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Newtonian Mechanics is the basis of all classical physics... but is there a mathematical formulation that is better? In many cases, yes indeed there is! Lagrangian mechanics, named after Joseph Louis Lagrange, is a formulation of classical physics that is often more convenient to use than Newtonian Mechanics. The first concept worth knowing about is that a quantity called the “Lagrangian“ is defined as L = T - V where T is the kinetic energy of the system we happen to be studying, and V is the potential energy. In this video, we see how to find the Lagrangian for a simple mass-spring system by considering the mass of the block, spring constant of the spring, and motion of the entire setup. We see how to write the kinetic energy (or more specifically the speed of the setup) in terms of the distance moved by the system. Once we have found the Lagrangian for the system, we then see that the “big boi“ equation of Lagrangian mechanics is the Euler-Lagrange Equation. This is a complicated (looking) equation that
