# Questions tagged [variational-calculus]

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### How do I find the equations of motions for a relativistic particle?

I have it working for the Lagrangian of a classical particle in a gravitational potential: ...
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### 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. ...
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### Find geodesics given two points

Suppose I want to find the geodesic on a paraboloid going through two points located on the paraboloid, using Mathematica 12. I chose the paraboloid parametrization as follows: ...
110 views

### How do I solve this variational problem?

I have to find the function $\rho(r)$ that extremizes the functional $F$: ...
1 vote
175 views

### 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 ...
1 vote
119 views

### 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 ... 108 views

### 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[y][x]^2], y[x], x] can solve the following Euler ...
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207 views

### How to solve the differential equation of a Brachistochrone Problem

This is a differential equation to solve the most brachistochrone line, but it can't find the exact analytical solution : ...
210 views

### How to interpolate {{xi,yi},... ,{xn,yn}} with minimum bending energy?

Thin Plate Splines are explained here, and a Mathematica implementation of that for real samples { { x1, y2, z1 }, { x2, y2, z2 }, ... , { xn, yn, zn } } is ...
144 views

### 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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921 views

### 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 ...
1 vote
493 views

### 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 ...