# Questions tagged [variational-calculus]

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2answers
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### Minimization problem in proving Fermat's principle

I am trying to prove the Fermat's Principle of least distance, the problem statement goes: ...
2answers
274 views

### 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 ...
1answer
96 views

### 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 ...
2answers
56 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: ...
1answer
198 views

0answers
37 views

0answers
130 views

### Variational derivative of a functional depending on multiple functions

I wanted to use the VariationalD command to calculate a list of variational derivatives. A simple example is the following and it works perfectly fine. ...
1answer
326 views

### How to do variation of an integration of a function with consideration of limits?

I have a function dependent on w(x,t) which is integrated in an interval. After integration of this function, I want to apply variation followed by integral by parts. Integral by parts results in to ...
0answers
124 views

### Could I take a variation of a functional in Mathematica? [closed]

In finite element, the weak form can be derived by taking the variation of a energy functional as: \begin{align} L(u(x,y)) &= -\dfrac{1}{2}\int_{\Omega}(\dfrac{\partial{u}}{\partial{x}}\dfrac{...
1answer
476 views

### Drawing geodesic lines on the membrane (Plot3D)

The most common method of creating patterns on a membrane involves drawing geodesic lines on the membrane. Justification of the layout of the geodesic lines is beyond the scope of this text . ...
0answers
129 views

### VariationalD with respect to two-variable function of integral over one variable

I have a function $q(x,t)=u(x,t)+iv(x,t),$ some functions $p_n$ and I want to find the following functional derivative: $$\frac{\delta}{\delta\overline{q}}\int p_ndt$$ Because Mathematica's ...
1answer
518 views

### Legendre Transform of a function of a 3-vector

I am trying to implement the Legendre transform of a function in Mathematica with the purpose of calculating the Hamiltonian of a system starting from the Lagrangian. I have found this page which ...
1answer
425 views

### How to formulate the Hamiltonian equations of motion? Part II

I've recently asked a question on an issue I was facing with numerically integrating Hamiltonian equations of motion. I got a great answer. Following on from this, I wanted to write a very similar ...
1answer
246 views

### Numerically Integrating a Hamiltonian but getting different results when compared with alternative equivalent equations

currently trying to perform an integration of the Hamiltonian for a Schwarzschild black hole. However, I'm coming up short. The code is as follows: ...
1answer
416 views

### how to find a function that minimizes the other function with a known function

The problem that i am facing is that of energy minimization. I have a function called totalenergy which is sum of two functions the elastic energy and the surface ...
0answers
1k views

### how to find stationary point of a multivariable function [closed]

I am quite new, how can I find minumum, maximum or saddle point the following multivariable function by using mathematica $f(x,y)= 2x^3 +6xy^2 −3y^3 −150x$
0answers
133 views

### Book Recommendations About Using Mathematica in Topics like Calculus of Variation and Optimization?

I want to use effectively Mathematica about topics like Calculus of variation and Optimization. Do you know books about it? or what do you suggest me?
0answers
211 views

### How to find the extremals of the functional?

How to find the extremals of the functional by Wolfram Mathematica? $$J(y(x))=\int_{0}^{1}\big(y(x)^3+y'(x)\big)dx$$
0answers
120 views

### Get the parametric equations of the Cycloid

How to get the parametric equations of the cycloid from the following differential equation? ...
0answers
179 views

### 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 ...
0answers
72 views

### 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 ...