An Improved State Space Model for Parts of
Non-linear
Oscillation Systems and Its Numerical Method
Wang Jianping(1), Liu Hongzhao(1), Yuan Daning(1), Su Zhixiao(2)
( Xi'an University of Technology) (2 Tsinghua University)
Abstract: In this paper a state space model for parts of
non-linear oscillation systems is deduced. The model is an improvement on the traditional
non-linear oscillation equations in state space. A numerical calculation method is presented
based on the analysis of the structure property of the model. The calculation
precision is improved greatly through using iterative method. Compared with the
traditional numerical methods, such as Houbolt method, Wilson-¦È method, Newmark-¦Â
method and the continuous linearization model as well as its numerical calculation using Taylor transform method[3,4]. The presented numerical method has higher calculation precision and efficiency. Numerical calculation examples, such as
non-linear single pendulum equation, Duffing equation, van der Pol equation and
two-degree-of-freedom non-linear spring pendulum, are presented by using the presented method. The higher calculation precision and efficiency of t
his method are demonstrated through comparing the results given in literatures[5¡«8].
Keywords: Nonª²linear equation, state space model, non-linear single pendulum, Duffing equation, van der Pol equation,
non-linear spring pendulum.