This is the famous medieval siege engine. The main beam (L=L₁ + L₂) is connected to a counterweight, M, and a projectile, m. After setting parameters, click the fire button to launch the projectile. The projectile is released when the angle ψ reaches ψ_R. Click on the diagrams for detailed geometry. The maximum distance thrown, x_p, is recorded in the table for each session. The simulation is derived using Lagrangian Mechanics - a very cool way to work out complicated mechanics problems. A detailed derivation is found HERE. This formulation is unique in that trebuchet recoil is included. This made the derivation somewhat more complicated, so the equations were developed with the aid of SageMath - a symbolic manipulator.

This is a work in process - subject to random updates. Currently using Euler integration, will update to include symplectic and 4th order Runge-Kutta at a later time.

For further stress relief - destroy the castle. Get those guys. Hint: Increase M, decrease ψ_R and θ₀.