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arXiv physics/0506111physics.gen-ph
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粒子碰撞牛顿经验公式的一种新的一般理论推导

A Novel General Theoretical Derivation of Newton-Experimental-Formula for Collision of Particles

R. C. Gupta, Ruchi Gupta, Sanjay Gupta

摘要:

实验公式,有时称为牛顿碰撞公式,(v1-v2)= - e。(u_1-u_2)是线性碰撞下两物体碰撞前后相对速度的关系,常用于碰撞动力学研究。虽然在教科书[1,2]中,假定(定义)e为恢复和变形过程中的冲量比,似乎可以导出这个关系式;但是,迄今为止,既没有一个好的理论基础,也没有一个基于明显的能量选择考虑的这个公式的一般推导。本文采用相对论理论基础,给出了一般公式的推导。有趣的是,牛顿碰撞公式的证明隐藏在爱因斯坦狭义相对论中。

英文摘要:

An experimental formula, sometimes named as Newton-collision-formula, (v1-v2) = - e.(u1-u2) relating relative-velocities before & after impact of two bodies under linear-collision, is commonly used successfully for study of collision-dynamics. Although it seems possible as shown in text-books [1,2] to derive this relation, assuming (defining) e as ratio of impulses during restitution & deformation; but as yet, neither a good theoretical-basis nor a general-derivation of this formula based on obvious choice of energy-consideration, has been reported. In this brief-paper a relativistic-theoretical-basis is adopted and a general formula-derivation is given. It is shown, interestingly, that proof of the Newton-collision-formula is hidden in Einstein-special-relativity.

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。

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