Questions tagged [variational-calculus]
79 questions
8
votes
1 answer
Natural boundary conditions variational methods
I am working on a problem of the calculus of variations. From the Variational Methods package, I can very conveniently use EulerEquations to get stationarity conditions in the form of Euler-Lagrange equations for my problem. Is there also a way to…
Marijnn
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4
votes
2 answers
Use of variational operator, in Mathematica
I am working in Hamilton's principle.
Part of deriving the equation of motion is to use the delta operator () which can be operated just like a differential operator.
It is not the function VariationalD in package VariationalMethods.
A post was…
ayman zayed
- 71
- 2
3
votes
1 answer
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 explained how to perform the transform on a function…
LastStarDust
- 87
- 5
2
votes
3 answers
Use of variational operator, in Wolfram Mathematica (Version 11.0)
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 can I find the variation of any parameter using the…
Kamran Ali Ahmed
- 27
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1
vote
1 answer
How to use the variational method to solve this problem
I see this mechanical problem here.
I want to solve this problem with the variational method. The Lagrangian of this system is obtained by subtracting potential energy from kinetic energy.
m = 1;
g = 9.8;
R = 1;
EulerEquations[
m*g*R (1 -…
A little mouse on the pampas
- 5,760
- 2
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1
vote
2 answers
How to find the variational result of this functional according to the definition of textbook
I see this variational problem here.
The functional is :
$$J(y)=y^{2}(x_{0})+\int_{x_{0}}^{x_{1}}(xy+y'^{2}) dx$$
In the textbook, the result of finding the functional variation according to the functional variation defined by Lagrange is :
The…
A little mouse on the pampas
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1
vote
1 answer
How to find the variation of this functional according to the definition of Lagrange
The functional is :
$$J(y)=y^{2}(x_{0})+\int_{x_{0}}^{x_{1}}(xy+y'^{2}) dx$$
In the textbook, the result of finding the functional variation according to the functional variation defined by Lagrange is :
The variation sign δ has the following basic…
user69323
1
vote
0 answers
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:
Needs["VariationalMethods`"]
r = {x, y,…
user40473
- 11
- 1
0
votes
1 answer
How do I solve this variational problem?
I have to find the function $\rho(r)$ that extremizes the functional $F$:
A = (Log[2] - 1)/(2 Pi^2);
b = 20.4562557;
rs[r_] := (3/(4 Pi \[Rho][r]))^(1/3);
F = 2.84 \[Rho][r]^(5/3) + (-(3/4) (3/Pi)^(1/3) \[Rho][r]^(1/3) + A*Log[b/rs[r] + b/rs[r]^2 +…
mattiav27
- 6,677
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0
votes
1 answer
How to find Euler equation of complex function by the textbook definition
In the help document, we know that EulerEquations[y[x] Sqrt[1 + Derivative[1][y][x]^2], y[x], x] can solve the following Euler equation of equation :$$∫_{x_{\min}}^{x_{\max}}y(x)\sqrt{1+y'(x)^{2}} dx$$
But how can we solve the Euler equation in the…
A little mouse on the pampas
- 5,760
- 2
- 13
- 40