Dissipation Induced Instabilities
A. M. Bloch; P. S. Krishnaprasad; J. E. Marsden; T. S. Ratiu
Annales de l'I.H.P. Analyse non linéaire (1994)
- Volume: 11, Issue: 1, page 37-90
- ISSN: 0294-1449
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topBloch, A. M., et al. "Dissipation Induced Instabilities." Annales de l'I.H.P. Analyse non linéaire 11.1 (1994): 37-90. <http://eudml.org/doc/78324>.
@article{Bloch1994,
author = {Bloch, A. M., Krishnaprasad, P. S., Marsden, J. E., Ratiu, T. S.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {mechanics; stability; symmetry},
language = {eng},
number = {1},
pages = {37-90},
publisher = {Gauthier-Villars},
title = {Dissipation Induced Instabilities},
url = {http://eudml.org/doc/78324},
volume = {11},
year = {1994},
}
TY - JOUR
AU - Bloch, A. M.
AU - Krishnaprasad, P. S.
AU - Marsden, J. E.
AU - Ratiu, T. S.
TI - Dissipation Induced Instabilities
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 1
SP - 37
EP - 90
LA - eng
KW - mechanics; stability; symmetry
UR - http://eudml.org/doc/78324
ER -
References
top- H.D.I. Abarbanel, D.D. Holm, J.E. Marsden and T.S. Ratiu, Nonlinear Stability Analysis of Stratified Fluid Equilibria, Phil. Trans. R. Soc. Lond., Vol. A318, 1986, pp. 349-409; also Phys. Rev. Lett, Vol. 52, 1984, pp. 2352-2355. Zbl0637.76119MR748636
- R. Abraham and J.E. Marsden, Foundations of Mechanics, second edition, Addison-Wesley Publishing, Co., Reading, Mass., 1978. Zbl0393.70001MR515141
- R. Abraham, J.E. Marsden and T.S. Ratiu, Manifolds, Tensor Analysis and Applications, second edition, Springer-Verlag, New York, 1988. Zbl0875.58002MR960687
- V. Arnold, Dynamical Systems III, Encyclopedia of Mathematics, Springer-Verlag, 1987. Zbl0623.00023MR1292465
- J. Baillieul and M. Levi, Rotational Elastic Dynamics, Physica, Vol. D 27, 1987, pp. 43-62. Zbl0644.73054MR912850
- J. Baillieul and M. Levi, Constrained Relative Motions in Rotational Mechanics, Arch. Rat. Mech. An, Vol. 115, 1991, pp. 101-135. Zbl0757.70004MR1106071
- R. Bellman, Matrix Analysis, Academic Press, New York, 1963.
- A.M. Bloch, P.S. Krishnaprasad, J.E. Marsden and T.S. Ratiu, Asymptotic Stability, Instability, and Stabilization of Relative Equilibria, Proc. of ACC., Boston I.E.E.E., 1992, pp. 1120-1125.
- A.M. Bloch, P.S. Krishnaprasad, J.E. Marsden and G. Sánchez De Alvarez, Stabilization of Rigid Body Dynamics by Internal and External Torques, Automatica, Vol. 28, 1992, pp. 745-756. Zbl0781.70020MR1168932
- R. Brockett, Finite Dimensional Linear Systems, Wiley, 1970. Zbl0216.27401
- K. Chandrasekhar, Ellipsoidal Figures of Equilibrium, Dover, 1977. Zbl0213.52304
- N.G. Chetaev, The Stability of Motion, Trans. by M. Nadler, Pergamon Press, New York, 1959. Zbl0092.42401
- F.R. Gantmacher, Theory of Matrices, Chelsea, N. Y., 1959. Zbl0085.01001
- J. Guckenheimer and A. Mahalov, Instability Induced by Symmetry Reduction, Phys. Rev. Lett., Vol. 68, 1992, pp. 2257-2260 Zbl1050.37516MR1157130
- W. Hahn, Stability of Motion, Springer-Verlag, New York, 1961. Zbl0189.38503MR223668
- G. Haller, Gyroscopic Stability and its Loss in Systems with Two Essential Coordinates, Int. J. Nonlinear Mech., Vol. 27, 1992, pp. 113-127. Zbl0761.70007MR1149191
- D.D. Holm, J.E. Marsden, T.S. Ratiu and A. Weinstein, Nonlinear Stability of Fluid and Plasma Equilibria, Phys. Rep., Vol. 123, 1985, pp. 1-116. Zbl0717.76051MR794110
- H.E. Kandrup, The Secular Instability of Axisymmetric Collisionless Star Cluster, Astrophy. J., Vol. 380, 1991, pp. 511-514. MR1130247
- 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. Zbl0767.35099MR1224532
- M.G. Krein, A Generalization of Some Investigations of Linear Differential Equations with Periodic Coefficients, Doklady Akad. Nauk S.S.S.R.N.S., Vol. 73, 1950, pp. 445-448. Zbl0041.05602MR36379
- P.S. Krishnaprasad, Lie-Poisson Structures, Dual-Spin Spacecraft and Asymptotic Stability, Nonl. An. Th. Meth. and Appl., Vol. 9, 1985, pp. 1011-1035. Zbl0626.70028MR806907
- P.S. Krishnaprasad and J.E. Marsden, Hamiltonian Structure and Stability for Rigid Bodies with Flexible Attachments, Arch. Rat. Mech. An., Vol. 98, 1987, pp. 137-158. Zbl0624.58010MR866725
- J.P. La Salle and S. Lefschetz, Stability by Lyapunov's Direct Method, Academic Press, New York, 1963. Zbl0098.06102
- M. Levi, Stability of Linear Hamiltonian Systems with Periodic Coefficients, Research Report RC 6610 (#28482), IBM F. J. Watson Research Center, 1977.
- D.K. Lewis, Nonlinear Stability of a Rotating Planar Liquid Drop, Arch. Rat. Mech. Anal., Vol. 106, 1989, pp. 287-333. Zbl0697.76067MR997107
- D.K. Lewis, Lagrangian Block Diagonalization, Dyn. Diff. Eqn's, Vol. 4, 1992, pp. 1-42. Zbl0747.58030MR1150395
- D.K. Lewis, Linearized Dynamics of Symmetric Lagrangian Systems, 1993, to appear in International Conference of Hamiltonian Dynamical Systems, Cincinnati, March 25-28, 1992. Zbl0842.58031
- D. Lewis, T.S. Ratiu, J.C. Simo and J.E. Marsden, The Heavy Top, a Geometric Treatment, Nonlinearity, Vol. 5, 1992, pp. 1-48. Zbl0753.70004MR1148788
- D.K. Lewis and J.C. Simo, Nonlinear Stability of Rotating Pseudo-Rigid Bodies, Proc. Roy. Soc. Lond., Vol. A427, 1990, pp. 281-319. Zbl0697.73045MR1039789
- R. Mackay, Movement of Eigenvalues of Hamiltonian Equilibria Under Non-Hamiltonian Perturbation, Phys. Lett., Vol. A 155, 1991, pp. 266-268. MR1107673
- J.E. Marsden and J. Scheurle, Lagrangian Reduction and the Double Spherical Pendulum, ZAMP, Vol. 44, 1992, pp. 17-43. Zbl0778.70016MR1208527
- J.E. Marsden, J.C. Simo, D.K. Lewis and T.A. Posbergh, A Block Diagonalization Theorem in the Energy Momentum Method, Cont. Math. AMS, Vol. 97, 1989, pp. 297-313. Zbl0692.70022
- 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. Zbl0757.70010MR1168913
- Y.G. Oh, N. Sreenath, P.S. Krishnaprasad and J.E. Marsden, The Dynamics of Coupled Planar Rigid Bodies Part 2: Bifurcations, Periodic Solutions, and Chaos, Dynamics and Diff. Eq'ns, Vol. 1, 1989, pp. 269-298. Zbl0693.70021MR1010968
- O. O'Reilly, N.K. Malhotra, and N.S. Namamchchivaga, Destabilization of the Equilibria of Reversible Dynamical Systems, preprint, 1993.
- Y.G. Oh, A Stability Criterion for Hamiltonian Systems with Symmetry, J. Geom. Phys., Vol. 4, 1981, pp. 163-182. Zbl0663.58013MR948559
- H. Poincaré, Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation, Acta. Math., Vol. 7, 1885, p. 259. JFM17.0864.02
- H. Poincaré, Les formes d'équilibre d'une masse fluide en rotation, Revue Générale des Sciences, Vol. 3, 1892, pp. 809-815.
- H. Poincaré, Sur la stabilité de l'équilibre des figures piriformes affectées par une masse fluide en rotation, Philosophical Transaction, Vol. A 198, 1901, pp. 333-373. Zbl33.0740.06JFM33.0740.06
- B. Riemann, Untersuchungen über die Bewegung eines flüssigen gleichartigen Ellipsoides, Abh. d. Königl. Gesell. der Wiss. zu Göttingen, Vol. 9, 1860, pp. 3-36.
- E.J. Routh, Stability of a Given State of Motion, reprinted in Stability of Motion, A. T. FULLER ed., Halsted Press, New York, 1975. Zbl17.0315.02
- J.C. Simo, D.K. Lewis and J.E. Marsden, Stability of Relative Equilibria I: The Reduced Energy Momentum Method, Arch. Rat. Mech. Anal., Vol. 115, 1991, pp. 15-59. Zbl0738.70010MR1104946
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