, 1959, Pergamon Press, New York.
    • (1959)
    • Chetaev, N.G.1
  • 13
    • 0004131235 scopus 로고
    • Theory of Matrices
    • Chelsea N. Y
    • Gantmacher, F.R., Theory of Matrices. 1959, Chelsea, N. Y.
    • (1959)
    • Gantmacher, F.R.1
  • 14
    • 0001413716 scopus 로고
    • Instability Induced by Symmetry Reduction
    • Guckenheimer, J., Mahalov, A., Instability Induced by Symmetry Reduction. Phys. Rev. Lett. Vol. 68 (1992), 2257–2260.
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 2257-2260
    • Guckenheimer, J.1    Mahalov, A.2
  • 15
    • 0003980507 scopus 로고
    • Stability of Motion
    • Springer-Verlag New York
    • Hahn, W., Stability of Motion. 1961, Springer-Verlag, New York.
    • (1961)
    • Hahn, W.1
  • 16
    • 0026685432 scopus 로고
    • Gyroscopic Stability and its Loss in Systems with Two Essential Coordinates
    • Haller, G., Gyroscopic Stability and its Loss in Systems with Two Essential Coordinates. Int. J. Nonlinear Mech. Vol. 27 (1992), 113–127.
    • (1992) Int. J. Nonlinear Mech. , vol.27 , pp. 113-127
    • Haller, G.1
  • 17
    • 0002245635 scopus 로고
    • Nonlinear Stability of Fluid and Plasma Equilibria
    • Holm, D.D., Marsden, J.E., Ratiu, T.S., Weinstein, A., Nonlinear Stability of Fluid and Plasma Equilibria. Phys. Rep. Vol. 123 (1985), 1–116.
    • (1985) Phys. Rep. , vol.123 , pp. 1-116
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.S.3    Weinstein, A.4
  • 18
    • 0040066401 scopus 로고
    • The Secular Instability of Axisymmetric Collisionless Star Cluster
    • Kandrup, H.E., The Secular Instability of Axisymmetric Collisionless Star Cluster. Astrophy. J. Vol. 380 (1991), 511–514.
    • (1991) Astrophy. J. , vol.380 , pp. 511-514
    • Kandrup, H.E.1
  • 19
    • 85012282016 scopus 로고
    • Hamiltonian Structure of the Vlasov-Einstein System and the Problem of Stability for Spherical Relativistic Star Clusters
    • preprint.
    • H. E. Kandrup and P. Morrison, Hamiltonian Structure of the Vlasov-Einstein System and the Problem of Stability for Spherical Relativistic Star Clusters, preprint, 1992.
    • (1992)
    • Kandrup, H.E.1    Morrison, P.2
  • 20
    • 0001123379 scopus 로고
    • A Generalization of Some Investigations of Linear Differential Equations with Periodic Coefficients
    • Krein, M.G., A Generalization of Some Investigations of Linear Differential Equations with Periodic Coefficients. Doklady Akad. Nauk S.S.S.R. N.S Vol. 73 (1950), 445–448.
    • (1950) Doklady Akad. Nauk S.S.S.R. N.S , vol.73 , pp. 445-448
    • Krein, M.G.1
  • 21
    • 0022135219 scopus 로고
    • Lie-Poisson Structures, Dual-Spin Spacecraft and Asymptotic Stability
    • Krishnaprasad, P.S., Lie-Poisson Structures, Dual-Spin Spacecraft and Asymptotic Stability. Nonl. An. Th. Meth. and Appl. Vol. 9 (1985), 1011–1035.
    • (1985) Nonl. An. Th. Meth. and Appl. , vol.9 , pp. 1011-1035
    • Krishnaprasad, P.S.1
  • 22
    • 0023271591 scopus 로고
    • Hamiltonian Structure and Stability for Rigid Bodies with Flexible Attachments
    • Krishnaprasad, P.S., Marsden, J.E., Hamiltonian Structure and Stability for Rigid Bodies with Flexible Attachments. Arch. Rat. Mech. An. Vol. 98 (1987), 137–158.
    • (1987) Arch. Rat. Mech. An. , vol.98 , pp. 137-158
    • Krishnaprasad, P.S.1    Marsden, J.E.2
  • 23
    • 0004050548 scopus 로고
    • Stability by Lyapunov's Direct Method
    • Academic Press New York
    • La Salle, J.P., Lefschetz, S., Stability by Lyapunov's Direct Method. 1963, Academic Press, New York.
    • (1963)
    • La Salle, J.P.1    Lefschetz, S.2
  • 24
    • 85012288073 scopus 로고
    • Stability of Linear Hamiltonian Systems with Periodic Coefficients
    • Research Report RC 6610 (#28482), IBM F. J. Watson Research Center.
    • M. Levi Stability of Linear Hamiltonian Systems with Periodic Coefficients, Research Report RC 6610 (#28482), IBM F. J. Watson Research Center, 1977.
    • (1977)
    • Levi, M.1
  • 25
    • 0002260849 scopus 로고
    • Nonlinear Stability of a Rotating Planar Liquid Drop
    • Lewis, D.K., Nonlinear Stability of a Rotating Planar Liquid Drop. Arch. Rat. Mech. Anal. Vol. 106 (1989), 287–333.
    • (1989) Arch. Rat. Mech. Anal. , vol.106 , pp. 287-333
    • Lewis, D.K.1
  • 26
    • 0002566429 scopus 로고
    • Lagrangian Block Diagonalization
    • Lewis, D.K., Lagrangian Block Diagonalization. Dyn. Diff. Eqn's Vol. 4 (1992), 1–42.
    • (1992) Dyn. Diff. Eqn's , vol.4 , pp. 1-42
    • Lewis, D.K.1
  • 27
    • 85012268752 scopus 로고
    • Linearized Dynamics of Symmetric Lagrangian Systems
    • 1993, to appear in International Conference of Hamiltonian Dynamical Systems, Cincinnati, March 25-28.
    • D. K. Lewis, Linearized Dynamics of Symmetric Lagrangian Systems, 1993, to appear in International Conference of Hamiltonian Dynamical Systems, Cincinnati, March 25-28, 1992.
    • (1992)
    • Lewis, D.K.1
  • 29
    • 0000635455 scopus 로고
    • Nonlinear Stability of Rotating Pseudo-Rigid Bodies
    • Lewis, D.K., Simo, J.C., Nonlinear Stability of Rotating Pseudo-Rigid Bodies. Proc. Roy. Soc. Lond. Vol. A 427 (1990), 281–319.
    • (1990) Proc. Roy. Soc. Lond. , vol.Vol. A 427 , pp. 281-319
    • Lewis, D.K.1    Simo, J.C.2
  • 30
    • 0006930895 scopus 로고
    • Movement of Eigenvalues of Hamiltonian Equilibria Under Non-Hamiltonian Perturbation
    • MacKay, R., Movement of Eigenvalues of Hamiltonian Equilibria Under Non-Hamiltonian Perturbation. Phys. Lett. Vol. A 155 (1991), 266–268.
    • (1991) Phys. Lett. , vol.Vol. A 155 , pp. 266-268
    • MacKay, R.1
  • 31
    • 0002893048 scopus 로고
    • Lagrangian Reduction and the Double Spherical Pendulum
    • Marsden, J.E., Scheurle, J., Lagrangian Reduction and the Double Spherical Pendulum. ZAMP Vol. 44 (1992), 17–43.
    • (1992) ZAMP , vol.44 , pp. 17-43
    • Marsden, J.E.1    Scheurle, J.2
  • 32
    • 0001364622 scopus 로고
    • A Block Diagonalization Theorem in the Energy Momentum Method
    • Marsden, J.E., Simo, J.C., Lewis, D.K., Posbergh, T.A., A Block Diagonalization Theorem in the Energy Momentum Method. Cont. Math. AMS, Vol. 97, 1989, 297–313.
    • (1989) Cont. Math. AMS , vol.97 , pp. 297-313
    • Marsden, J.E.1    Simo, J.C.2    Lewis, D.K.3    Posbergh, T.A.4
  • 33
    • 0005441252 scopus 로고
    • The Free Energy Principle, Negative Energy Modes and Stability
    • Proc. 4th Int. Workshop on Nonlinear and Turbulent Processes in Physics, World Scientific Press.
    • P. J. Morrison and M. Kotschenreuther, The Free Energy Principle, Negative Energy Modes and Stability, Proc. 4th Int. Workshop on Nonlinear and Turbulent Processes in Physics, World Scientific Press, 1989.
    • (1989)
    • Morrison, P.J.1    Kotschenreuther, M.2
  • 34
    • 0342858244 scopus 로고
    • The Dynamics of Coupled Planar Rigid Bodies Part 2: Bifurcations, Periodic Solutions, and Chaos
    • Oh, Y.G., Sreenath, N., Krishnaprasad, P.S., Marsden, J.E., The Dynamics of Coupled Planar Rigid Bodies Part 2: Bifurcations, Periodic Solutions, and Chaos. Dynamics and Diff Eq'ns Vol. 1 (1989), 269–298.
    • (1989) Dynamics and Diff Eq'ns , vol.1 , pp. 269-298
    • Oh, Y.G.1    Sreenath, N.2    Krishnaprasad, P.S.3    Marsden, J.E.4
  • 35
    • 85012244973 scopus 로고
    • Destabilization of the Equilibria of Reversible Dynamical Systems
    • preprint.
    • O. O'Reilly, N. K. Malhotra, and N. S. Namamchchivaga, Destabilization of the Equilibria of Reversible Dynamical Systems, preprint, 1993.
    • (1993)
    • O'Reilly, O.1    Malhotra, N.K.2    Namamchchivaga, N.S.3
  • 36
    • 0008993661 scopus 로고
    • A Stability Criterion for Hamiltonian Systems with Symmetry
    • Oh, Y.G., A Stability Criterion for Hamiltonian Systems with Symmetry. J. Geom. Phys Vol. 4 (1981), 163–182.
    • (1981) J. Geom. Phys , vol.4 , pp. 163-182
    • Oh, Y.G.1
  • 37
    • 34250577313 scopus 로고
    • Sur l’équilibre d'une masse fluide animée d'un mouvement de rotation
    • Poincaré, H., Sur l’équilibre d'une masse fluide animée d'un mouvement de rotation. Acta. Math., Vol. 7, 1885, 259.
    • (1885) Acta. Math. , vol.7 , pp. 259
    • Poincaré, H.1
  • 38
    • 0039474629 scopus 로고
    • Les formes d’équilibre d'une masse fluide en rotation
    • Poincaré, H., Les formes d’équilibre d'une masse fluide en rotation. Revue Générale des Sciences Vol. 3 (1892), 809–815.
    • (1892) Revue Générale des Sciences , vol.3 , pp. 809-815
    • Poincaré, H.1
  • 39
    • 0007029095 scopus 로고
    • Sur la stabilité de l’équilibre des figures piriformes affectées par une masse fluide en rotation
    • Poincaré, H., Sur la stabilité de l’équilibre des figures piriformes affectées par une masse fluide en rotation. Philosophical Transaction Vol. A 198 (1901), 333–373.
    • (1901) Philosophical Transaction , vol.Vol. A 198 , pp. 333-373
    • Poincaré, H.1
  • 40
    • 0011649976 scopus 로고
    • Untersuchungen über die Bewegung eines flüssigen gleichartigen Ellipsoïdes
    • Riemann, B., Untersuchungen über die Bewegung eines flüssigen gleichartigen Ellipsoïdes. Abh. d. Königl. Gesell, der Wiss. zu Göttingen Vol. 9 (1860), 3–36.
    • (1860) Abh. d. Königl. Gesell, der Wiss. zu Göttingen , vol.9 , pp. 3-36
    • Riemann, B.1
  • 42
    • 0002985376 scopus 로고
    • Stability of Relative Equilibria I: The Reduced Energy Momentum Method
    • Simo, J.C., Lewis, D.K., Marsden, J.E., Stability of Relative Equilibria I: The Reduced Energy Momentum Method. Arch. Rat. Mech. Anal. Vol. 115 (1991), 15–59.
    • (1991) Arch. Rat. Mech. Anal. , vol.115 , pp. 15-59
    • Simo, J.C.1    Lewis, D.K.2    Marsden, J.E.3
  • 43
    • 13844261332 scopus 로고
    • Stability of Coupled Rigid Bodies and Geometrically Exact Rods: Block Diagonalization and the Energy-Momentum Method
    • Simo, J.C., Posbergh, T.A., Marsden, J.E., Stability of Coupled Rigid Bodies and Geometrically Exact Rods: Block Diagonalization and the Energy-Momentum Method. Physics Reports Vol. 193 (1990), 280–360.
    • (1990) Physics Reports , vol.193 , pp. 280-360
    • Simo, J.C.1    Posbergh, T.A.2    Marsden, J.E.3
  • 44
    • 34249924347 scopus 로고
    • Stability of Relative Equilibria II: Three Dimensional Elasticity
    • Simo, J.C., Posberg, T.A., Marsden, J.E., Stability of Relative Equilibria II: Three Dimensional Elasticity. Arch. Rat. Mech. Anal Vol. 115 (1991), 61–100.
    • (1991) Arch. Rat. Mech. Anal , vol.115 , pp. 61-100
    • Simo, J.C.1    Posberg, T.A.2    Marsden, J.E.3
  • 45
    • 0021898933 scopus 로고
    • On the Dynamic Stability of Gyroscopic Systems
    • Sri Namachchivaya, N., Ariaratnam, S.T., On the Dynamic Stability of Gyroscopic Systems. SM Archives Vol. 10 (1985), 313–355.
    • (1985) SM Archives , vol.10 , pp. 313-355
    • Sri Namachchivaya, N.1    Ariaratnam, S.T.2
  • 46
    • 0038881931 scopus 로고
    • A Generalization of a Theorem of Lyapunov
    • Taussky, O., A Generalization of a Theorem of Lyapunov. SIAM J. Appl., Math. Vol. 9 (1961), 640–643.
    • (1961) SIAM J. Appl., Math. , vol.9 , pp. 640-643
    • Taussky, O.1
  • 47
    • 0003729988 scopus 로고
    • Treatise on Natural Philosophy
    • Cambridge University Press
    • Tompson, W., Tait, P.G., Treatise on Natural Philosophy. 1987, Cambridge University Press.
    • (1987)
    • Tompson, W.1    Tait, P.G.2
  • 48
    • 0000173986 scopus 로고
    • Hopf Bifurcation with Non-Semisimple 1:1 Reasonance
    • Van Gils, S.A., Krupa, M., Langford, W.F., Hopf Bifurcation with Non-Semisimple 1:1 Reasonance. Nonlinearity Vol. 3 (1990), 825–830.
    • (1990) Nonlinearity , vol.3 , pp. 825-830
    • Van Gils, S.A.1    Krupa, M.2    Langford, W.F.3
  • 49
    • 0001726726 scopus 로고
    • Gyroscopic Control and Stabilization
    • Wang, L.S., Krishnaprasad, P.S., Gyroscopic Control and Stabilization. J. Nonlinear Sci. Vol. 2 (1992), 367–415.
    • (1992) J. Nonlinear Sci. , vol.2 , pp. 367-415
    • Wang, L.S.1    Krishnaprasad, P.S.2
  • 50
    • 0003591959 scopus 로고
    • A Treatise on the Analytical Dynamics of Particles and Rigid Bodies
    • 4th ed. Cambridge University Press reprinted, 1989
    • Whittaker, E.T., A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. 4th ed., 1937, Cambridge University Press reprinted, 1989.
    • (1937)
    • Whittaker, E.T.1
  • 51
    • 77956820531 scopus 로고
    • On the Concept of Elastic Stability
    • Ziegler, H., On the Concept of Elastic Stability. Adv. Appl. Mech. Vol. 4 (1956), 351–403.
    • (1956) Adv. Appl. Mech. , vol.4 , pp. 351-403
    • Ziegler, H.1


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