Two Particle Collision

Setup

1. Two spheres of masses \(m_1, m_2\)

2. Initial velocities \(\vec{u_1}, \vec{u_2}\)

Detection

TODO

Handling

Conserving linear momentum,

(1)\[m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\]

By the definition of the coefficient of restitution,

(2)\[\frac{v_2 - v_1}{u_1 - u_2} = e\]

From (1) and (2)

Let,

(3)\[\Delta u = e \cdot (u_1 - u_2)\]

Then,

(4)\[v_1 = \frac{m_1u_1 + m_2u_2 - \Delta u}{m_1 + m_2}\]

(5)\[v_2 = \Delta u + v_1\]