恒量

At first,the Noether symmetry and Noether conserved quantity under special infinitesimal transformations are.

自1918年Noether首次揭示对称性与守恒量之间的潜在关系以来，Noether对称性理论已取得重大进展[1～4]。20世纪70年代末发展起来的Lie对称性理论也取得重要进展[3～5]。

The main purpose of this dissertation is to study the problems of symmetries and conserved quantities of controllable nonholonomic systems and mechanico-electrical dynamical systems, based on the invariance of the Hamilton action under the infinitesimal Lie group transformation.

本文基于Hamilton作用量在无限小Lie群变换下的不变性，研究可控非完整系统与机电动力系统的对称性和守恒量问题。

Discrete mechanics,dynamical equation,infinitesimal transformation group,symmetry,conserved quantity

中文关键词离散力学，动力学方程，无限小变换群，对称性，守恒量

First, the principle of Jourdain for the nonholonomic systems of variable mass in event space is presented.

1918年，Noether从研究Hamilton作用量在无限小变换下的不变性出发，找到了力学系统存在守恒量的条件和形式。

Secondly, by introducing the generators of the infinitesimal transformations of Jourdain, the Noether′s theorem for the above nonholonomic systems of variable mass in event space has been obtained, which is based upon the invariance of the differential variational principle under the infinitesimal transformations of group.

这一成果揭示了力学系统的守恒量和其内在的对称性的关系，极大地推动了力学、物理学的发展。在近20年来，国内外的许多学者相继对Noether定理做了多方面的推广，不但用Hamilton作用量而且用微分变分原理研究完整和非完整系统的守恒律。

If only conservation forces act, the kinetic energy plus the potential energy remains constant.

如果只受保守力的作用，则动能加势能是一个恒量。

Note also that lambda is a constant as long as we rely on the same basic data.

同时请注意，只要我们依据的是相同的基础数据，那么，λ是一个恒量。

Shallow water wave systems; Painleve property; solitary wave; classification; Backlund transformation; Hamilton structure; conservation laws; orbital stability; linear stability; tsunamis models

浅水波系统； Painleve性质；孤立波； Backlund变换；分类； Hamilton结构；守恒量；轨道稳定性；线性稳定性；海啸模型

Conserved laws ; phase space ; path integral

守恒量；相空间；路径积分

Max Planck discovered a constant that when multiplied by the frequency of any wave gives the energy of the wave.

马克斯·普朗克发现乘以任何给出波能量的波的频率时恒量。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。