🏰 Counterweight Trebuchet - 2D Side View: Arm and Sling Dynamics, Release Angle and Energy Transfer

2D companion of the trebuchet launch dynamics sim: a counterweight lever arm with a sling solved as a two-degree-of-freedom Lagrangian system, with release-angle control, a range scan, energy-transfer readout and checks of energy conservation, the mass matrix and the vacuum flight formula. Classical mechanics only.