Two Particle Collision#

Detection#

Setup#

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

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

Handling#

Equations#

By the Law of Conservation of Linear Momentum,

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

By the definition of the coefficient of restitution,

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

Solution#

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)#\[v_2 = \Delta u + v_1\]