Has anyone developed an approach to teaching mechanics based on Lagrangian/Hamiltonian mechanics from the ground up. I mean from high school on up. This is akin to explicitly not talking about components of vectors or developing pre-calculus in a coordinate-free (coordinate agnostic).
Perhaps I'm missing the point of Lagrangian/Hamiltonian formalism, but I am to emphasise the coordinate free approach rather than the specifics of deriving the equations. For example, the pendulum can be described as a system with 2 spatial coordinates(x,y) or one angle coordinate(theta). The latter is better.
Or does the Lagrangian/Hamiltonian approach require more advanced maths than a high school student is capable of.