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http://en.wikipedia.org/wiki/Potential_energy
Potential energy is energy that is stored within a system. It exists when there is a force that tends to pull an object back towards some original position when the object is displaced. This force is often called a restoring force. For example, when a spring is stretched to the left, it exerts a force to the right so as to return to its original, unstretched position. Similarly, when a weight is lifted up, the force of gravity will try to bring it back down to its original position. The initial steps of stretching the spring or lifting the weight both require energy to perform. According to the principle of conservation of energy, energy cannot be created or destroyed; hence this energy cannot disappear. Instead, it is stored as potential energy. If the spring is released or the weight is dropped, this stored energy will be converted into kinetic energy by the restoring force — elasticity in the case of the spring, and gravity in the case of the weight
将势能当做泛函是一种视角,在用拉格朗日定理建立方程的时候有优越性。
势能具有明确的物理意义,从物理上理解更加容易。
泛函的变分为零,不等于泛函为零。能量既然是个相对量,其绝对值就没有太大意义,其作用要在一个变化过程中才得以体现。
个人意见,仅供参考
[ 本帖最后由 nonlinear 于 2009-8-28 18:39 编辑 ] |
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