那用什么坐标系来计算这个积分呢？
但还是可以建立这个积分，然后转换到极坐标系下去求结果。
But still we could set this up and then switch to polar coordinates to evaluate this integral.
我们目前已经学习了三重积分，以及如何在各种坐标系中建立它们。
We have been working with triple integrals and seeing how to set them up in all sorts of coordinate systems.
(毕竟，牛顿发明了微积分本来就是为了解决一个物理问题通常你可以申请在：太阳系中的月球和行星轨道问题)。
After all, Newton invented calculus in order to solve a physics problem: the orbit of the moon and planets in the solar system.
这是极坐标系下的二重积分。
如果给出了积分区域，你就要找出积分边界，也许通过选择适当的坐标系来做。
If it is the region of integration then it will go into the bounds of the integral and maybe in the choice of the coordinate system that you use for integrating.
请说，你想知道极坐标系下的积分边界，这是一个二重积分。
Yes? In case you want the bounds for this region in polar coordinates, indeed it would be double integral.
通常你转换到极坐标系下，有可能积分区域更容易建立。
I mean usually you will switch to polar coordinates either because the region is easier to set up.
做三重积分，和二重一样，当然，我们会有更多的坐标系。
When we do triple integrals in space, well, it is the same kind of story, except now we have, of course, more coordinate systems.
关于在xy坐标系里建立二重积分有问题吗？
OK, any questions about how to set up double integrals in xy coordinates?
相对简单的、找出边界的办法,就是在u、v坐标系下画出积分区域。
And to find the bounds perhaps the easiest is to draw a picture of a region in u, v coordinates.
在极坐标系里，要记住在积分一侧,只是把x变成rcosθ，y变成rsinθ
So, when you go to polar coordinates, basically all you have to remember on the side of integrate is that x becomes r cosine theta. y becomes r sine theta.
采用熔盐的静电硬球模型，对熔盐系的位形积分和有关熔盐物性作量刚分析。
Based on electrostatic potential hard sphere model, the dimensional analysis of the configurational integral of molten salts and related physical properties has been made.
首先证明二元插值函数的不定积分也是由迭代函数系迭代生成的，并得到了其迭代函数系。
At first, the indefinite integral of binary fractal interpolating function generated by IFS is proved, and its IFS is given.
本文讨论了大气气溶胶吸收系数的测量，并介绍了我系根据毛玻璃屏积分法设计的测量系统。
A system for measuring the absorption coefficient of atmospheric aerosol based on the principle of integrating plate has been developed.
本文提出了机械手在关节坐标系中的引入积分作用的线性扰动自适应控制和引入重力补偿的模型跟随自适应控制方案。
This paper proposes a linear perturbation adaptive control scheme with integrators and a model following control scheme with gravity compensation for robot manipulators.
在太阳系动力学中，辛积分器已成为研究哈密顿系统的长期定性演化的最佳工具。
A symplectic integrator is viewed as promise of being a valuable tool in the numerical exploration of planetary and satellite n-body systems in the solar system dynamics.
在圆柱坐标系中利用积分变换法，求解热传导和热弹性力学方程组。
The equations of heat conduction and thermoelastic dynamics are solved through integral-transform method in circular cylindrical coordinates.
另一方面，发现可以通过选取合适的坐标系可有效地降低积分动量的维数，同样可以求得关联函数的解析式来。
On the other hand, it is found that choosing the appropriate coordinate system can effectively reduce the integration variable dimension and finally arrive at the same result.
通过把极坐标系作为该运动参照系而继续对模式进行积分。
The model is continued by imposing a polar coordinate system on the moving reference frame.
文中对汽轮机叶片—叶轮系统(轮系)耦合振动特性进行了理论和实验研究。首先介绍了一种简便实用的计算轮系振动特性的数值积分方法。
This paper proceeds the theoretical and experimental researches on the coupled vibration features of blade-blade wheel system (wheel system) for steam turbines.
文中对汽轮机叶片—叶轮系统(轮系)耦合振动特性进行了理论和实验研究。首先介绍了一种简便实用的计算轮系振动特性的数值积分方法。
This paper proceeds the theoretical and experimental researches on the coupled vibration features of blade-blade wheel system (wheel system) for steam turbines.
应用推荐