1) Canonical equation
正则方程
1.
Then we introduce the model to the Hamilton system and obtain the Hamilton canonical equation.
首先利用Hamilton原理对耦合结构进行建模,然后利用有限元方法将空间连续模型离散化,得到有限元模型,然后将模型导入到Hamilton系统中,获得Hamilton正则方程。
2.
From the mixed variational principle of thin plates, by selection of the statevariables and its dual variables the Hamilton type generalized variational principleand the Hamilton canonical equation are deduced.
本文通过薄板问题混合能变分原理，选用状态变量及其对偶变量，导出了一般的Ｈａｍｉｌｔｏｎ型广义变分原理和Ｈａｍｉｌｔｏｎ正则方程，这样就突破了欧几里德空间的限制，在Ｈａｍｉｌｔｏｎ力学的数学框架辛几何空间中，对全状态相变量进行分离变量，并采用共轭辛正交归一关系，给出任意支承条件下薄板问题的辛精确解。
3.
In this paper, plane stress elastic problem is taken for example, Galerkin variational equation of canonical equation of its is firstly introduced.
首先引入了Ｈａｍｉｌｔｏｎ体系中平面应力弹性力学问题正则方程的Ｇａｌｅｒｋｉｎ变分方程，证 明了Ｇａｌｅｒｋｉｎ变分方程和目前文献中所用的Ｒｉｔｚ。
2) canonical equations
正则方程
1.
The momentum via quasi--coordinate is derived according to Kane S definition so as to establish the canonical equations.
针对多刚体系统动力学数值计算精度的关键问题，首先采用Ｋａｎｅ方程导出了二阶形式的动力学方程，并研究了其中系数矩阵的恒等关系，进而建立了多刚体系统动力学的哈密顿体系并获得正则方程。
3) regular equation
正则方程
1.
In this paper the regular equations of AR and MA models built for multipath channels are derived,and an iterative algorithm of direct signal and multipath clutter cancellation is proposed.
文中推导了采用AR模型和MA模型对多径信道建模的正则方程,提出了采用混合模型消除直达波与杂波的迭代算法。
2.
This paper presents the Hanilton regular equation and the conclusion through the Hamilton principle,that is,the conversational law of momentum or conversational law of mechanic energy,and discusses the conditions for the Hamilton in the conservative and non-conservative systems.
本文通过哈密顿原理 ,给出了哈密顿正则方程及结论 ,即广义动量守恒 ,机械能量守恒。
3.
The regular equations on the constraint variables are established for LQ and nonlinear control problems in this paper,then the extreme-value principles of the constraint variables are discussed for the equality and unequality constraint cases respectively.
本文分别对ＬＱ控制问题及非线性控制问题建立了约束变量的正则方程，进而讨论了等式约束和不等式约束时约束变量的极值原理，最后通过例题验证了本文所得到的结论。
4) Hamilton canonical equation
Hamilton正则方程
1.
The semi-analytical solution for Hamilton canonical equation is employed widely in the engineering problems in recent years.
近年来,Hamilton正则方程半解析法在工程问题上的应用越来越广泛,但至今未见有关这种方法收敛性和对称性问题研究的文献。
2.
In terms of the generalized Hamilton variation principle,the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived.
根据广义的Hamilton变分原理推导出了压电热弹性体非齐次的Hamilton正则方程。
3.
Based on the semi-analytical solution for Hamilton canonical equation,the linear equation of each layer is established separately.
将厚度不连续梁板视为层合板,分别应用Hamilton正则方程半解析法建立每一层的线性方程。
6) canonical systems
正则方程组
1.
Tree Hamiltonian canonical systems of four order rod vibration equation is obtained by substituting symmetry difference quotient for high order partial derivative.
本文用中心差商代替高阶偏导数, 将四阶杆振动方程转化成三种 Hamilton 正则方程组,然后利用辛欧拉中点格式分别对其数值求解,并对三种数值结果进行比较。
2.
The canonical systems of four order rod vibration equation is obtained by substituting symmetry difference quotient for high order partial derivative, and the numerical solution is computed by using symplectic Eulers mid-point scheme in this paper.
本文用中心差商代替高阶偏导数，将四阶杆振动方程转化成正则方程组，并利用辛欧拉中点格式数值求解。
补充资料：正则方程
| 正则方程 canonical equations 用广义坐标qi和广义动量pi（i＝1，2，…，N）联合表示 受理想约束的完整保守系统的力学方程。又称哈密顿方程。可写为：  ， （i＝1，2，…，N）式中H＝T2－T0＋V为哈密顿函数，T2和T0分别为动能T中用广义动量表示的二次齐次式和零次齐次式(即不含pi，仅含qi和t之式)，V为用广义坐标表示的势函数，对于定常系统（约束方程不包含时间t）T0＝0，T＝T2，则H＝T＋V，即这种力学系统的哈密顿函数就是这系统用广义动量和广义坐标表示的机械能。正则方程是2N个一阶微分方程组，其形式上的优点是每一式只有一个导数，且都在等号左边，右边是q，p，t的函数。若令 q1＝x1，p2＝x2…，qN＝xN，p1＝xN+1，p2＝xN +2…，pN＝x2N，则正则方程可写成：
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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