Dynamics: Forces and torques on a solid

• - Given a local force \(f(p_i)\) acting on a position \(p_i\in\Omega\)
• - Contribute to 2 global components applied on the body:

• • - Total net force \(F\) applied on the shape
  • • Induce change of linear momentum (a displacement of COM)
    • \(\displaystyle F=\int_{p_i\in\Omega} f(p_i)\,\mathrm{d}\Omega\)

• • - Torque \(\tau\) applied on the body
  • • Induce change of angular momentum (spin of the solid)

• • • \(\displaystyle \tau=\int_{p_i\in\Omega} (p_i-p)\times f(p_i)\,\mathrm{d}\Omega\)