scholarly journals Higher-order Melnikov method and chaos for two-degree-of-freedom Hamiltonian systems with saddle-centers

2011 ◽  
Vol 29 (1) ◽  
pp. 387-402
Author(s):  
Kazuyuki Yagasaki ◽  
Keyword(s):  
Hamiltonian Systems ◽  
Melnikov Method ◽  
Higher Order ◽  
Degree Of Freedom ◽  
Two Degree Of Freedom

scholarly journals Higher order stochastic averaging method for mechanical systems having two degrees of freedom

2004 ◽  
Vol 26 (2) ◽  
pp. 103-110
Author(s):  
Nguyen Duc Tinh
Keyword(s):  
Degrees Of Freedom ◽  
Averaging Method ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Higher Order ◽  
Degree Of Freedom ◽  
Approximation Solution ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Two Degree Of Freedom

Higher order stochastic averaging method is widely used for investigating single-degree-of-freedom nonlinear systems subjected to white and coloured random noises.In this paper the method is further developed for two-degree-of-freedom systems. An application to a system with cubic damping is considered and the second approximation solution to the Fokker-Planck (FP) equation is obtained.

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