# Tag Info

Accepted

### Minimum energy path of a potential energy surface

Smooth Equations Let $\varphi \colon \mathbb{R}^d \to \mathbb{R}$ denote a potential function (e.g., from OP's data file). We attempt to solve the system  \left\{ \begin{aligned} \gamma(0) &...
Accepted

### Lagrangian to Hamiltonian

Here is how you would do it using the standard add-on package VariationalMethods, which is meant for calculations like this: ...
• 97.5k

### Minimum energy path of a potential energy surface

Interesting problem. Decided to treat it as a graph problem, rather than fitting an InterpolatingFunction to it and getting descent directions from there. If I knew ...
• 7,173

### Computing a functional derivative using the VariationalMethods package

You could use FunctionalD from my answer to Non-trivial functional derivatives, which I repeat here: ...
• 131k

### Lagrangian to Hamiltonian

genCoords = {x[t]}; ke = 1/2 m x'[t]^2; v = 1/2 k x[t]^2; q = -c x'[t]; l = ke - v; Solve for x'[t] in terms of ...
• 23.9k

### Minimum energy path of a potential energy surface

If I understand the problem correctly, we just need to extract the path from StreamPlot, don't we? If you have difficulty in accessing the data in dropbox in the ...
• 67k
Accepted

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

Plot the surface. surface = Plot3D[x + y - x y, {x, -5, 5}, {y, -5, 5}, AxesLabel -> {"x", "y", "z"}] The aim is to draw geodesics - i.e. minimum distance ...
• 5,044

### Methods of Numerically Finding Function Minimizing Functional

I'd typically go for "discretize and optimize". Here is a quick and dirty implementation of this strategy that avoids all symbolic computation and that utilizes Sobolev gradient descent with ...

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

You are trying to minimize time, $T$, among all possible paths of a point moving from height $y$ to direction, $x$ from $x_1 = a$ to $x_2=b$. We know that by definition $dx/dt = v$, were $v$ - ...
• 4,885
Accepted

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

Direct answer: The function you were trying to transform in the question is not a scalar and can therefore not be used as an example. Here is a version of ...
• 97.5k
Accepted

### Euler-Lagrange equation with a damping term

Yes, it is possible. First of all I recommend you to read these two papers: J. Guerrero, F. F. López-Ruiz, V. Aldaya, and F. Cossio A round trip from Caldirola to Bateman systems, J. Phys.: Conf. Ser....
• 19.1k

### Geodesics on arbitrary 2D surfaces

The problem above calls for determining the geodesic curve between points {2,1} and {5,2} on a paraboloid. This can be done as ...
• 61.7k
Accepted

### Increasing the time constraint on EulerEquations

Sometimes a function has a Method option that can be used to modify the options used by an internal function. This is not true for ...
• 131k
Accepted

Try this: ...
• 39.6k
Accepted

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

First, I think p=... has a typo, and should read p = FullSimplify[Table[D[L, vel[[i]]], {i, 1, n}]] One way to use Hamilton's ...
• 3,483

### Black hole orbit in Mathematica

I wonder if the problem lies in the numerical solution of the differential equation. With all due respect, I question the differential equation itself you obtained. Because this might tell a different ...
• 9,823

### Black hole orbit in Mathematica

If you change the intial condition to w'[0]=.01 you get a variing solution ...
• 54.5k

### Use of variational operator, 𝛿 in Wolfram Mathematica (Version 11.0)

Maybe you are looking for D[u[x] + x^2 u[x] - 2 u[x] u'[x] + 2 x*Sin[u[x]], {{u[x], u'[x]}, 1}] $\left\{-2 u'(x)+2 x \cos (u(x))+x^2+1,-2 u(x)\right\}$ or for ...

### Use of variational operator, 𝛿 in Wolfram Mathematica (Version 11.0)

You can use the the function VariationalD in package VariationalMethods: ...
• 398k
Accepted

### How to use the variational method to solve this problem

This is the problem I solved sometime ago. Same problem as you show. The angle $\theta$ used is measured from x-axis, positive anti-clockwise, as it was simpler to do so, but it does not affect the ...
• 146k

### Roots, multivariable functions and Mathematica

Perhaps you mean real roots?: ...
• 238k
Accepted

### Speeding up minimization problem related to a minimal surface

Calculating the integral without any assumptions we obtain a ConditionalExpression which may not work quite seamlessly with ...
• 57.5k
Accepted

### Does Mathematica understand the concept of infinitesimal increment?

I don't really approve of your intention but anyway. You can use ...
Accepted

### How to take derivative of a expression with respect to a function?

It is straightforward. Let us take a Lagrangian L = 1/2 D[y[x, t], t]^2 - 1/(2 c^2) D[y[x, t], x]^2 + 1/2 y[x, t]^2; We need to load the package: ...
• 39.6k
Accepted

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

Here's my guess at how it should be done. There were a couple of changes. You need separate q and p variables in order to ...
• 238k
Accepted

### Natural boundary conditions variational methods

As far as I know there is no function currently in the Variational Methods package that does that. This function however should do the trick: ...
Accepted

### How to find the variation of this functional according to the definition of Lagrange

You should notice that $y$ is a function, and $J$ is a function with function as argument, then things become clearly ...
• 1,943

### Finding a possible Lagrangian corresponding to a differential equation

There doesn't seem to be an easily identifiable function for this: ...
• 23.8k
Accepted

### Do not evaluate function composition in total derivative

You can change a system option so that derivatives of Conjugate are not performed: ...
• 131k