Linked Questions

Is there a anything like a proof of Hamilton's principle? Where would I find it?

Let $\mathscr L (\phi(\mathbf x), \partial \phi(\mathbf x))$ denote the Lagrangian density of field $\phi(\mathbf x)$. Then then actual value of the field $\phi(\mathbf x)$ can be computed from the ...

I remember asking my second year Mechanics teacher about why do the Lagrangians give the equations of motion. His answer was that there is no answer to that, it is an empirical fact, and that asking ...

I want to understand the principal of least action intuitively, away from any mathematical proof.

This is more of a request for clarification of understanding and intuition rather than a question, but I hope people can help me with it. I have learned calculus of variations and have subsequently ...

I have read about the principle of least action. This principle suggests that nature would allow a particle to travel in a path along which the integral of the difference between kinetic energy and ...

I've been trying to wrap my head around Lagrangian mechanics and Lagrangians in general, and I've found it difficult. After some thinking, I believe that the issue I have is with action principles. ...

My question is not rigidly related to physics. The principle of least actions says that for any dynamical system there exists a function parameterized by $q$'s and $\dot{q}$'s such that the line ...

In all discussions regarding the Lagrangian formulation it has always been said that $L = T - V $, only is a correct guess that when operated via through the Euler -Lagrange equation yields something ...

Whilst studying Field Theory and after checking numerous sources it appears that people always just state the action without providing some sort of motivation/intuition as to why we should/can use the ...

We have recently covered the Lagrangian in our lectures, whereby it was shown that all equations of motion ($x(t)$) satisfying the Euler-Lagrange equation with Lagrangian $L=T-V$, where $T=\frac{1}{2}...

We define the action of a system as $$S(q)=\int_{t_1}^{t_2}L(t,q(t),q'(t))dt,$$ where $q(t)$ is the evolution of the system and $L$ is the Lagrangien. How can a stationary point of $S$ can describe ...

Why the principle of least action is true? I mean it is equivalent with Newton's laws(Lagrangian and Newtonian equations are equivalent) but is that the way it was formulated? I read somewhere the ...

I had learned the principle of least action.But I didn't get the motive behind taking the least action. Or why should the particle follow a path where it have a least action?

What is Lagrangian mechanics, and what's the difference compared to Newtonian mechanics? I'm a mathematician/computer scientist, not a physicist, so I'm kind of looking for something like the ...