力学

See [90]. The theoretical work by these mathematicians supplied many of the ideas and approaches that were later used in more applied situations in physics, celestial mechanics, chemistry, biology, and other fields.

这些数学家的理论工作提供了很多思想和方法，这些后来都被应用于物理、天体力学、化学、生物学和其它领域更为复杂的情形。

The study of the mathematical model for such motion is called celestial mechanics , and involves a finite number of bodies moving under the effects of gravitational attraction given by the Newtonian laws.

对于这种运动的数学模型的研究称作天体力学，包括研究在牛顿万有引力定律作用下的有限个天体的运动。

Celestial mechanics: numerical method, N-body simulation; planetary systems: Solar System

天体力学：数值算法，N体模拟；行星系统：太阳系

The great English scientist Newton(1643~1727) published the book Mathematical Principles of Natural Philosophy in 1687. It sums up all his studies and brings forward the three fundamental laws of mechanics, the law of universal gravitation and the laws at celestial mechanics.

英国伟大科学家牛顿(1643~1727)在1687年版的《自然哲学的数学原理》一书总其大成，提出动力学的三个基本定律，万有引力定律，天体力学等。

At that time, however, nonlinear differential equations had no universal solutions and some problems of celestial mechanics were still required to be resolved.

而非线性微分方程没有普遍解法以及一些天体力学问题的未决，促使庞加莱在微分方程求解过程中引入定性思想，创立了常微分方程实域定性理论这一新分支，突破了原有的微分方程求解的思维束缚，是微分方程研究历史上的一次重大飞跃。

Based on the fundamental theory of celestial mechanics and the discussion of two body problem under the action of universal gravitation ,the general model which can be continuously used to calculate the apparent place of celestial body in the solar system was derived. Then ,for the specific celestial body ,the material simulating method and the precision verification was given ,and the reason why the error was caused was analyzed and the corresponding method was offered .

摘 要：基于天体力学的基本理论和对万有引力作用下二体问题的讨论，推导出太阳系天体视位置长期计算的一般模型，然后针对特定天体给出了具体的仿真方法和计算结果的精度检验，深入分析了误差的产生原因并提出了相应的改进办法。

Furthermore the laws of celestial mechanics www.readinggroupguides.com/ credited to Copernicus, Kepler and Galileo were know by the Chinese and used to create a very accurate calender in 1280 for Kublai Khan (page 23 -28) that was later adopted by the Europeans.

此外天体力学定律 www.readinggroupguides.com/贷记哥白尼，开普勒和伽利略系统是由中国的了解和用于创建一个非常准确的在1280年忽必烈汗（页日历23 -28），后来由欧洲人通过。

This problem, which was certainly known to the ancients, became especially acute in the seventeenth century with the invention of celestial mechanics, which first gave philosophers a certain picture of a way the world might be: it might be a world whose future states were entirely determined by the past and the laws of nature (of which Newton's laws of motion and law of universal gravitation served as paradigms).

这个从很早就被知道的问题，在十七世纪之后变得尖锐起来，因为引力力学第一次给予了哲学家一个明确的世界图景：可能世界的未来事态完全可以被过去和自然律（Newton的运动律和万有引力定律是范例）所决定。

Birkhoff, Siegel, Kolmogorov, Arnold, Moser, Herman, and many others investigated the ideas of stability and found complicated behavior for systems arising in celestial mechanics and other such physical systems, which could be described by what are called Hamiltonian differential equations .

Birkhoff ， Siegel ， Kolmogorov ， Arnold ， Moser ， Herman 和其他很多研究者研究稳定性的思想，发现了具有复杂行为的系统出现在天体力学和其它相似的物理系统中，这些都可以用称为 Hamilton 微分方程来描述。

Based on the Cell model and the theory of mesomechanics,the evolution equation of void volume was derived.

本文基于细观塑性理论，采用体胞模型和里兹法，推导出了大锻件内部空洞的体积演化方程，通过分析空洞闭合的力学条件，建立了大锻件内部空洞的热锻闭合准则。

They go to town. Would you just ask them?

他们在城里你能问他们吗？

Ossein pretreated for a2 weeks period exhibited the maximum% yield incase of bone gelatin, while the yield from intact skin was higher than that realized incase of de-scaled skin.

预处理时间达2星期的骨胶原表现出最高的骨明胶百分产量，然而从未处理鱼皮中得到的产率比去鳞的鱼皮得到的要高。