A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,w...A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,which is expressed by complex amplitudes,of the first order is obtained.And solvable conditions satisfied by the complex amplitudes are given,and then the relative result is generalized.展开更多
计算机代数是近三十年发展起来的关于数学、计算机及人工智能方面的交叉学科,是数学发展的前沿学科,应用广泛.应用计算机代数系统的强大的符合运算功能以及该系统提供的控制语句,对一类弱非线性系统的有效渐近展开式解进行了研究,不但...计算机代数是近三十年发展起来的关于数学、计算机及人工智能方面的交叉学科,是数学发展的前沿学科,应用广泛.应用计算机代数系统的强大的符合运算功能以及该系统提供的控制语句,对一类弱非线性系统的有效渐近展开式解进行了研究,不但能使其自动求解,而且自动实现在平衡点附近降低微分方程阶数和实行中心流形方法,并试图解决了G r bner基在图论中关于连通图的最短路径问题.展开更多
基金Supported by the NNSF of China(10471039)Supported by the Natural Science Foundation of Zhejiang Province(Y606268)Supported by the E-Institutes of Shanghai Municipal Education Commission(E03004)
文摘A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed.Using the multiple scale method,its uniformly valid asymptotic solution,which is expressed by complex amplitudes,of the first order is obtained.And solvable conditions satisfied by the complex amplitudes are given,and then the relative result is generalized.
文摘计算机代数是近三十年发展起来的关于数学、计算机及人工智能方面的交叉学科,是数学发展的前沿学科,应用广泛.应用计算机代数系统的强大的符合运算功能以及该系统提供的控制语句,对一类弱非线性系统的有效渐近展开式解进行了研究,不但能使其自动求解,而且自动实现在平衡点附近降低微分方程阶数和实行中心流形方法,并试图解决了G r bner基在图论中关于连通图的最短路径问题.
