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Volumn 79, Issue 2, 2007, Pages 519-553

Dissipation-induced instabilities in finite dimensions

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY DISSIPATION; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

EID: 34147153245     PISSN: 00346861     EISSN: 15390756     Source Type: Journal    
DOI: 10.1103/RevModPhys.79.519     Document Type: Article
Times cited : (134)

References (114)
  • 1
    • 0022661079 scopus 로고
    • Local feedback stabilization and bifurcation control, I. Hopf bifurcation
    • SCLEDC 0167-6911 10.1016/0167-6911(86)90095-2
    • Abed, E. H., and J.-H. Fu, 1986, " Local feedback stabilization and bifurcation control, I. Hopf bifurcation, " Syst. Control Lett. SCLEDC 0167-6911 10.1016/0167-6911(86)90095-2 7, 11-17.
    • (1986) Syst. Control Lett. , vol.7 , pp. 11-17
    • Abed, E.H.1    Fu, J.-H.2
  • 2
    • 15544376737 scopus 로고    scopus 로고
    • Stability and motion stabilization of nonconservative mechanical systems
    • JMTSEW 1072-3374
    • Agafonov, S. A., 2002, " Stability and motion stabilization of nonconservative mechanical systems, " J. Math. Sci. (N.Y.) JMTSEW 1072-3374 112, 4419-4497.
    • (2002) J. Math. Sci. (N.Y.) , vol.112 , pp. 4419-4497
    • Agafonov, S.A.1
  • 3
    • 13844319690 scopus 로고    scopus 로고
    • Fluid-flow-induced flutter of a flag
    • PNASA6 0027-8424 10.1073/pnas.0408383102
    • Argentina, M., and L. Mahadevan, 2005, " Fluid-flow-induced flutter of a flag, " Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0408383102 102, 1829-1834.
    • (2005) Proc. Natl. Acad. Sci. U.S.A. , vol.102 , pp. 1829-1834
    • Argentina, M.1    Mahadevan, L.2
  • 4
    • 0001687530 scopus 로고
    • On conditions for non-linear stability of plane stationary flows of an ideal fluid
    • ZZZZZZ 0197-6788
    • Arnold, V. I., 1965, " On conditions for non-linear stability of plane stationary flows of an ideal fluid, " Sov. Math. Dokl. ZZZZZZ 0197-6788 6, 773-777.
    • (1965) Sov. Math. Dokl. , vol.6 , pp. 773-777
    • Arnold, V.I.1
  • 5
    • 0000945983 scopus 로고
    • On an apriori estimate in the theory of hydrodynamic stability
    • ZZZZZZ 0065-9290
    • Arnold, V. I., 1969, " On an apriori estimate in the theory of hydrodynamic stability, " Am. Math. Soc. Transl. ZZZZZZ 0065-9290 19, 267-269.
    • (1969) Am. Math. Soc. Transl. , vol.19 , pp. 267-269
    • Arnold, V.I.1
  • 6
    • 84927914894 scopus 로고
    • On matrices depending on parameters
    • RMSUAF 0036-0279
    • Arnold, V. I., 1971, " On matrices depending on parameters, " Russ. Math. Surveys RMSUAF 0036-0279 26, 29-43.
    • (1971) Russ. Math. Surveys , vol.26 , pp. 29-43
    • Arnold, V.I.1
  • 11
    • 33746763011 scopus 로고    scopus 로고
    • The Levitron: An adiabatic trap for spins
    • PRLAAZ 1364-5021
    • Berry, M. V., 1996, " The Levitron: An adiabatic trap for spins, " Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 452, 1207-1220.
    • (1996) Proc. R. Soc. London, Ser. A , vol.452 , pp. 1207-1220
    • Berry, M.V.1
  • 13
    • 0030539817 scopus 로고    scopus 로고
    • The Euler-Poincare equations and double bracket dissipation
    • CMPHAY 0010-3616 10.1007/BF02101622
    • Bloch, A., P. S. Krishnaprasad, J. E. Marsden, and T. S. Ratiu, 1996, " The Euler-Poincare equations and double bracket dissipation, " Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02101622 175, 1-42.
    • (1996) Commun. Math. Phys. , vol.175 , pp. 1-42
    • Bloch, A.1    Krishnaprasad, P.S.2    Marsden, J.E.3    Ratiu, T.S.4
  • 14
    • 3543028667 scopus 로고    scopus 로고
    • Gyroscopically stabilized oscillators and heat baths
    • JSTPBS 0022-4715
    • Bloch, A. M., P. Hagerty, A. G. Rojo, and M. I. Weinstein, 2004, " Gyroscopically stabilized oscillators and heat baths, " J. Stat. Phys. JSTPBS 0022-4715 115, 1073-1100.
    • (2004) J. Stat. Phys. , vol.115 , pp. 1073-1100
    • Bloch, A.M.1    Hagerty, P.2    Rojo, A.G.3    Weinstein, M.I.4
  • 15
    • 0031345417 scopus 로고    scopus 로고
    • Stabilization of mechanical systems using controlled Lagrangians
    • Bloch, A. M., N. Leonard, and J. E. Marsden, 1997, " Stabilization of mechanical systems using controlled Lagrangians, " Proc. CDC 36, 2356-2361.
    • (1997) Proc. CDC , vol.36 , pp. 2356-2361
    • Bloch, A.M.1    Leonard, N.2    Marsden, J.E.3
  • 16
    • 0037322526 scopus 로고    scopus 로고
    • The physics of stone skipping
    • AJPIAS 0002-9505 10.1119/1.1519232
    • Bocquet, L., 2003, " The physics of stone skipping, " Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1519232 71, 150-155.
    • (2003) Am. J. Phys. , vol.71 , pp. 150-155
    • Bocquet, L.1
  • 18
    • 0035413432 scopus 로고    scopus 로고
    • On force stabilization of a dissipative system
    • IAMEEU 1063-7095
    • Borisenko, S. D., V. A. Goncharenko, and J. Mataracco, 2001, " On force stabilization of a dissipative system, " Int. Appl. Mech. IAMEEU 1063-7095 37, 1098-1102.
    • (2001) Int. Appl. Mech. , vol.37 , pp. 1098-1102
    • Borisenko, S.D.1    Goncharenko, V.A.2    Mataracco, J.3
  • 19
    • 33748096464 scopus 로고    scopus 로고
    • Strange attractors in rattleback dynamics
    • PHUSEY 1063-7869
    • Borisov, A. V., and I. S. Mamaev, 2003, " Strange attractors in rattleback dynamics, " Phys. Usp. PHUSEY 1063-7869 46, 393-403.
    • (2003) Phys. Usp. , vol.46 , pp. 393-403
    • Borisov, A.V.1    Mamaev, I.S.2
  • 20
    • 0001764541 scopus 로고
    • Rotation of artificial Earth satellites
    • NATUAS 0028-0836
    • Bracewell, R. N., and O. K. Garriot, 1958, " Rotation of artificial Earth satellites, " Nature (London) NATUAS 0028-0836 182, 760.
    • (1958) Nature (London) , vol.182 , pp. 760
    • Bracewell, R.N.1    Garriot, O.K.2
  • 21
    • 0033466324 scopus 로고    scopus 로고
    • A multiplicity result for solitary-capillary waves in deep water via critical point theory
    • AVRMAW 0003-9527
    • Buffoni, B., and M. D. Groves, 1999, " A multiplicity result for solitary-capillary waves in deep water via critical point theory, " Arch. Ration. Mech. Anal. AVRMAW 0003-9527 146, 183-220.
    • (1999) Arch. Ration. Mech. Anal. , vol.146 , pp. 183-220
    • Buffoni, B.1    Groves, M.D.2
  • 23
    • 0032453249 scopus 로고    scopus 로고
    • Negative energy modes and gravitational instability of interpenetrating fluids
    • ANYAA9 0077-8923
    • Casti, A. R. R., P. J. Morrison, and E. A. Spiegel, 1998, " Negative energy modes and gravitational instability of interpenetrating fluids, " Ann. N.Y. Acad. Sci. ANYAA9 0077-8923 867, 93-108.
    • (1998) Ann. N.Y. Acad. Sci. , vol.867 , pp. 93-108
    • Casti, A.R.R.1    Morrison, P.J.2    Spiegel, E.A.3
  • 25
    • 31144478148 scopus 로고
    • Some examples of trajectories defined by differential equations of a generalized dynamical type
    • TCPSAE 0371-5779
    • Cherry, T. M., 1925, " Some examples of trajectories defined by differential equations of a generalized dynamical type, " Trans. Cambridge Philos. Soc. TCPSAE 0371-5779 23, 165-200.
    • (1925) Trans. Cambridge Philos. Soc. , vol.23 , pp. 165-200
    • Cherry, T.M.1
  • 27
    • 0035671380 scopus 로고    scopus 로고
    • Dissipation-induced instabilities in an optical cavity laser: A mechanical analog near the 1:1 resonance
    • PLEEE8 1063-651X 10.1103/PhysRevE.64.067603
    • Clerc, M. G., and J. E. Marsden, 2001, " Dissipation-induced instabilities in an optical cavity laser: A mechanical analog near the 1:1 resonance, " Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.067603 64, 067603.
    • (2001) Phys. Rev. e , vol.64 , pp. 067603
    • Clerc, M.G.1    Marsden, J.E.2
  • 28
    • 0039474939 scopus 로고
    • The tippe top revisited
    • AJPIAS 0002-9505 10.1119/1.10926
    • Cohen, R. J., 1977, " The tippe top revisited, " Am. J. Phys. AJPIAS 0002-9505 10.1119/1.10926 45, 12-17.
    • (1977) Am. J. Phys. , vol.45 , pp. 12-17
    • Cohen, R.J.1
  • 31
    • 0000894149 scopus 로고
    • Generic bifurcation of Hamiltonian vector fields with symmetry
    • NONLE5 0951-7715 10.1088/0951-7715/5/4/008
    • Dellnitz, M., I. Melbourne, and J. E. Marsden, 1992, " Generic bifurcation of Hamiltonian vector fields with symmetry, " Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/5/4/008 5, 979-996.
    • (1992) Nonlinearity , vol.5 , pp. 979-996
    • Dellnitz, M.1    Melbourne, I.2    Marsden, J.E.3
  • 32
    • 0041972630 scopus 로고    scopus 로고
    • Unstable manifolds of relative equilibria in Hamiltonian systems with dissipation
    • NONLE5 0951-7715
    • Derks, G., and T. Ratiu, 2002, " Unstable manifolds of relative equilibria in Hamiltonian systems with dissipation, " Nonlinearity NONLE5 0951-7715 15, 531-549.
    • (2002) Nonlinearity , vol.15 , pp. 531-549
    • Derks, G.1    Ratiu, T.2
  • 33
    • 84941460449 scopus 로고
    • Über die Stabilität des Gleichgewichts
    • Dirichlet, G. L., 1846, " Ü die Stabilität des Gleichgewichts, " Crelle 32, 85-88.
    • (1846) Crelle , vol.32 , pp. 85-88
    • Dirichlet, G.L.1
  • 34
    • 0002253899 scopus 로고
    • On the nature of the molecular forces which regulate the constitution of the luminiferous ether
    • TCPSAE 0371-5779
    • Earnshaw, S., 1842, " On the nature of the molecular forces which regulate the constitution of the luminiferous ether, " Trans. Cambridge Philos. Soc. TCPSAE 0371-5779 7, 97-112.
    • (1842) Trans. Cambridge Philos. Soc. , vol.7 , pp. 97-112
    • Earnshaw, S.1
  • 35
    • 2442567242 scopus 로고
    • A new analysis of the tippe top: Asymptotic states and Liapunov stability
    • APNYA6 0003-4916
    • Ebenfeld, S., and F. Scheck, 1995, " A new analysis of the tippe top: Asymptotic states and Liapunov stability, " Ann. Phys. (N.Y.) APNYA6 0003-4916 243, 195-217.
    • (1995) Ann. Phys. (N.Y.) , vol.243 , pp. 195-217
    • Ebenfeld, S.1    Scheck, F.2
  • 38
    • 0000297673 scopus 로고    scopus 로고
    • Instabilities in fluid motion
    • AMNOAN 0002-9920
    • Friedlander, S., and V. Yudovich, 1999, " Instabilities in fluid motion, " Not. Am. Math. Soc. AMNOAN 0002-9920 46, 1358-1367.
    • (1999) Not. Am. Math. Soc. , vol.46 , pp. 1358-1367
    • Friedlander, S.1    Yudovich, V.2
  • 39
    • 0002867258 scopus 로고
    • Versal deformations of linear Hamiltonian systems
    • ZZZZZZ 0065-9290
    • Galin, D. M., 1975, " Versal deformations of linear Hamiltonian systems, " Am. Math. Soc. Transl. ZZZZZZ 0065-9290 118, 1-12.
    • (1975) Am. Math. Soc. Transl. , vol.118 , pp. 1-12
    • Galin, D.M.1
  • 43
    • 0001454797 scopus 로고
    • Generic bifurcations of Hamiltonian systems with symmetry
    • PDNPDT 0167-2789 10.1016/0167-2789(87)90087-X
    • Golubitsky, M., I. N. Stewart, and J. E. Marsden, 1987, " Generic bifurcations of Hamiltonian systems with symmetry, " Physica D PDNPDT 0167-2789 10.1016/0167-2789(87)90087-X 24, 391-405.
    • (1987) Physica D , vol.24 , pp. 391-405
    • Golubitsky, M.1    Stewart, I.N.2    Marsden, J.E.3
  • 44
    • 0001413716 scopus 로고
    • Instability induced by symmetry reduction
    • PRLTAO 0031-9007 10.1103/PhysRevLett.68.2257
    • Guckenheimer, J., and A. Mahalov, 1992, " Instability induced by symmetry reduction, " Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.2257 68, 2257-2260.
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 2257-2260
    • Guckenheimer, J.1    Mahalov, A.2
  • 46
    • 2542419103 scopus 로고    scopus 로고
    • Radiation induced instability
    • SMJMAP 0036-1399 10.1137/S0036139902418717
    • Hagerty, P., A. M. Bloch, and M. I. Weinstein, 2003, " Radiation induced instability, " SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139902418717 64, 484-524.
    • (2003) SIAM J. Appl. Math. , vol.64 , pp. 484-524
    • Hagerty, P.1    Bloch, A.M.2    Weinstein, M.I.3
  • 47
    • 34147153966 scopus 로고
    • Harrigan, R. M., 1983, U.S. Patent No. 4,382,245.
    • (1983)
    • Harrigan, R.M.1
  • 48
    • 0002378422 scopus 로고
    • Stability of equilibrium of elastic systems subjected to nonconservative forces
    • AMREAD 0003-6900
    • Herrman, G., 1967, " Stability of equilibrium of elastic systems subjected to nonconservative forces, " Appl. Mech. Rev. AMREAD 0003-6900 20, 103-108.
    • (1967) Appl. Mech. Rev. , vol.20 , pp. 103-108
    • Herrman, G.1
  • 49
    • 0002245635 scopus 로고
    • Nonlinear stability of fluid and plasma equilibria
    • PRPLCM 0370-1573 10.1016/0370-1573(85)90028-6
    • Holm, D. D., J. E. Marsden, T. Ratiu, and A. Weinstein, 1985, " Nonlinear stability of fluid and plasma equilibria, " Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(85)90028-6 123, 1-116.
    • (1985) Phys. Rep. , vol.123 , pp. 1-116
    • Holm, D.D.1    Marsden, J.E.2    Ratiu, T.3    Weinstein, A.4
  • 50
    • 0002674020 scopus 로고
    • Abzweigung einer periodischen Lösung von einer stationären Losüng eines Differentialsystems
    • Hopf, E., 1942, " Abzweigung einer periodischen Lösung von einer stationären Losüng eines Differentialsystems, " Akad. Wiss. (Leipzig) 94, 3-22.
    • (1942) Akad. Wiss. (Leipzig) , vol.94 , pp. 3-22
    • Hopf, E.1
  • 51
    • 23044522614 scopus 로고    scopus 로고
    • A precise bound for gyroscopic stabilization
    • ZAMMAX 0044-2267
    • Hryniv, R. O., W. Kliem, P. Lancaster, and C. Pommer, 2000, " A precise bound for gyroscopic stabilization, " Z. Angew. Math. Mech. ZAMMAX 0044-2267 80, 507-516.
    • (2000) Z. Angew. Math. Mech. , vol.80 , pp. 507-516
    • Hryniv, R.O.1    Kliem, W.2    Lancaster, P.3    Pommer, C.4
  • 52
    • 0034249314 scopus 로고    scopus 로고
    • Stabilization of relative equilibria
    • IETAA9 0018-9286 10.1109/9.871756
    • Jalnapurkar, S. M., and J. E. Marsden, 2000, " Stabilization of relative equilibria, " IEEE Trans. Autom. Control IETAA9 0018-9286 10.1109/9.871756 45, 1483-1491.
    • (2000) IEEE Trans. Autom. Control , vol.45 , pp. 1483-1491
    • Jalnapurkar, S.M.1    Marsden, J.E.2
  • 53
    • 0018051523 scopus 로고
    • A realistic solution of the symmetric top problem
    • JAMCAV 0021-8936
    • Kane, T. R., and D. A. Levinson, 1978, " A realistic solution of the symmetric top problem, " J. Appl. Mech. JAMCAV 0021-8936 45, 903-909.
    • (1978) J. Appl. Mech. , vol.45 , pp. 903-909
    • Kane, T.R.1    Levinson, D.A.2
  • 54
    • 31144450831 scopus 로고
    • Stability and transition through the critical speed of fast rotating shafts with friction
    • ZTEFA3 0044-4642
    • Kapitsa, P. L., 1939, " Stability and transition through the critical speed of fast rotating shafts with friction, " Zh. Tekh. Fiz. ZTEFA3 0044-4642 9, 124-147.
    • (1939) Zh. Tekh. Fiz. , vol.9 , pp. 124-147
    • Kapitsa, P.L.1
  • 55
    • 0004178386 scopus 로고    scopus 로고
    • Prentice Hall, Englewood Cliffs, NJ).
    • Khalil, H. K., 2001, Nonlinear Systems (Prentice Hall, Englewood Cliffs, NJ).
    • (2001) Nonlinear Systems
    • Khalil, H.K.1
  • 56
    • 0011581571 scopus 로고
    • Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics
    • PDNPDT 0167-2789 10.1016/0167-2789(94)90225-9
    • Knobloch, E., A. Mahalov, and J. E. Marsden, 1994, " Normal forms for three-dimensional parametric instabilities in ideal hydrodynamics, " Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)90225-9 73, 49-81.
    • (1994) Physica D , vol.73 , pp. 49-81
    • Knobloch, E.1    Mahalov, A.2    Marsden, J.E.3
  • 57
    • 0034343777 scopus 로고    scopus 로고
    • Dynamics and stability of resonant rings in galaxies
    • ATROES 1063-7729 10.1134/1.163851
    • Kondrat'ev, B. P., 2000, " Dynamics and stability of resonant rings in galaxies, " Astron. Rep. ATROES 1063-7729 10.1134/1.163851 44, 279-285.
    • (2000) Astron. Rep. , vol.44 , pp. 279-285
    • Kondrat'Ev, B.P.1
  • 58
    • 0003988657 scopus 로고
    • Stanford University Press, Stanford, CA).
    • Krasovskii, N. N., 1963, Stability of Motion (Stanford University Press, Stanford, CA).
    • (1963) Stability of Motion
    • Krasovskii, N.N.1
  • 60
    • 31144454766 scopus 로고    scopus 로고
    • On destabilizing effects of two fundamental non-conservative forces
    • PDNPDT 0167-2789
    • Krechetnikov, R., and J. E. Marsden, 2006, " On destabilizing effects of two fundamental non-conservative forces, " Physica D PDNPDT 0167-2789 214, 25-32.
    • (2006) Physica D , vol.214 , pp. 25-32
    • Krechetnikov, R.1    Marsden, J.E.2
  • 62
    • 34147164883 scopus 로고    scopus 로고
    • Hopf meets hamiltonian under whitney's umbrella
    • edited by N. S. Namachchivaya and Y. K. Lin (Kluwer, Dordrecht), pp.
    • Langford, W. F., 2003, " Hopf meets Hamiltonian under Whitney's umbrella, " in IUTAM Symposium on Nonlinear Stochastic Dynamics, edited by, N. S. Namachchivaya, and, Y. K. Lin, (Kluwer, Dordrecht), pp. 157-165.
    • (2003) IUTAM Symposium on Nonlinear Stochastic Dynamics , pp. 157-165
    • Langford, W.F.1
  • 63
    • 0034513601 scopus 로고    scopus 로고
    • Dynamic stability of columns subjected to follower loads: A survey
    • JSVIAG 0022-460X 10.1006/jsvi.2000.3137
    • Langthjem, M. A., and Y. Sugiyama, 2000, " Dynamic stability of columns subjected to follower loads: A survey, " J. Sound Vib. JSVIAG 0022-460X 10.1006/jsvi.2000.3137 238, 809-851.
    • (2000) J. Sound Vib. , vol.238 , pp. 809-851
    • Langthjem, M.A.1    Sugiyama, Y.2
  • 64
    • 0002566429 scopus 로고
    • Lagrangian block diagonalization
    • JDDEEH 1040-7294
    • Lewis, D., 1992, " Lagrangian block diagonalization, " J. Dyn. Differ. Equ. JDDEEH 1040-7294 4, 1-41.
    • (1992) J. Dyn. Differ. Equ. , vol.4 , pp. 1-41
    • Lewis, D.1
  • 65
    • 0025517223 scopus 로고
    • Stabilization of thethered satellities during station keeping
    • IETAA9 0018-9286
    • Liaw, D.-C., and E. H. Abed, 1990, " Stabilization of thethered satellities during station keeping, " IEEE Trans. Autom. Control IETAA9 0018-9286 35, 1186-1196.
    • (1990) IEEE Trans. Autom. Control , vol.35 , pp. 1186-1196
    • Liaw, D.-C.1    Abed, E.H.2
  • 66
    • 0029734493 scopus 로고    scopus 로고
    • Active control of compressor stall inception: A bifurcation-theoretic approach
    • ATCAA9 0005-1098 10.1016/0005-1098(95)00096-8
    • Liaw, D.-C., and E. H. Abed, 1996, " Active control of compressor stall inception: A bifurcation-theoretic approach, " Automatica ATCAA9 0005-1098 10.1016/0005-1098(95)00096-8 32, 109-115.
    • (1996) Automatica , vol.32 , pp. 109-115
    • Liaw, D.-C.1    Abed, E.H.2
  • 69
    • 0006930895 scopus 로고
    • Movement of eigenvalues of Hamiltonian equilibria under non-Hamiltonian perturbation
    • PYLAAG 0375-9601 10.1016/0375-9601(91)90480-V
    • MacKay, R., 1991, " Movement of eigenvalues of Hamiltonian equilibria under non-Hamiltonian perturbation, " Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(91)90480-V 155, 266-268.
    • (1991) Phys. Lett. A , vol.155 , pp. 266-268
    • MacKay, R.1
  • 70
    • 0003610563 scopus 로고
    • Cambridge University Press, Cambridge).
    • Marsden, J. E., 1992, Lectures on Mechanics (Cambridge University Press, Cambridge).
    • (1992) Lectures on Mechanics
    • Marsden, J.E.1
  • 71
    • 0002893048 scopus 로고
    • Lagrangian reduction and the double spherical pendulum
    • ZAMPDB 0044-2275 10.1007/BF00914351
    • Marsden, J. E., and J. Scheurle, 1993, " Lagrangian reduction and the double spherical pendulum, " ZAMP ZAMPDB 0044-2275 10.1007/BF00914351 44, 17-43.
    • (1993) ZAMP , vol.44 , pp. 17-43
    • Marsden, J.E.1    Scheurle, J.2
  • 72
    • 0001364622 scopus 로고
    • Block diagonalization and the energy-momentum method
    • CTMAEH 0271-4132
    • Marsden, J. E., J. C. Simo, D. Lewis, and T. A. Posbergh, 1989, " Block diagonalization and the energy-momentum method, " Contemp. Math. CTMAEH 0271-4132 97, 297-313.
    • (1989) Contemp. Math. , vol.97 , pp. 297-313
    • Marsden, J.E.1    Simo, J.C.2    Lewis, D.3    Posbergh, T.A.4
  • 76
    • 0001379563 scopus 로고
    • A paradigm for joined Hamiltonian and dissipative systems
    • PDNPDT 0167-2789
    • Morrison, P. J., 1986, " A paradigm for joined Hamiltonian and dissipative systems, " Physica D PDNPDT 0167-2789 18, 410-419.
    • (1986) Physica D , vol.18 , pp. 410-419
    • Morrison, P.J.1
  • 77
    • 0032364496 scopus 로고    scopus 로고
    • Hamiltonian description of the ideal fluid
    • RMPHAT 0034-6861 10.1103/RevModPhys.70.467
    • Morrison, P. J., 1998, " Hamiltonian description of the ideal fluid, " Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.467 70, 467-521.
    • (1998) Rev. Mod. Phys. , vol.70 , pp. 467-521
    • Morrison, P.J.1
  • 78
    • 0010808647 scopus 로고
    • Dynamical effects of drag in the circular restricted three-body problem
    • ICRSA5 0019-1035
    • Murray, C. D., 1994, " Dynamical effects of drag in the circular restricted three-body problem, " Icarus ICRSA5 0019-1035 112, 465-484.
    • (1994) Icarus , vol.112 , pp. 465-484
    • Murray, C.D.1
  • 79
    • 0000815588 scopus 로고    scopus 로고
    • Bifurcations in gyroscopic systems with application to rotating shafts
    • PRLAAZ 1364-5021
    • Nagata, W., and N. S. Namachchivaya, 1998, " Bifurcations in gyroscopic systems with application to rotating shafts, " Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 454, 543-585.
    • (1998) Proc. R. Soc. London, Ser. A , vol.454 , pp. 543-585
    • Nagata, W.1    Namachchivaya, N.S.2
  • 82
    • 0041086803 scopus 로고
    • The instability of the tippe-top explained by sliding friction
    • PRIAAK 0035-8975
    • O'Brien, S., and J. L. Synge, 1953, " The instability of the tippe-top explained by sliding friction, " Proc. R. Ir. Acad., Sect. A PRIAAK 0035-8975 56, 23-35.
    • (1953) Proc. R. Ir. Acad., Sect. A , vol.56 , pp. 23-35
    • O'Brien, S.1    Synge, J.L.2
  • 83
    • 0028448329 scopus 로고
    • The dynamics of a tippe top
    • SMJMAP 0036-1399 10.1137/S0036139992235123
    • Or, A. C., 1994, " The dynamics of a tippe top, " SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139992235123 54, 597-609.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 597-609
    • Or, A.C.1
  • 85
    • 0000702395 scopus 로고
    • A simple three-dimensional model for the study of large scale extratropical flow patterns
    • JOMYAP 0095-9634
    • Phillips, N. A., 1951, " A simple three-dimensional model for the study of large scale extratropical flow patterns, " J. Meteorol. JOMYAP 0095-9634 8, 381-394.
    • (1951) J. Meteorol. , vol.8 , pp. 381-394
    • Phillips, N.A.1
  • 87
    • 84980196930 scopus 로고
    • Periodic solutions of Hamiltonian systems
    • CPMAMV 0010-3640
    • Rabinowitz, P. H., 1978, " Periodic solutions of Hamiltonian systems, " Commun. Pure Appl. Math. CPMAMV 0010-3640 31, 157-184.
    • (1978) Commun. Pure Appl. Math. , vol.31 , pp. 157-184
    • Rabinowitz, P.H.1
  • 88
    • 0001926545 scopus 로고
    • The effects of friction and β on finite-amplitude baroclinic waves
    • JAHSAK 0022-4928 10.1175/1520-0469(1977)034<1689:TEOFAO>2.0.CO;2
    • Romea, R. A., 1977, " The effects of friction and β on finite-amplitude baroclinic waves, " J. Atmos. Sci. JAHSAK 0022-4928 10.1175/1520-0469(1977)034<1689:TEOFAO>2.0.CO;2 34, 1689-1695.
    • (1977) J. Atmos. Sci. , vol.34 , pp. 1689-1695
    • Romea, R.A.1
  • 90
    • 31144474616 scopus 로고
    • On the instability of the equilibrium of holonomic conservative systems
    • JAMMAR 0021-8928 10.1016/0021-8928(93)90088-4
    • Rumyantsev, V. V., and S. P. Sosnitskii, 1994, " On the instability of the equilibrium of holonomic conservative systems, " J. Appl. Math. Mech. JAMMAR 0021-8928 10.1016/0021-8928(93)90088-4 57, 1101-1122.
    • (1994) J. Appl. Math. Mech. , vol.57 , pp. 1101-1122
    • Rumyantsev, V.V.1    Sosnitskii, S.P.2
  • 91
    • 0001212419 scopus 로고
    • Periodische Bewegungen mechanischer Systeme
    • MAZEAX 0025-5874
    • Seifert, H., 1948, " Periodische Bewegungen mechanischer Systeme, " Math. Z. MAZEAX 0025-5874 51, 197-216.
    • (1948) Math. Z. , vol.51 , pp. 197-216
    • Seifert, H.1
  • 94
    • 0002985376 scopus 로고
    • Stability of relative equilibria. Part I: The reduced energy-momentum method
    • AVRMAW 0003-9527 10.1007/BF01881678
    • Simo, J. C., D. Lewis, and J. E. Marsden, 1991, " Stability of relative equilibria. Part I: The reduced energy-momentum method, " Arch. Ration. Mech. Anal. AVRMAW 0003-9527 10.1007/BF01881678 115, 15-59.
    • (1991) Arch. Ration. Mech. Anal. , vol.115 , pp. 15-59
    • Simo, J.C.1    Lewis, D.2    Marsden, J.E.3
  • 95
    • 0031535329 scopus 로고    scopus 로고
    • Spin stabilized magnetic levitation
    • AJPIAS 0002-9505 10.1119/1.18488
    • Simon, M. D., L. O. Heflinger, and S. L. Ridgway, 1997, " Spin stabilized magnetic levitation, " Am. J. Phys. AJPIAS 0002-9505 10.1119/1.18488 65, 286-292.
    • (1997) Am. J. Phys. , vol.65 , pp. 286-292
    • Simon, M.D.1    Heflinger, L.O.2    Ridgway, S.L.3
  • 96
    • 22244441450 scopus 로고
    • Topology and mechanics. i
    • INVMBH 0020-9910 10.1007/BF01418778
    • Smale, S., 1970, " Topology and mechanics. I, " Invent. Math. INVMBH 0020-9910 10.1007/BF01418778 10, 305-331.
    • (1970) Invent. Math. , vol.10 , pp. 305-331
    • Smale, S.1
  • 97
    • 0033460613 scopus 로고    scopus 로고
    • Resonances, radiation damping and instability in Hamiltonian wave equations
    • INVMBH 0020-9910 10.1007/s002220050303
    • Soffer, A., and M. I. Weinstein, 1999, " Resonances, radiation damping and instability in Hamiltonian wave equations, " Invent. Math. INVMBH 0020-9910 10.1007/s002220050303 136, 9-74.
    • (1999) Invent. Math. , vol.136 , pp. 9-74
    • Soffer, A.1    Weinstein, M.I.2
  • 101
    • 0001203818 scopus 로고
    • Hamiltonian Hopf bifurcation with symmetry
    • NONLE5 0951-7715 10.1088/0951-7715/3/4/005
    • van der Meer, J.-C., 1990, " Hamiltonian Hopf bifurcation with symmetry, " Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/3/4/005 3, 1041-1056.
    • (1990) Nonlinearity , vol.3 , pp. 1041-1056
    • Van Der Meer, J.-C.1
  • 102
    • 0022796923 scopus 로고
    • Stabilization of Hamiltonian systems
    • NOANDD 0362-546X
    • van der Shaft, A. J., 1986, " Stabilization of Hamiltonian systems, " Nonlinear Anal. Theory, Methods Appl. NOANDD 0362-546X 10, 1021-1035.
    • (1986) Nonlinear Anal. Theory, Methods Appl. , vol.10 , pp. 1021-1035
    • Van Der Shaft, A.J.1
  • 103
    • 29544441630 scopus 로고
    • The mysterious "rattleback:" A stone that spins in one direction and then reverses
    • SCAMAC 0036-8733
    • Walker, J., 1979, " The mysterious "rattleback:" A stone that spins in one direction and then reverses, " Sci. Am. SCAMAC 0036-8733 241 (10), 144-149.
    • (1979) Sci. Am. , vol.241 , Issue.10 , pp. 144-149
    • Walker, J.1
  • 104
    • 0001726726 scopus 로고
    • Gyroscopic control and stabilization
    • JNSCEK 0938-8794 10.1007/BF01209527
    • Wang, L.-S., and P. S. Krishnaprasad, 1992, " Gyroscopic control and stabilization, " J. Nonlinear Sci. JNSCEK 0938-8794 10.1007/BF01209527 2, 367-415.
    • (1992) J. Nonlinear Sci. , vol.2 , pp. 367-415
    • Wang, L.-S.1    Krishnaprasad, P.S.2
  • 105
    • 34249929435 scopus 로고
    • Hamiltonian dynamics of a rigid body in a central gravitational field
    • CMDAEP 0923-2958
    • Wang, L.-S., P. S. Krishnaprasad, and J. H. Maddocks, 1991, " Hamiltonian dynamics of a rigid body in a central gravitational field, " Celest. Mech. Dyn. Astron. CMDAEP 0923-2958 50, 349-386.
    • (1991) Celest. Mech. Dyn. Astron. , vol.50 , pp. 349-386
    • Wang, L.-S.1    Krishnaprasad, P.S.2    Maddocks, J.H.3
  • 106
    • 0001251052 scopus 로고
    • Periodic orbits for convex Hamiltonian systems
    • ANMAAH 0003-486X
    • Weinstein, A., 1978, " Periodic orbits for convex Hamiltonian systems, " Ann. Math. ANMAAH 0003-486X 108, 507-518.
    • (1978) Ann. Math. , vol.108 , pp. 507-518
    • Weinstein, A.1
  • 107
    • 84972495863 scopus 로고
    • The general type of singularity of a set of 2n-1 smooth functions of n variables
    • DUMJAO 0012-7094
    • Whitney, H., 1943, " The general type of singularity of a set of 2n-1 smooth functions of n variables, " Duke Math. J. DUMJAO 0012-7094 10, 161-172.
    • (1943) Duke Math. J. , vol.10 , pp. 161-172
    • Whitney, H.1
  • 112
    • 0001963097 scopus 로고
    • The Kelvin-Tait-Chetaev theorem and extensions
    • JALSA6 0021-9142
    • Zajac, E. E., 1964, " The Kelvin-Tait-Chetaev theorem and extensions, " J. Astronaut. Sci. JALSA6 0021-9142 11, 46-49.
    • (1964) J. Astronaut. Sci. , vol.11 , pp. 46-49
    • Zajac, E.E.1
  • 113
    • 34347142065 scopus 로고
    • Die Stabilitätskriterien der Elastomechanik
    • INARAS 0020-1154 10.1007/BF00536796
    • Ziegler, H., 1952, " Die Stabilitätskriterien der Elastomechanik, " Ing.-Arch. INARAS 0020-1154 10.1007/BF00536796 20, 49-56.
    • (1952) Ing.-Arch. , vol.20 , pp. 49-56
    • Ziegler, H.1
  • 114
    • 0002474552 scopus 로고
    • Linear elastic stability
    • ZAMPA8 0044-2275
    • Ziegler, H., 1953, " Linear elastic stability, " Z. Angew. Math. Phys. ZAMPA8 0044-2275 4, 89-121.
    • (1953) Z. Angew. Math. Phys. , vol.4 , pp. 89-121
    • Ziegler, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.