The dynamics of resonant capture
作者： D. Quinn , R. Rand , J. Bridge
DOI: 10.1007/978-94-011-0367-1_1
关键词: Mathematics 、 Bounded function 、 Phase space 、 Topology 、 Atomic physics 、 Invariant (mathematics) 、 Flow (mathematics) 、 Manifold (fluid mechanics) 、 Invariant manifold 、 Center manifold 、 Resonance
摘要: Resonant capture describes the behavior of a weakly coupled multi-degree-of-freedom system when two or more its uncoupled frequencies become locked in resonance. Flow on region phase space near resonance (the manifold) involves bounded by separatrix (e = 0) system. Capture corresponds to motions which appear cross into interior separated for e > 0.
springer.com
sci-hub.st 参考文章(16)
Pierre Lochak, Claude Meunier, Multiphase Averaging for Classical Systems Applied Mathematical Sciences. ,(1988) , 10.1007/978-1-4612-1044-3
Jacqueline Delores Bridge, Chaos in dynamical systems with periodically disappearing separatrices UMI Dissertation Services. ,(1992)
Ferdinand Verhulst, Jan A. Sanders, Averaging Methods in Nonlinear Dynamical Systems ,(1985)
John R. Cary, Rex T. Skodje, Phase change between separatrix crossings Physica D: Nonlinear Phenomena. ,vol. 36, pp. 287- 316 ,(1989) , 10.1016/0167-2789(89)90086-9
D. L. Bosley, J. Kevorkian, Sustained Resonance in very Slowly Varying Oscillatory Hamiltonian Systems SIAM Journal on Applied Mathematics. ,vol. 51, pp. 439- 471 ,(1991) , 10.1137/0151022
J. Henrard, CAPTURE INTO RESONANCE: AN EXTENSION OF THE USE OF ADIABATIC INVARIANTS Celestial Mechanics and Dynamical Astronomy. ,vol. 27, pp. 3- 22 ,(1982) , 10.1007/BF01228946
Clark Robinson, Sustained Resonance for a Nonlinear System with Slowly Varying Coefficients SIAM Journal on Mathematical Analysis. ,vol. 14, pp. 847- 860 ,(1983) , 10.1137/0514066
R.H. Rand, R.J. Kinsey., D.L. Mingori, Dynamics of spinup through resonance International Journal of Non-Linear Mechanics. ,vol. 27, pp. 489- 502 ,(1992) , 10.1016/0020-7462(92)90015-Y
Vincent T. Coppola, Richard H. Rand, Chaos in a system with a periodically disappearing separatrix Nonlinear Dynamics. ,vol. 1, pp. 401- 420 ,(1990) , 10.1007/BF01893171
J. Henrard, A. Lemaitre, A Second Fundamental Model for Resonance Celestial Mechanics and Dynamical Astronomy. ,vol. 30, pp. 197- 218 ,(1983) , 10.1007/BF01234306