I like constraint based physics, and phase-space/Lagrangian/Hamiltonian methods are very useful both for solving difficult mechanical problems, as well as, seeing connections with QM, optics, etc. However, for most freshmen, the math is simply beyond them in their first year. Unless you can delay until multivariate, partial differentitals, and at least ODE... it won't stick. On casual examination SICM looks more like a substitute for Goldstien's Classical Mechanics, but perhaps it is better. Nominally, I'd recommend that in the late 2nd or 3rd undergraduate year.

One thing that I'm quite happy with in my physics education is that the faculty went to quite some effort to make sure that the math and physics tracked each other so that you would see the theory and practice twice and intertwined.

One thing that was missing (as other's have mentioned) was numerical methods and programming techniques, which I think could also be covered in a parallel track.

> However, for most freshmen, the math is simply beyond them in their first year.

You can introduce Lagrangian and Hamiltonian mechanics very early on if you're okay with hand-waving over some of the analytical details and presenting it mostly as a problem solving tool. E.g. David Morin's Introduction to Classical Mechanics does a great job with minimal formal prerequisites (freshman calculus is adequate for the majority of the book) though its exercises and problems, which are the book's highlight, will be too challenging for most freshmen.

I think a low-brow problem solving centric approach is ideal as an introduction to Lagrangian mechanics in particular (not so much Hamiltonian mechanics) since the advantages are so stark and obvious compared to the Newtonian formalism. You don't have to worry about how velocities and forces transform to write down the equations of motion. You just write down the Lagrangian and take derivatives. That's something every student will immediately appreciate.

A bit of a side note, but you caught my eye with the phase-space/Lagrangian/Hamiltonian methods. I always loved those methods (including Fourier Transforms).. but that seems to make me an oddity for having both struggled to pass Calculus 2 (as in with a B) while aceing the Classical Mechanics math for Hamiltonian and Lagrange methods and all those phase space problem domains. Makes me suspect that people tend to comprehend certain subsets of math better than others. Still those mathematical methods are going to beyond most first year undergrads.

A thread in the physics education I received was "we used to have (old model), but then that experiment caused us to think (new model)" ad infinitum. Maybe there's just a problem with my own brain, but I experience significant interference between the old models and newer models. In particular, mass is super confusing to me in a way that, say, electric charge is not.