On destabilizing effects of two fundamental non-conservative forces

Physica D: Nonlinear Phenomena

Volumn 214, Issue 1, 2006, Pages 25-32

  Krechetnikov, R ^a   Marsden, J E ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Classical mechanics; Dissipation; Instabilities; Positional forces

Indexed keywords

CONTINUUM MECHANICS; ELASTICITY; HAMILTONIANS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; RESEARCH;

CLASSICAL MECHANICS; DISSIPATION; INSTABILITIES; POSITIONAL FORCES;

FORCE MEASUREMENT;

EID: 31144454766     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.12.003     Document Type: Article

References (27)

1. A. Bloch, P.S. Krishnaprasad, J.E. Marsden, and T.S. Ratiu Dissipation induced instabilities Ann. Inst. H. Poincaré Anal. Non Linéaire 11 1994 37 90
2. A. Bloch, P.S. Krishnaprasad, J.E. Marsden, and T.S. Ratiu The Euler-Poincaré equations and double bracket dissipation Comm. Math. Phys. 1975 1996 1 42
3. W. Thomson, and P.G. Tait Treatise on Natural Philosophy 1879 Cambridge University Press
4. N.G. Chetayev The Stability of Motion 1961 Pergamon Press
5. D.R. Merkin Introduction to the Theory of Stability 1997 Springer-Verlag
6. D.R. Merkin Gyroscopic Systems 1974 Nauka Moscow (in Russian) (first edition, 1956)
7. A.V. Karapetyan, and V.V. Rumyantsev Stability of conservative and dissipative systems Itogi Nauki Tekh. 6 1983 3 128
8. P. Hagerty, A.M. Bloch, and M.I. Weinstein Radiation induced instability in interconnected systems Proceedings of the 38th CDC, IEEE 1999 651 656
9. T.M. Cherry Some examples of trajectories defined by differential equations of a generalized dynamical type Trans. Cambridge Philos. Soc. 23 1925 165 200
10. P. Painlevé Sur la stabilité de l'équilibre C. R. Acad. Sci. Paris 138 1904 1555 1557
11. A. Wintner The Analytical Foundations of Celectial Mechanics 1947 Princeton University Press
12. V.V. Rumyantsev, and S.P. Sosnitskii On the instability of the equilibrium of holonomic conservative systems J. Appl. Math. Mech. 57 1994 1101 1122
13. E.E. Zajac The Kelvin-Tait-Chetaev theorem and extensions J. Astronaut. Sci. 11 1964 46 49
14. S.A. Agafonov Stability and motion stabilization of nonconservative mechanical systems J. Math. Sci. 112 2002 4419 4497
15. P.L. Kapitsa Stability and transition through the critical speed of fast rotating shafts with friction Zh. Tekh. Fiz. 9 1939 124 147
16. A. Soffer, and M.I. Weinstein Resonances, radiation damping and instability in Hamiltonian wave equations Invent. Math. 136 1999 9 74
17. R.M. Harrigan, U.S. patent 4,382,245, 1983
18. S. Earnshaw On the nature of the molecular forces which regulate the constitution of the luminiferous ether Trans. Cambridge Philos. Soc. 7 1842 97 112
19. M.V. Berry The levitron: an adiabatic trap for spins Proc. R. Soc. A 452 1996 1207 1220
20. M.D. Simon, L.O. Heflinger, and S.L. Ridgway Spin stabilized magnetic levitation Amer. J. Phys. 65 1997 286 292
21. H. Ziegler Die Stabilitätskriterien der Elastomechanik Ing.-Arch. 20 1952 49 56
22. F.R. Gantmacher The Theory of Matrices 1977 Chelsea Pub. Co.
23. E.L. Nikolai Theoretical Mechanics 1939 GONTI, Moscow (in Russian)
24. N.M. Bou-Rabee, L.A. Romero, and A.G. Sallinger A multiparameter, numerical stability analysis of a standing cantilever conveying fluid SIAM J. Appl. Dyn. Syst. 1 2002 190 214
25. R. Krechetnikov, J.E. Marsden, Dissipation-induced instability phenomena in infinite-dimensional systems, 2005 (submitted for publication)
26. J.M. Ball, and J.E. Marsden Quasiconvexity at the boundary, positivity of the second variation and elastic stability Arch. Ration. Mech. Anal. 86 1984 251 277
27. L. Bocquet The physics of stone skipping Amer. J. Phys. 71 2003 150 155