Linked Questions
13 questions linked to/from The time-like geodesics (orbits) in the Schwarzschild spacetime
53
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6
answers
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How to calculate scalar curvature, Ricci tensor and Christoffel symbols in Mathematica?
I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. Sometimes,...
- 665
2
votes
3
answers
446
views
Optimization of ODE with respect to the initial condition
One has a (system) of ODEs with a one-parameter family of initial conditions. For example,
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- 207
6
votes
4
answers
405
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A fraught with incorrect results ODE
I mean the following ODE
$$y''(x)+y'(x)=\exp (-2 x) y(x)^3.$$
Trying to solve it in version 13.1 on Windows 10 by
...
- 24.1k
0
votes
3
answers
515
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Solving elliptic integrals in Mathematica
I have an integral
$$\int_{a2}^{a1}\frac{dx}{\sqrt{(a1 -x)(a2 - x)(a3 - x)}}$$
And I'm trying to integrate it with
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- 157
4
votes
3
answers
304
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Transforming implicit solutions of an ODE involving InverseFunction to an explicit form
When I DSolve a nonlinear differential equation:
...
- 209
1
vote
2
answers
1k
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How do I get the Schwarzschild solution from the Einstein Equations?
Consider the Schwartzchild-like metric $$ds^2=-A(r)dt^2+B(r)dr^2+r^2(d\theta^2+\sin^2\theta d\phi^2).$$ The Einstein field equations for this metric reduce to $$R_{\mu\nu}=0,$$ which is also known as ...
- 119
1
vote
2
answers
304
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Integrating and plotting solutions of a nonlinear dynamical system
So I have an ODE
$k^2\; u'(\theta)^2 = -\frac{1}{3}u^3 + \frac{\omega}{k}u^2-2B\;u+2A$
where $B,A$ are constants.
I attempted to directly integrate in Mathematica with
...
- 157
1
vote
1
answer
449
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Confluent Heun function
Does the confluent Heun function exist in Mathematica?
I try to evaluate the following,
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- 763
2
votes
3
answers
209
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First order Differential equation with boundary condition
I'm wondering why it is not solving with the Mathematica??
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- 447
0
votes
1
answer
173
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Get the trajectory of an object in a gravitational field
Given the initial position and velocity, I want get the trajectory of an object in a gravitational field. Instead of using Kepler's Laws, I want to solve the following differential equations:
...
- 143
1
vote
3
answers
249
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Solving Geodesics from Christoffel Symbols
I am somewhat new to using Mathematica and I am facing difficulties with a specific problem related to the geodesics of Einstein's field equation in a vacuum.
The metric I am working with is derived ...
- 11
2
votes
1
answer
206
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Nonlinear first order equation with DSolve
I am trying to solve a geodesic equation on Mathematica and would like to get a precise result, using DSolve would be a good start for me.
My problem is the following: I have a squared expression for ...
user72371
1
vote
0
answers
99
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Construction of numerical solution of differential equations geodesic on the sphere
I have differential equations of geodesics. I need to solve them numerically and the solution must be on a sphere.This is what the equations looks like
The geodetic on the sphere should look like ...
- 19