Conservation of Momentum: In isolated systems, total linear momentum is strictly conserved: $\sum m_i \vec{v}_i = \sum m_i \vec{v}'_i$.
Elastic Collisions ($e = 1$): Both total momentum and total kinetic energy ($KE = \frac{1}{2}mv^2$) are conserved. Velocities follow: $v'_1 = \frac{m_1 - m_2}{m_1 + m_2}v_1 + \frac{2m_2}{m_1 + m_2}v_2$.
Inelastic Collisions ($e < 1$): Kinetic energy is converted into internal thermal/deformation energy. In perfectly inelastic collisions ($e = 0$), objects stick together: $v' = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}$.
Operating Instructions: Select Elastic or Inelastic mode, set masses and initial velocities, fire the collision, and track momentum vector preservation.