Daily reminder that classical mechanics (Hamiltonian and Lagrangian mechanics) is the most beautiful and useful topic in physics today. All other concepts are built from Hamiltonian and Lagrangian mechanics, and obtaining a intuition around these topics in terms of real systems that you see and touch daily is the most useful endeavor to advance your theoretical understanding of EVERYTHING.

If you can't derive the attached Hamilton's equations of motion in at least 3 different ways then you have no hope of TRULY understanding anything in physics.