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# Elastic Collisions (One Dimension)
## 1. Introduction
## 2. Relevance ## 2. Relevance
There are numerous reasons why this project is relevant, as well as a wide range of potential applications. The following will outline the primary reasons and applications: There are numerous reasons why this project is relevant, as well as a wide range of potential applications. The following will outline the primary reasons and applications:
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Consider two particles, designated as particles `1` and `2`, with respective masses $m_1$ and $m_2$. Before the collision, the velocities of particles 1 and 2 are $v_1$ and $v_2$, respectively. After the collision, the velocities of particles 1 and 2 are $v_1'$ and $v_2'$, respectively. Consider two particles, designated as particles `1` and `2`, with respective masses $m_1$ and $m_2$. Before the collision, the velocities of particles 1 and 2 are $v_1$ and $v_2$, respectively. After the collision, the velocities of particles 1 and 2 are $v_1'$ and $v_2'$, respectively.
In any collision, momentum is conserved. An elastic collision is an collision, as a result of which the total kinetic energy of the colliding particles is conserved. In any collision, momentum is conserved. A collision between to particles is said to be elastic if it involves no change in their internal state. Accordingly, when the law of conservation of energy is applied to such a collision, the internal energy of the particles may be neglected.[^2]
The conservation of momentum before and after the collision is expressed by the following equation: The conservation of momentum before and after the collision is expressed by the following equation:
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* If you have any interesting projects that I could be involved in, or if you would like to contact me, you can do so [here](https://arbuz.icu/mail). * If you have any interesting projects that I could be involved in, or if you would like to contact me, you can do so [here](https://arbuz.icu/mail).
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## Reference ## Reference
[^1]: Galperin G. A., ["PLAYING POOL WITH π (THE NUMBER π FROM A BILLIARD POINT OF VIEW)"](http://rcd.ics.org.ru/RD2003v008n04ABEH000252/), Regular and Chaotic Dynamics, 2003, Volume 8, Number 4, pp. 375-394 DOI: [10.1070/RD2003v008n04ABEH000252](http://rcd.ics.org.ru/RD2003v008n04ABEH000252/) [^1]: Galperin, G. A., _[PLAYING POOL WITH π (THE NUMBER π FROM A BILLIARD POINT OF VIEW)](http://rcd.ics.org.ru/RD2003v008n04ABEH000252/)_, _Regular and Chaotic Dynamics_, 2003, Volume 8, Number 4, pp. 375-394.
[^2]: Landau, L.D. and Lifshitz, E.M., _Course of Theoretical Physics_, vol. 1: _Mechanics_, Elsevier Science, 1982.