Elastic Collision Impulse

Given two discs with masses \(m_1, m_2\), velocities \(\mathbf{v}_1, \mathbf{v}_2\), and unit normal \(\mathbf{n}\) from 1 to 2 at contact, the normal relative speed is \(v_{rel,n} = (\mathbf{v}_2 - \mathbf{v}_1)\cdot\mathbf{n}\).

With restitution \(e\), the scalar impulse is \( j = -\frac{(1+e)\, v_{rel,n}}{1/m_1 + 1/m_2}. \)

Velocity updates: \( \mathbf{v}_1' = \mathbf{v}_1 - \frac{j}{m_1} \mathbf{n},\qquad \mathbf{v}_2' = \mathbf{v}_2 + \frac{j}{m_2} \mathbf{n}. \)

ElectroSim uses \(e=1\) (perfectly elastic). Fixed particles are treated as \(m=\infty\) so the corresponding inverse mass is zero.

Penetration correction displaces positions along \(\mathbf{n}\) proportionally to masses (or entirely on the mobile body if the other is fixed).

See implementation: electrosim.simulation.physics.resolve_collisions().

References: :cite:baraff_rigid_body.