Two Particle Collision#
Detection#
Setup#
Two spheres of masses \(m_1, m_2\)
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#
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)#\[v_2 = \Delta u + v_1\]