Two Particle Collision¶

Setup¶

TODO

(1)¶

m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{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)¶

Δ u = e \cdot (u_{1} - u_{2})

Then,

(4)¶

v_{1} = \frac{m_{1} u_{1} + m_{2} u_{2} - Δ u}{m_{1} + m_{2}}

(5)¶

v_{2} = Δ u + v_{1}