PX155 - F2 - collisions in 3D

{\vec{p}}_{1} + {\vec{p}}_{2} = {\vec{q}}_{1} + {\vec{q}}_{2}

problem: 6 unknowns (components of ${\vec{q}}_{1}$ , ${\vec{q}}_{2}$ ), but only 3 equations
- need further 3 pieces of information: an assumption about the energy, and two geometrical constraints, eg: angles
in COM frame:

{\vec{v}}_{c m} = \frac{m_{1} \vec{u_{1}} + m_{2} \vec{u_{2}}}{m_{1} + m_{2}}

{\vec{v}}_{1} + {\vec{v}}_{2} = {\vec{v}}_{c m}

| {\vec{u}}_{1 |} = - | {\vec{v}}_{1} | a n d | {\vec{u}}_{2} | = - | {\vec{v}}_{2} |