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

Abstract

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