Questions tagged [variational-principle]

Any of several principles that find the physical trajectory of a system by minimizing or maximizing some value computed over the proposed path (for instance geometric optics can be reproduced by insisting on a minimum time principle).

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Lagrangian Formulation in Non-Conservative Systems

I am working in a non-conservative system. Would it make a difference if I Formulate the Lagrange Equation with an additional term on the right hand side of the equation to account for the Rayleigh ...
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Deriving electrostatics problems using variational methods

I was thinking, as a new method, we can use the variational method to find σ (charge density) on the surface of a metal if total charge Q in put on it. My idea was that, the total electrostatic energy,...
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How does $\dot{q}_i p_i - H = \dot{Q}_i P_i - K + \frac{d}{dt}F$ will give the same EL and EoM for corresponding coords? [duplicate]

How does $\dot{q}_i p_i - H = \dot{Q}_i P_i - K + \frac{d}{dt}F$ give the same Euler-Lagrange equations and Equations of motion (EoM) for corresponding coordinates and allow us to determine a ...
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Euler-Lagrange equations for fields

I am following the discussion presented on Hobson's book "General Relativity: An Introduction for Physicists" where he deduct the Euler-Lagrange equation for fields and I am stuck in a ...
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Lagrangian of a multi-dimensional scalar field

We know that the Lagrangian has to be a scalar. Would it be possible if this scalar is multi-dimensional (for example $m\times m$)? Let's say a field $\phi$ is represented with an $m\times m$ matrix ...
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Are there any experiments that examine Hamilton's Principle directly?

Or can it be examined? I 'd glad if you can share some ideas about "principles" in general.
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Does quasi-symmetry preserve the solution of the equation of motion?

In some field theory textbooks, such as the CFT Yellow Book (P40), the authors claim that a theory has a certain symmetry, which means that the action of the theory does not change under the symmetry ...
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Independence of the equations resulting from the action principle $\delta (I_{\text{gravity}} + I_{\text{other fields}}) = 0$

In Dirac's "GTR", Chap. $30$, he discusses the "comprehensive action principle" and shows that variation of the combined action of the Hilbert-Einstein action plus all other matter-...
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Relating Brachistochrone problem to Fermat's principle of least time [closed]

When I came across the Brachistochrone problem, my teacher said we could relate it to Fermat's principle of least time. So, we could make many glass slabs of high $\mathrm dx$, and every slab has a ...
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Does Hamilton's principle allow a path to have both a process of time forward evolution and a process of time backward evolution?

This is from Analytical Mechanics by Louis Hand et al. The proof is about Maupertuis' principle. The author seems to say that Hamilton's principle allow a path to have both a process of time forward ...
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What does the optical Hamiltonian mean?

So I was trying to demonstrate Snell's law with Hamilton's equations, and when I got the Hamiltonian: $$H = -\sqrt{n^2-p_{1}^2-p_{2}^2}.$$ I had a question about what this Hamiltonian indicates. I ...
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Derivation of the geodesic equation. Why do we start with the special relativistic action?

I'm working on a derivation of the geodesic equation from the action functional. In special relativity, specifically for flat spacetime, we assume that the metric tensor is constant (not necessarily ...
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