Hamiltonian and Lagrangian Dynamics (HLD) are two interrelated regimes and sets of techniques that can be used to solve Classical Mechanics problems, like Newtonian Physics does, but HLD is much more powerful and flexible, making manageable the otherwise intractable. In addition, HLD provides intuitive insight and guides approximation techniques. Most importantly, HLD is a foundation for Quantum Mechanics, Quantum Field Theory, Elementary Particle...