六维非线性动力系统三阶规范形的计算  

COMPUTATION OF THE THIRD ORDER NORMAL FORM FOR SIX-DIMENSIONAL NONLINEAR DYNAMICAL SYSTEMS

作　　者：陈祎[1] 张伟[1] 

机构地区：[1]北京工业大学机电学院,北京100022

出　　处：《动力学与控制学报》2004年第3期31-35,共5页Journal of Dynamics and Control

摘　　要：首次用一种改进的共轭算子法研究了六维非线性系统的三阶规范形以及所用的非线性变换.首先简要介绍了这种改进的共轭算子法,然后通过一般形式的六维非线性系统推导出计算三阶规范形的公式.最后用MAPLE符号算法语言编写计算程序,给出了六维非线性系统的三阶规范形的具体形式.该方法可以用同一个主程序计算具有不同线性情况的六维非线性系统的三阶规范形.An improved adjoint operator method was proposed to compute the third order normal form of six dimensional nonlinear dynamical systems and the associated nonlinear transformation for the first time. First the improved adjoint operator method was briefly introduced. Then, a general six dimensional nonlinear system was analyzed to derive the formula of computing the third order normal form. Finally, the MAPLE symbolic program for calculating the third order normal form was given. The concrete normal form of six dimensional nonlinear systems was obtained. The results indicate that we may respectively obtain the normal forms, the coefficients of the normal forms and the associated nonlinear transformations for six dimensional nonlinear systems in four different cases by using the same main MAPLE symbolic program.

关 键 词：非线性动力学 共轭算子法 规范形理论 MAPLE符号语言 非线性变换 

分 类 号：O302[理学—力学]