Hamiltonian function

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。

Then , using the energy shaping and feedback stabilization theory of PCH system , the desired Hamiltonian function of closed-loop system is given . The interconnection and damping matrix are assigned , and the controller is designed . The equilibrium stability of the system is also analyzed .

然后，利用PCH系统的能量成形和反馈镇定原理，给出了闭环系统期望的哈密顿函数，配置了互联和阻尼矩阵，设计了控制器，并分析了平衡点的稳定性。

The solutions of this optimization model were obtained by using the Hamiltonian function and the Minimum Principle of Pontryagin .

通过引入哈密尔顿函数和庞特雅金最小值原理，求解了这个最优化模型。

The Schrdinger equation is given directly from the classical Hamiltonian function of a damping harmonic oscillator , and its solution is obtained by the separation of variables .

写出阻尼谐振子的哈密顿函数，对其直接量子化，用分离变量法得出了薛定谔方程的解。

Hamiltonian function was fitted with the test data , which were the value sets of phase coordinates measured in free oscillation of the systems , and the parameters were identified with the least square method .

利用系统自由振荡条件下相坐标测量值集合对系统的哈密尔顿函数进行拟合，并用最小二乘法进行参数识别。

The model of sound radiated from two connected rectangular enclosures consisting of one elastically supported flexible panel and five rigid panels is deduced by using Hamiltonian function and Rayleigh-Ritz method in this paper .

利用汉密尔顿函数和瑞利-李兹方法，建立了分别由1块四边弹性支承的弹性板及5块刚性板构成的两连接封闭矩形腔外的辐射声场模型，推导了腔体外辐射声场的解析解。

In this paper , Hamiltonian energetic function is employed to research neural activity and mechanism of neural information processing , and motion equation of neural activity described by means of energy function is established on the basis of experimental data of electrophysiology .

在这篇文章中，能量原理被用于神经活动和神经信息处理机制的研究，在电生理实验数据的基础上，建立神经元活动的用能量函数表示的运动方程。

Here we show that Hamiltonian energetic function can be employed to express electronic activity of couple neurons at sub-threshold value and action potential of couple neurons at supra-threshold stimulation . The exact solutions of the motion equation agree with action potential described by means of Hodgkin-Huxley equation .

结果表明用能量函数表达耦合神经元的阈下电活动和动作电位，数值计算结果与用Hodgkin-Huxley方程所描述的动作电位一致。

Secondly , we use a gauge transformation to change the Hamiltonian into a function of the Cartan operators of the dynamical Lie algebra ;

接着，采用幺正算符对系统进行规范变换，将Hamiltonian量变换成Cartan算子的函数；

In the third subsection , we introduce a good approach ( Floquet theory ) to study of quantum systems with their Hamiltonian being a periodic function in time .

第3节我们系统的介绍了用于研究周期含时哈密顿量的一个好的数值方法：Floquet理论方法。