Deriving equations of motion using Euler-Lagrange equation and determining efficiency factors of a trebuchet

A Trebuchet is a non-holonomic system which modelled after catapult. Lagrangian mechanics was formulation introduced by Professor Joseph Louis Lagranage predicts the minimum path body follows during its motion of travel. In this paper, I built wooden trebuchet to experiment with shooting range under different counterweight loads. The model customized adding sling swing arm changes dynamics setup as essentially adds scope trebuchet’s increasing rotational energy. paper compares readings based on several settings and uses Euler-Lagrange equation analyze ranges trebuchet. By considering frictional forces, we will derive three equations solely depend degrees freedom determine how efficient for particular counterweight.