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In this article, I explain to Fidello from Foci's Discord server some prerequisite knowledge he needs to effectively derive the equations of motion for a double rigid pendulum and then cover Hamiltonian mechanics and Noether's theorem. In theory, the derivation of the equations of motion for a double rigid pendulum can be done with Newtonian mechanics with $\textbf{F}=m\mathbf{a}$, but given our second pendulum is in a moving reference frame and Newtonian mechanics does not easily adapt to alternative coordinate systems, like polar coordinates, Lagrangian mechanics makes the equations of motion easier to derive. Lagrangian mechanics also leads nicely into Hamiltonian mechanics and the path integral formulation of quantum mechanics. Figure shows a frame from the double pendulum animation this page does by default.