一类时滞方程的近似解  

Approximate solution to a class of time delay equations

作　　者：赵杰民[1] 

机构地区：[1]北京联合大学基础部,北京100101

出　　处：《兰州理工大学学报》2005年第6期144-145,共2页Journal of Lanzhou University of Technology

摘　　要：研究了一类时滞微分方程的近似解问题.对于一类带阻尼和一般力的时滞微分方程问题求得一致有效渐近展开式,给出了共振解简洁的近似解析表达公式.应用该公式,大量工程中的时滞动力系统共振问题可方便地得到近似解析解以及振幅、频率、周期和相位等.所得结果使文[1～3]等的研究结论成为简单推论.The problem of approximate solution to a class of time delay differential equations was studied. The uniformly valid asymptotic expansion of the solution to a class of time delay differential equations with damping term and general forcing term was obtained and a simple analytic approximate expression for the resonance solution was given. By using this expression,the approximate analytic solution to the resonance problem in time delay dynamic system met in great number of engineering practice can easily be obtained, so that the amplitude, frequency,period,and phase can be easily obtained,also. The research conclusions of paper [1], [2] and [3] etc. are also included in our paper as simple corollaries.

关 键 词：时滞微分方程 非线性 主共振 近似解析解 

分 类 号：O175.7[理学—数学]