再论动量守恒与牛顿第三定律的关系
The relation between momentum conservation and Newton's third law revisited
摘要：
在经典力学通常满足的某些条件下，线动量守恒原理与牛顿第三定律是等价的。然而，教科书中对这一事实的论证通常是不完整的。我们将在这里表明，为了证明等价性，我们需要明确使用牛顿第二定律中包含的叠加原理。另一方面，在某些附加条件下，线动量和角动量守恒的组合定律等价于有心力的牛顿第三定律。这种等价性的条件适用于经典力学的许多情况;牛顿第二定律中的叠加原理再次成为线索。
英文摘要：
Under certain conditions usually fulfilled in classical mechanics, the principle of conservation of linear momentum and Newton's third law are equivalent. However, the demonstration of this fact is usually incomplete in textbooks. We shall show here that to demonstrate the equivalence, we require the explicit use of the principle of superposition contained in Newton's second law. On the other hand, under some additional conditions the combined laws of conservation of linear and angular momentum, are equivalent to Newton's third law with central forces. The conditions for such equivalence apply in many scenarios of classical mechanics; once again the principle of superposition contained in Newton's second law is the clue.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
