This article reviews the history and recent development of the nonlinear dynamics theory of the stochastic layer in nonlinear Hamiltonian systems. The exponentially small splitting of separatrix, standard and whisker map approaches, Chirikov overlap criterion, renormalization group technique, and incremental energy method are presented herein for analytic predictions of the onset of resonance in stochastic layers. An energy spectrum technique is also presented for the numerical prediction of such an onset, and the numerical computation of stochastic layer widths is introduced as well. Some technical problems in this area are pointed out. The objective of this review is to excite more research in nonlinear dynamic systems. There are 47 references cited in this review article.
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Nonlinear dynamics theory of stochastic layers in Hamiltonian systems
Albert CJ Luo
Albert CJ Luo
Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville IL 62026-1805
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Albert CJ Luo
Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville IL 62026-1805
Appl. Mech. Rev. May 2004, 57(3): 161-172 (12 pages)
Published Online: June 10, 2004
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Online:
June 10, 2004
Citation
Luo , A. C. (June 10, 2004). "Nonlinear dynamics theory of stochastic layers in Hamiltonian systems ." ASME. Appl. Mech. Rev. May 2004; 57(3): 161–172. https://doi.org/10.1115/1.1683699
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