[lokedhs]

In Susskinds book The Theoretical Minimum, he explains this and suggests that the word stationarising would be more accurate, as the goal is to make the lagrangian stationary and not minimal.

I haven't read any other textbooks on the topic so I don't know how common this is. I do suspect you're right though, as he made a point of explaining this

[psychphysic]

I believe he also goes over the legendre transform which lets you move between Hamiltonian and Lagrangian mechanics.

Just occured to me that the above poster may believe that QM is Hamiltonian only and classical is Lagrangian only. That'd be a forgivable but fatal mistake to understanding the subject!

Hamilton Jacobi equation may also help them remember QM is distinctly less intrusive than classical mechanics.