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The aim of this paper is twofold: First, we give a formal introduction to thebasics of the mathematical framework of classical mechanics. Along the way, weprove a Hamiltonian and a Lagrangian version of Noether's Theorem, an importantresult concerning continuous symmetries of physical systems. At the end, weprove a new statement about orbit cylinders on homotopies of stable regularenergy hypersurfaces. The main question we answer is what is the dynamicalmeaning of stability? The second aim is to provide a didactical framework forintroducing advanced mathematics, which can also be of used in other topics. Abroad range of established methods belonging to the realm of cognitiveactivation as well as formative assessment techniques are used.

Lectures on Classical Mechanics -- A Didactical Approach to Higher Mathematics