Authors: Eduardo E. Salgado
The Principle of Least Action is a fundamental pillar of theoretical physics that unifies diverse phenomena under a variational formulation. This deeply elegant formulation of physics provides an alternative and powerful approach to derive Newton’s Laws. This principle states that the path followed by a physical system between two states is the one that minimizes (or makes stationary) a quantity called action, defined as the time integral of the Lagrangian. In this article, weexplore how the Principle of Least Action connects with Newton’s laws, showing that the latter are a direct consequence of a variational approach. We present an introduction to the action and the Lagrangian, followed by an application of variational calculus to obtain the Euler-Lagrange equations, which translate into Newton’s second laws under specific conditions. This approach demonstrates the elegance and generality of the Lagrangian formalism.
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[v1] 2025-01-07 22:03:12
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