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

I recently started reading about Lagrangian Mechanics. I observed that it uses some basic expressions that are derived by taking Newton's laws of motion as fundamental such as kinetic energy, ...

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. ...

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 ...

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 ...

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 ...

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 ...

All the fundamental laws of physics can be written in terms of an action principle. This includes electromagnetism, general relativity, the standard model of particle physics, and attempts to go ...

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}...

For example, hen working with general relativity, one sees that Einstein equations can be derived from an action principle via the Einstein-Hilbert action. This occurs too in classical mechanics, ...

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 ...