@article{AIHPC_1994__11_1_37_0, author = {Bloch, A. M. and Krishnaprasad, P. S. and Marsden, Jerrold E. and Ratiu, T. S.}, title = {Dissipation Induced Instabilities}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {11}, year = {1994}, pages = {37-90}, mrnumber = {1259101}, zbl = {0834.58025}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1994__11_1_37_0} }
Bloch, A. M.; Krishnaprasad, P. S.; Marsden, J. E.; Ratiu, T. S. Dissipation Induced Instabilities. Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) pp. 37-90. http://gdmltest.u-ga.fr/item/AIHPC_1994__11_1_37_0/
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. | MR 748636 | Zbl 0637.76119
, , and ,Foundations of Mechanics, second edition, Addison-Wesley Publishing, Co., Reading, Mass., 1978. | MR 515141
and ,Manifolds, Tensor Analysis and Applications, second edition, Springer-Verlag, New York, 1988. | MR 960687 | Zbl 0875.58002
, and ,Dynamical Systems III, Encyclopedia of Mathematics, Springer-Verlag, 1987. | MR 1292465 | Zbl 0623.00023
,Rotational Elastic Dynamics, Physica, Vol. D 27, 1987, pp. 43-62. | MR 912850 | Zbl 0644.73054
and ,Constrained Relative Motions in Rotational Mechanics, Arch. Rat. Mech. An, Vol. 115, 1991, pp. 101-135. | MR 1106071 | Zbl 0757.70004
and ,Matrix Analysis, Academic Press, New York, 1963.
,Asymptotic Stability, Instability, and Stabilization of Relative Equilibria, Proc. of ACC., Boston I.E.E.E., 1992, pp. 1120-1125.
, , and ,Stabilization of Rigid Body Dynamics by Internal and External Torques, Automatica, Vol. 28, 1992, pp. 745-756. | MR 1168932 | Zbl 0781.70020
, , and ,Finite Dimensional Linear Systems, Wiley, 1970. | Zbl 0216.27401
,Ellipsoidal Figures of Equilibrium, Dover, 1977.
,The Stability of Motion, Trans. by M. Nadler, Pergamon Press, New York, 1959.
,Theory of Matrices, Chelsea, N. Y., 1959. | Zbl 0085.01001
,Instability Induced by Symmetry Reduction, Phys. Rev. Lett., Vol. 68, 1992, pp. 2257-2260 | MR 1157130 | Zbl 1050.37516
and ,Stability of Motion, Springer-Verlag, New York, 1961. | MR 223668 | Zbl 0189.38503
,Gyroscopic Stability and its Loss in Systems with Two Essential Coordinates, Int. J. Nonlinear Mech., Vol. 27, 1992, pp. 113-127. | MR 1149191 | Zbl 0761.70007
,Nonlinear Stability of Fluid and Plasma Equilibria, Phys. Rep., Vol. 123, 1985, pp. 1-116. | MR 794110 | Zbl 0717.76051
, , and ,The Secular Instability of Axisymmetric Collisionless Star Cluster, Astrophy. J., Vol. 380, 1991, pp. 511-514. | MR 1130247
,Hamiltonian Structure of the Vlasov-Einstein System and the Problem of Stability for Spherical Relativistic Star Clusters, preprint, 1992. | MR 1224532
and ,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. | MR 36379 | Zbl 0041.05602
,Lie-Poisson Structures, Dual-Spin Spacecraft and Asymptotic Stability, Nonl. An. Th. Meth. and Appl., Vol. 9, 1985, pp. 1011-1035. | MR 806907 | Zbl 0626.70028
,Hamiltonian Structure and Stability for Rigid Bodies with Flexible Attachments, Arch. Rat. Mech. An., Vol. 98, 1987, pp. 137-158. | MR 866725 | Zbl 0624.58010
and ,Stability by Lyapunov's Direct Method, Academic Press, New York, 1963. | Zbl 0098.06102
and ,Stability of Linear Hamiltonian Systems with Periodic Coefficients, Research Report RC 6610 (#28482), IBM F. J. Watson Research Center, 1977.
,Nonlinear Stability of a Rotating Planar Liquid Drop, Arch. Rat. Mech. Anal., Vol. 106, 1989, pp. 287-333. | MR 997107 | Zbl 0697.76067
,Lagrangian Block Diagonalization, Dyn. Diff. Eqn's, Vol. 4, 1992, pp. 1-42. | MR 1150395 | Zbl 0747.58030
,Linearized Dynamics of Symmetric Lagrangian Systems, 1993, to appear in International Conference of Hamiltonian Dynamical Systems, Cincinnati, March 25-28, 1992. | Zbl 0842.58031
,The Heavy Top, a Geometric Treatment, Nonlinearity, Vol. 5, 1992, pp. 1-48. | MR 1148788 | Zbl 0753.70004
, , and ,Nonlinear Stability of Rotating Pseudo-Rigid Bodies, Proc. Roy. Soc. Lond., Vol. A427, 1990, pp. 281-319. | MR 1039789 | Zbl 0697.73045
and ,Movement of Eigenvalues of Hamiltonian Equilibria Under Non-Hamiltonian Perturbation, Phys. Lett., Vol. A 155, 1991, pp. 266-268. | MR 1107673
,Lagrangian Reduction and the Double Spherical Pendulum, ZAMP, Vol. 44, 1992, pp. 17-43. | MR 1208527 | Zbl 0778.70016
and ,A Block Diagonalization Theorem in the Energy Momentum Method, Cont. Math. AMS, Vol. 97, 1989, pp. 297-313. | Zbl 0692.70022
, , and ,The Free Energy Principle, Negative Energy Modes and Stability, Proc. 4th Int. Workshop on Nonlinear and Turbulent Processes in Physics, World Scientific Press, 1989. | MR 1168913 | Zbl 0757.70010
and ,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. | MR 1010968 | Zbl 0693.70021
, , and ,Destabilization of the Equilibria of Reversible Dynamical Systems, preprint, 1993.
, , and ,A Stability Criterion for Hamiltonian Systems with Symmetry, J. Geom. Phys., Vol. 4, 1981, pp. 163-182. | MR 948559 | Zbl 0663.58013
,Sur l'équilibre d'une masse fluide animée d'un mouvement de rotation, Acta. Math., Vol. 7, 1885, p. 259. | JFM 17.0864.02
,Les formes d'équilibre d'une masse fluide en rotation, Revue Générale des Sciences, Vol. 3, 1892, pp. 809-815.
,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. | JFM 33.0740.06
,Untersuchungen über die Bewegung eines flüssigen gleichartigen Ellipsoides, Abh. d. Königl. Gesell. der Wiss. zu Göttingen, Vol. 9, 1860, pp. 3-36.
,Stability of a Given State of Motion, reprinted in Stability of Motion, A. T. FULLER ed., Halsted Press, New York, 1975.
,Stability of Relative Equilibria I: The Reduced Energy Momentum Method, Arch. Rat. Mech. Anal., Vol. 115, 1991, pp. 15-59. | MR 1104946 | Zbl 0738.70010
, and ,