# Questions tagged [variational-calculus]

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### performance of the NDEigensystem and DEigensystem

I can't find any result and I can't understand what is going wrong. Any help please? My code is: ...
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### Varying Einstein-Hilbert action through xAct gives extra terms

I am trying to find the associated field equation by varying this action: $$S=\int d^4x \sqrt{-g}(\kappa \mathcal{R}+\Lambda)$$ This should give me the below field equation when I vary above w.r.t the ...
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### Speeding up minimization problem related to a minimal surface

I am trying to find the minimum of the function $$f(x)=\int_0^1(1+t^x)\sqrt{1+x^2 t^{2(x-1)}}dt$$ which arises from trying to minimize the surface area of a function rotated around the $x$ axis. Here ...
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### Expression for an integral

I am facing a problem obtaining an expression for my integral. My code goes in a time-consuming loop whenever I execute this integral. The code is: ...
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### Variation of Lagrangian with respect to components of inverse of metric tensor

I am super new to Mathematica, so I apologize if the question is trivial. I have defined metric tensor (4x4 matrix), inverse metric and Lagrangian: ...
1 vote
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### Geodesics on arbitrary 2D surfaces

Geodesics on 2D Function Surfaces I am trying to approximately find the shortets path between two point on a surface defined as z=F[x,y]. I am solving for X,Y as function t. However, when trying to ...
41 views

### Solving constraint optimization problem for different intervals using VariationalD

I have been trying to solve for a constraint optimization problem (which eventually yields to a Laplace distribution). Consider the following equation (1) \begin{equation*} J=\int^{\infty}_{-\infty} p(...
1 vote
84 views

### Using VariationalD, getting derivative of Implicit Functions, derivative independent variables [closed]

Hey I am trying to solve this problem with wolfram: I figured using VariationalD was the way. However I can not figure out how this package works. It would be nice if someone could help me. I ...
134 views

### Minimization problem in proving Fermat's principle

I am trying to prove the Fermat's Principle of least distance, the problem statement goes: ...
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1 vote
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### Plot of the derivative of a function

I have a function functionSL as a function of t (t<0) where I want to find the extremum ...
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### Use of variational operator, 𝛿 in Mathematica

I am working in Hamilton's principle. Part of deriving the equation of motion is to use the delta operator (𝛿) which can be operated just like a differential operator. It is not the function ...
105 views

### Do not evaluate function composition in total derivative

How to achieve that Dt[] does not touch certain function compositions, but still applies all the other derivative transformations. Example: ...
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1 vote