Questions tagged [variational-calculus]

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• 948
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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: ...
• 131
1 vote
187 views

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. ...
1k views

• 11
411 views

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: ...
• 147
110 views

How do I solve this variational problem?

I have to find the function $\rho(r)$ that extremizes the functional $F$: ...
• 6,114
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[1][y][x]^2], y[x], x] can solve the following Euler ...
1 vote
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 ...
• 6,630
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 ...
592 views

• 309
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 ...
• 113