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Recently I am studying lagrangian mechanics where I came across the topic "principle of least action" which states that a system always takes the path of least action or when the action is minimum but I cannot understand why it should be true so can anyone give me the mathematical proof behind it and what is the original Idea behind it and again I want to understand what action actually is? In lagrangian mechanics it is defined as the total path integration of difference between Kinetic energy and potential energy, but what does it actually defining?

Qmechanic
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Ganesh Khadanga
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1 Answers1

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This question is something I didn't completely understand when I was doing Classical Mechanics, but it's mostly up to how it's taught. We begin with $\delta S=0$, then construct the Lagrangian s.t. it reproduces Newton's Second Law $\textbf{F}=m\textbf{a}$ (or more accurately $\textbf{F}=-\nabla U$ where $U$ is the potential energy. The variational principle is used as a tool to produce a new way to reproduce Newton's Second Law, which governs all of Classical Mechanics.

Redcrazyguy
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