# Questions tagged [variational-calculus]

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### Using VariationalD on previously defined functions [closed]

Do you know whether there is a way to get around the following problem? Say we define a very simple function: f[t] = 2 y[t] and want to use the ...
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### NDSolve with Functions Depending on time and time dependent Functions

EDIT: following the advice of using Raw Input Form, the equations have the following form ...
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### Use of variational operator, 𝛿 in Wolfram Mathematica (Version 11.0) [closed]

I have been working on a problem which requires the use of Energy Methods which is based on the variational principles. I am finding it hard to replicate my formulated equations in Mathematica. How ...
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### Does Mathematica understand the concept of infinitesimal increment?

Commonly, in textbooks, differential of differential increment vanishes, good example is how Euler-Lagrange equations are derived using the differential (from step 2 to step 3 here, you can see ...
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### Get the parametric equations of the Cycloid

How to get the parametric equations of the cycloid from the following differential equation? ...
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### Symbolic second variation (quadratic form matrix)

Mathematica has a calculus of variations package that can compute the first variational derivative symbolically, rather nicely. Does anyone know if there is a way to compute the quadratic form matrix ...
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### VariationalBound with and interpolated trial function

I am trying to solve a Sturm-Liouville problem using the VariationalBound function of Mathematica, as recomended in the wolfram mathworld site. The example given in the Mathematica documentation is ...
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### NVariationalBound

I am trying to use the NVariationalBound to find the eigenvalues and eigenfunctions. NVariationalBound documentation example ...
285 views

### Help to solve the brachystochrone problem using Euler equations?

I'm trying to find the soltution of the brachystochrone problem. I'm was wondering if there is a way to solve it directly using Mathematica. The problem is the following: I have to find the equation ...
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### Variating the derivative of the metric using xTensor

I would like Mathematica to be able to use the following expression in a more complicated computation: \begin{equation} \tag{1}\frac{\delta{}g^{\alpha\beta}_{\;{},\gamma}\left(x\right)}{\delta{}g^{\mu\...
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### Compute second functional derivative with VariationalD?

I have problems to compute the second functional derivative of a general function. The following lines generate the first derivative: ...
1k views

### Lagrangian to Hamiltonian

I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like: ...
230 views

### NIntegrate (Helium Singlet and Triplet) [closed]

I have two integrals that I am calculating using nested NIntegrate. One is for the singlet helium atom and another for triplet. (here, I am calculating variationally the approximate energies and ...
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### Geodesics on a torus

Is it possible to draw geodesics between the points in a path on a torus - toroidal surface? geodesics: generalization of the notion of a "straight line" to "curved spaces" ...
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### Optimizing a functional using variational calculus

Here I am, trying to get the trajectory $(x(t),y(t))$ that will minimize the following Lagrangian (i.e. the integrand of the functional) between $(-1,-1)$ and $(-1,y_{eff})$ where $x_{eff}$ is defined ...
I need help with minimizing a functional in Mathematica. I have a function $V(\xi)=\sum_{i=1}^\infty C_{3_i}J_0(\xi/C_i)+C_{4_i}Y_0(\xi/C_i),~~~\Sigma\leq\xi\leq\xi_1$, and want to find such \$\{C_{...