Introduction

So far, we have studied mechanics using Newton’s laws, which focus on forces acting on objects. While this approach is powerful, it becomes complicated when dealing with:

• Systems with many particles
• Constraints (e.g., motion on a surface)
• Complex coordinate systems

An alternative and more elegant formulation is Lagrangian mechanics, which is based on energy rather than force.

This approach is widely used in advanced physics, including quantum mechanics and field theory.