Analytical Mechanics

Analytical Mechanics is where you stop pushing F=ma around and start thinking about motion as a consequence of deeper principles — least action, symmetry, and conservation — that recast Newtonian problems in the language of generalized coordinates. You'll work through Thornton & Marion, grinding out problem sets and quizzes on Lagrangians, central forces, rotating frames, rigid bodies, and Hamilton's equations, building the formal machinery you actually use later. It's the bridge between freshman mechanics and everything theoretical that follows: quantum mechanics, statistical mechanics, and field theory all assume you're fluent in this formalism.