Prog. Theor. Phys. Vol. 108 No. 1 (2002) pp. 1-12
Evaluation of Mean Values for a Forced Pendulum with a Projection Operator Method
1Department of Earth System Science and Technology,
Interdisciplinary Graduate School of Engineering Sciences,
Kyushu University, Kasuga 816-8580, Japan
2Research Institute for Applied Mechanics, Kyushu University,
Kasuga 816-8580, Japan
(Received September 26, 2001)
Employing a projection operator method, an averaged equation
is derived from the equations of motion
for a periodically forced pendulum with a damping term.
A model equation for the ensemble average
is derived from the averaged equation
under some assumptions. In addition, the ensemble average is obtained by
direct numerical simulation of the pendulum equations.
The solutions of the model equation exhibit fair agreement with
the numerical solutions for chaotic motion.
DOI : 10.1143/PTP.108.1
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Citing Article(s) :
Progress of Theoretical Physics Vol. 116 No. 1 (2006) pp. 47-59
Evaluation of the Time Correlation Function for the Kuramoto-Sivashinsky Equation with a Projection Operator Method