That is very definitely classical mechanics, just that it emphasises the Lagrangian and Hamiltonian formulations rather than the Newtonian one (they explain the

That is very definitely classical mechanics, just that it emphasises the Lagrangian and Hamiltonian formulations rather than the Newtonian one (they explain their rationale for this in the beginning). These three formulations of classical mechanics are entirely equivalent though. When you learn mechanics at first you don’t learn the Hamiltonian at all and the Lagrangian isn’t mentioned by name but by formulating some problems in terms of kinetic and potential energy rather than equations of motion and showing that is equivalent. (Eg when I did mechanics we did that for simple harmonic motion). I mean Newton wouldn’t recognize most of what we teach as Calculus because we use Leibnitz’ notation[1] or Lagrange’s notation almost exclusively, and only use Newton’s notation for derivatives with respect to time and don’t ever use Newton’s terminology (fluxions etc). [1] So named because it was mostly invented by Euler.