The Lagrangian formulation of classical mechanics is more than just a formal device for obtaining Newton's second law. The power of this formulation is that it provides an immediate method for deriving the equations of motion in any set of coordinates, not just the Cartesian coordinates we have considered thus far. Moreover, it provides a formal structure for deriving the Euler-Lagrange equations through the so called action principle to be discussed in the next lecture.
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Mark Tuckerman