Invariance and Conservation Laws in Classical Mechanics. II
Invariance and Conservation Laws in Classical Mechanics. II
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经典力学中的不变性和守恒定律。
DOI：
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发表时间：
1965
期刊：
影响因子：
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通讯作者：
H. Denman
中科院分区：
文献类型：
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作者：
H. Denman
在经典力学中，人们通常认为，物理系统坐标平移的不变性意味着线性动量守恒。“不变性”的定义有多种。如果定义为运动方程的平均不变性，则该方程相对于坐标平移的不变性并不意味着线性动量守恒。研究了尺度变换和坐标反演不变性的影响。同时考虑了拉格朗日方法和牛顿第二定律方法。结果表明，上述每个不变性都隐含着运动方程的一个条件，而要获得一般的动量守恒，则需要将这些不变性和时间反转不变性结合起来。
It is commonly supposed that, in classical mechanics, invariance of a physical system to coordinate translation implies conservation of linear momentum. ``Invariance'' may be defined in a number of ways. If it is defined to mean invariance of the equation of motion, it is shown that invariance of this equation with respect to coordinate translation does not imply conservation of linear momentum. The effects of scale transformation and coordinate inversion invariance are also investigated. Both the Lagrangian approach and Newton's (second) law approach are considered. It is shown that each of the above invariances implies a condition on the equation of motion, while a combination of these and time‐inversion invariance is needed to obtain ordinary momentum conservation.