# Lagrangian/Hamiltonian mechanics at high school?

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.

• Perhaps I'm missing the point of Lagrangian/Hamiltonian formalism, but what I was looking for more was to emphasise the coordinate free approach rather than the specifics of deriving the equations. – pdmclean Apr 19 '15 at 21:29

The most fundamental parts of Lagrangian mechanics involve calculus. The action principle involves an integral and the Euler-Lagrange equation is a partial differential equation. Unless the students are pretty good with calculus it will be quite hard to teach.

If all you are looking for is a basic introduction without the calculus of variations, then the following article (which, however, assumes knowledge of elementary calculus as a prerequisite) may be of help:

Hanc, Jozef, Edwin F. Taylor, and Slavomir Tuleja. "Deriving Lagrange’s equations using elementary calculus." American Journal of Physics 72.4 (2004): 510-513.

There is an online version available here.

Source: I've seen this method successfully used in a first year undergraduate course on classical mechanics.

Maybe you can give a rough idea about what the subject is about. You can introduce first for example the Fermat's principle of least time and maybe kind of make an analogy like.

"There is a similar principle of minimization in mechanics where you minimize another quantity called action".

Maybe if an student is interested you can give him more information. There is a Feynman lecture when he said that a High school teacher told him a little bit about the principle here is the link :

http://www.feynmanlectures.caltech.edu/II_19.html