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Li Zhenbo, Tang Jiashi, Cai Ping. HOMOCLINIC ORBIT OF STRONGLY NONLINEAR AUTONOMOUS OSCILLATOR VIA GENERALIZED PADÉ APPROXIMATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 461-464. DOI: 10.6052/0459-1879-12-277
Citation: Li Zhenbo, Tang Jiashi, Cai Ping. HOMOCLINIC ORBIT OF STRONGLY NONLINEAR AUTONOMOUS OSCILLATOR VIA GENERALIZED PADÉ APPROXIMATION METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3): 461-464. DOI: 10.6052/0459-1879-12-277
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HOMOCLINIC ORBIT OF STRONGLY NONLINEAR AUTONOMOUS OSCILLATOR VIA GENERALIZED PADÉ APPROXIMATION METHOD

  • College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China

Funds: The project was supported by the National Natural Science Foundation of China (11172093, 11032004) and the Hunan Provincial Innovation Foundation for Postgraduate (CX2012B159).
  • Received Date: November 29, 2012
  • Revised Date: December 23, 2012
    Graphical Abstract
    • Abstract
  • The generalized Padé approximate definition is proposed based on classical definition of Padé approximation. By utilizing the hyperbolic function, a new form of generalized Padé approximation is constructed for determining the homoclinic orbit of strongly nonlinear autonomous oscillator. The Taylor expansion of generalized Padé approximation in this paper is simpler than existing ones, which means that the proposed method has less complexity in calculation. The precision of the solutions is high when the nonlinear parameters are large. The proposed method is not restricted to solve some certain systems. It can be utilized in many kinds of systems, which means that the proposed method is generally applicable. So the investigation in generalized Padé approximation is meaningful.
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    • References (10)
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    Melnikov VK. On the Stability of the Center for Time Periodic Perturbations. Moscow: Trans Moscow Math, 1963
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    Chen YY, Chen SH, Sze KY. A hyperbolic Lindstedt-Poincaré method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators. Acta Mechanica Sinica, 2009, 25(5): 721-729
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    张琪昌,冯晶晶,王炜. 类Padé逼近方法在二维振动系统的应用. 力学学报, 2011, 43(5): 914-921 (Zhang Qichang, Feng Jingjing, Wang Wei. The construction of homoclinic and heterclinic orbit in two-dimensional nonlinear system based on the quasi-Padé approximation. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 914-921 (in Chinese))
    Emaci E, Vakakis AF, Andrianov IV, et al. Study of two-dimensional axisymmetric breathers using Padé approximants. Nonlinear Dynamics, 1997, 13: 327-338
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