Collisions in rigid bodies

• Collisions at position \(p\) change both linear and angular velocity
• Use of impulse (sudden change of velocity) \(J\).
• • \(J=\int_{t_0}^{t_0+\Delta t}\,F(t)\mathrm{d}t \)
• Impulse split into
• • - Force impulse \(\Delta P=m\,\Delta v=J\)
  • - Torque impulse \(\Delta L=I\,\Delta \omega=(p-p_{com})\times J\)

• Elastic collision between two solids at position \(p_i\):
• • \(J=j\,n\), \(n\): normal of the separating planes
  • \(j=(v_1(p_i)-v_2(p_i))\cdot n / K\)
  • \(K=1/m_1+1/m_2+n\cdot\left( I_1^{-1} (r_1 \times n) \times r_1 + I_2^{-1} (r_2 \times n) \times r_2\right)\)