保守场

谈矢量的旋度和保守场

A Discussion about the Turning Degree and the Conservative Field of Vector

那么，什么是保守场？

OK , so what a conservative field ?

然后要证明F是保守场。

Then , well , we 'd like to conclude that F is conservative .

它用来衡量向量场是不是保守场的。

It measures failure of a vector field to be conservative .

另一个概念是保守场。

And we have another notion which is being conservative .

所以，这个向量场不是保守场。

So , this vector field is not conservative .

这是一个非保守场的例子。

So , it 's an example of a vector field that is not conservative .

它度量了，向量场与保守场的距离。

And , we said this measures how far that vector field is from being conservative .

如果有一个梯度场，它也是一个保守场。

So , if you have a gradient field , it 's what 's called conservative .

特别地，仅当是保守场，即有势场时才可以使用。

So , in particular , only if you have a conservative field , a gradient field .

非保守场守恒定理及某类连续介质力学的守恒律

The theorem of conservation of non-conservative field and the conservation laws for a certain class of continuum mechanics

对一个保守场来说，表征这个场的矢量的旋度处处为零；

As to a conservative field , the turning degree of the vector of the surface field is zero .

如果你找到一条曲线，沿之做功为零的话，还不足以说明这是一个保守场。

If you find a curve where the work is zero , that 's not enough to say it 's conservative .

如果旋度为0，而且场处处有定义，那么它就是保守场。

If the curl is zero , and if the field is defined everywhere , then it 's going to be conservative .

反之，一个矢量的旋度处处为零，这个场不一定是保守场。

On the contrary , if the turning degree of the vector is zero , the field is uncertain to be a conservative field .

根据磁力做功的特点，在非保守场&磁场中也可以引入势能的概念。

According to the characters of the work of magnetic force , the concept of potential energy can be brought in the non conservative system-magnetic field .

接下来，我们介绍一个量，你可能在物理上听过很多次，它可以用来判断一个场是否保守场。

Now let me just introduce a quantity that probably a lot of you have heard about in physics that measures precisely fairly ought to be conservative .

论证了保守场与有势场的关系，并着重分析了在非惯性系与分析力学中的能量问题。

The relation between conservation field and potential field is expounded and proved in this paper . The problems about energy in noninertial frame and analytical mechanics are analysed emphatically .

实际上我们知道它不是任意函数的梯度，因为如果它是，它就是保守场了。

And so , now we know actually it 's not the gradient of anything because if it were a gradient , then it would be conservative and it 's not .

本文通过微分变分原理导出非保守场守恒定理及给出某类连续介质力学的守恒定律。

The theorem of conservation of non-conservative field has been derived based on the differential variational principle and the conservation laws for a certain class of continuum mechanics are given in this paper .

主要结果是：①高能电子在高功率激光场中运动是一保守场运动，由此得到同位相耦合的条件；

The major results are : ( 1 ) the movement of high energy electrons in a powerful laser field is a conservative field movement , thus the condition for in-phase coupling is obtained ;

力没有做任何功，当你有一个非保守场的时候，或者可以找到一个回路，绕它运动所做的的功是正的。

There 's no work coming from the force , while if you have a force field that 's not conservative then you can try to actually maybe find a loop where the work would be positive .

寻找Pdx+Qdy+Rdz的积分因子是应用数学领域中极为重要的积分计算方法，同时也是判断一个三维向量场是否为保守场的重要方法。

It is an important method of integral calculation in the area of applied mathematics to find the integral factor of Pdx + Qdy + Rdz , which is also an important method to judge if a three dimensional vector field is conservative .

有趣的结果是，如果一个力场F，是由势产生的&，也就是，我们在保守力场中遇见过的情况。

The cool consequence of this is if a force field F derives from a potential & That is what we have seen about conservative forces .

什么是不可抗力微极弹性动力学中非保守力场问题的变分方法

Variational Methods for the Problems of Nonconservative Force Fields in the Micropolar Elastodynamics

微分形式与经典力学中的保守力场

Differential Form and Conservative Force Field in Classical Mechanics

理想气体分子在保守力场中按势能的分布规律

The Characteristics of the Potential Energy Distribution of Ideal Gases in a Conservative Field

在能量守恒下的振动，在保守力场中的情况，能量图。

Collisions using energy conservation , conditions for a force-field to be conservative , energy landscape .

当需要判断一个向量场是否保守向量场时，旋度也会派上用场的。

One place where it comes up is when we try to understand whether a vector field is conservative .

文章从静电场力作功的特点出发，说明静电场是保守力场。

The article proceeds from the characteristic of doing work of electrostatic field strength and proves that electrostatic field is a conservative force field .