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The chaotic attitude motion of an asymmetric satellite moving on a Keplerian orbit in the central gravitational field was discussed. The Hamiltonian function of the system can be expressed by using Serret-Andoyer variables.

基於土星卫星上所观察到的混沌运动，研究了中心引力场中Kepler椭圆轨道上非对称卫星的姿态运动，其系统的Hamilton函数可用Serret-Andoyer变量写出。

Topics covered include oscillations, Keplerian orbits, two-body scattering, rotating frames of reference, rotation of rigid bodies in three dimensions, Lagrangian mechanics, Hamiltonian mechanics, and coupled oscillations.

内容包括振荡，开普勒轨道，两体散射，旋转参考坐标系，在三个方面，拉格朗日力学，哈密顿力学刚体转动，和耦合振荡。

By choosing the special values of parameters in the hierarchy, the hierarchies of the general TD, TD, the general C-KdV and C-KdV can be obtained. In order to investigate the Hamiltonian structure of this soliton hierarchy, a new Lenard gradient sequence {Gj} and its corresponding 2×2 Lenard pair of operators are introduced.

对该方程族中的参数取不同的值，可得到广义TD族，TD族，广义C-KdV族和C-KdV族；为研究其Hamilton结构，通过定义新的Lenard递推序列{G_j}得到了该等谱方程族的2×2 Lenard算子对

In addition, there exists the high dimensional oscillator in physics, In its Hamiltonian coordinates and momenta are coupled. For instance, quantumHall system does so.

另外，物理问题中有一类型振子是高维的，在其哈密顿量中动量和坐标是相互耦合的，比如量子霍尔系统就是如此。

Thirdly, a multi-component form of equation(8)in reference[40]is worked out, then its Hamiltonian structure is presented byuse of the extended trace identity. Nextly, the expanding integrable model ofmulti-component integrable equation hierarchy is obtianed.

最后，将文献[40]中Liouville可积的方程族(8)式扩为多分量的形式，然后利用扩展的迹恒等式得到了该多分量方程族的HamiIton结构，接下来求出了多分量方程族的一类扩展可积模型。

The purpose of this paper is to give the way of solving the noncommutative KP hierarchy and noncommutative constraint KP hierarchy and their bi-Hamiltonian structures.

本文试图解决一般情形下的非交换KP系列及其对应约束下的cKP系列的求解问题和它们的双Hamiltonian结构。

Finally, we phenomenologically separate phase according to magnetic fields, the results is consistent with our new idea where we use the Hamiltonian with curved surface to analyze XY model. In chapter Ⅳ, we make two hypotheses: the system has one-step time correlation and two-step time correlation. We find the effect of Ratchet potential is similar to OSTC which changes the system's relaxation. TSTC may facilitate the system to move forward or backward along the nonlinear wave of the thermal fluctuation.

第四章，我们进一步作了两个唯象的假设：体系有一步和两步时间关联；发现Ratchet势与一步时间关联有相似效果——改变了体系对热噪声的驰豫；而两步时间关联项则能够促使体系在热噪声的非线性波形上定向&冲浪&，或者促使体系躲避热噪声的扰动保持在势阱底部。

Some solvability conditions, including sublinear ,subquadralic and superquadratic, and the corresponding existence results are summed up for periodic solutions of the second order Hamiltonian systems obtained by using the minimax methods.

本文综述了用极小极大方法得到的关于二阶Hamilton系统周期解的可解性条件及相关结果，包括次线性条件，次二次条件和超二次条件等方面的近期结果。

Using the Hamiltonian constructed above, in theMajorana operator describing the vibrational interactions, we separate in the matrixelements the local mode couplings from the Fermi couplings, in order toinvestigate the Fermi resonance for linear triatomic molecules solely.

利用上一章建立的Hamiltonian，将描写振动相互作用的Majorana算子中的Darling-Dennison耦合项与Fermi耦合项分开，从而可以单独研究线形分子的Fermi共振现象。

A general form of Hamiltonian for vibronic Jahn-Teller systems is derived on the basis of adiabatic approximation and group theory. The electronic operators and active Jahn-Teller modes appeared in a vibronic system are also discussed.

本文基于绝热近似和群论导出了电声耦合系统的哈密顿量的一般形式，讨论了电声耦合系统中的电子算符和活跃的声子模式。

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。