The canonical transformation method is proposed for symplectic conservative perturbation approximation. 然后给出正则变换的摄动保辛方法。
Pontryagin maximum principle is adopted to solve as follows: introduce "adjoint" variables to obtain Hamiltonian function, then find required control function and motion equation of the oscillator by canonical perturbation theory. 对于非线性阻尼振子的能量最优控制问题,本文采用庞特里亚金最大值原理来求解:引入伴随变量,得出哈密顿函数,通过正则摄动理论得到待求的控制函数和振予的运动规律。
Perturbation analysis of the canonical subspaces: This paper gives the least perturbation bound of the unitary factor on the unitary decomposition. 标准子空间的扰动分析:本文给出了矩阵的酉分解中酉因子的最小扰动界。
Based on the canonical perturbation theory, a second independent variable is defined beside the time t. This means a new approach to analytical solutions of nonlinear vibrations& the Canonical Double Variables Perturbation Method is developed in this paper. 在正则摄动理论的基础上,引进了新的独立自变量,从而形成了一种研究非线性振动的新的解析近似方法&双时间变量正则摄动法。
Canonical double variables perturbation method for nonlinear vibrations 研究非线性振动的双时间变量正则摄动法
The Modified of the canonical representation formulation method and TTF formulation method is stable to a certain extent. And we still get well simulation result when add the perturbation data to inverse problem. 而修正的标准表达式变换算法和TTF变换法,具有一定的稳定性,对于加扰动的数据反演问题,仍然可以获得较好的计算结果。