Questions tagged [differential-geometry]
165 questions
4
votes
1 answer
Curvature and torsion of this curve
i was trying to get curvature and torsion of curve in mathematica. of this curve
r[t_]:=…
shamim riten
- 41
- 2
3
votes
2 answers
How can I calculate exponential map for cylinder?
I want to calculate the exp map and log map for cylinder. But as shown figure, I only know the geodesic equation of cylinder is helix. And I search it in some books and website like the google scholar and differential geommetry, etc. But I also…
sy shen
- 31
- 1
3
votes
1 answer
How can I draw a sphere in the Minkowski space?
If the equation of the circle in the Minkowski 3 space is given as
$S_1^2 = \{x \in E_1^3:- x_1^2 + x_2^2 + x_3^2 \}$, how can I replace it in the following code?
f[u_] :=
(eqns = {t'[s] == κ[s] n[s],
n'[s] == -κ[s] t[s] + τ[s] b[s],
…
Heba Serry
- 63
- 4
2
votes
1 answer
Please explain what's going on with this Geodesic Equation of a Sphere
I'm using the Christoffel Symbols found on this link to generate a set of three coupled differential equations as solutions to the Geodesic Equation of a Sphere, I…
Quark Soup
- 1,610
- 9
- 14
1
vote
0 answers
How Can I draw a curve on a sphere in Minkowski 3 space?
There is a curve, which evolves with time, in the the Euclidean space. And the solution of its evolution equations has been used to draw it using this code:
gm[u_] :=
(eqns = {t'[s] == \kappa[s] n[s],
n'[s] == -\kappa[s] t[s] + \tau[s] b[s],
…
Heba Serry
- 63
- 4
1
vote
1 answer
How do I get this to reduce/simplify further?
These equations set up an operation I'm trying to do to calculate the Christoffel Symbol:
X[r_, theta_] := r*Cos[theta];
Y[r_, theta_] := r*Sin[theta];
R[x_, y_] := Sqrt[x^2 + y^2];
Theta[x_, y_] := ArcTan[x, y];
So I now perform the calculation…
Quark Soup
- 1,610
- 9
- 14
1
vote
0 answers
Wedge product of one-forms
I want to check my hand calculations of wedge products of 1-forms such as
yz dx and sin(z) dx
I see that
Wedge
has no built-in meaning. Should I try to define
Wedge
myself?
I want to use symbols to refer to 1-forms, perhaps a list
phi = {y*z, 0,…
Gene Naden
- 327
- 2
- 9
1
vote
1 answer
Extract coefficient list of a differential form
I know may be this could be a duplicate of Extract coefficients of differential form in package RGTC, but the question was not solved and in a sense different from mine. I am going to explain better:
I have a differential form written in a symbolic…
Oscar
- 203
- 1
- 7
0
votes
1 answer
How to solve the einstein field equation symbolically?
How can I use Mathematica to solve the disturbed Einstein field equation? Is there any notebook that introduces this subject or package like diffgeo?
Isabella Nunes
- 75
- 4
0
votes
0 answers
How to calculate the Gauss curvature of any point of function with two variables
I see many methods to calculate the Gaussian curvature of parametric surfaces in SE.But how to calculate the Gaussian curvature of any point of the following explicit function:
f[x_, y_] := x^2 + y^2
A little mouse on the pampas
- 5,760
- 2
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- 40
0
votes
1 answer
How do you typeset a fraction as a variable?
I want to keep track of a large number of variables, and the only way to express them properly is as a fraction. Is there a way to typeset a variable as a fraction? For instance, I would like to do the following:
$$\frac {\partial^2 R}{\partial…
Quark Soup
- 1,610
- 9
- 14
0
votes
1 answer
How do you use DSolve with Vector?
I'm trying to create an ODE for motion in 2 dimensions. What I have so far is:
x0 = {1.5, -4.};
v = {0, 8};
DSolve[{x'[t] == v, x[0] == x0}, x[t], t]
This works with one dimension, but when I try and expand the idea for a vector/matrix, I…
Quark Soup
- 1,610
- 9
- 14
0
votes
1 answer
How do you reduce an equation involving Trig identities in Mathematica?
I'm trying to automatically generate the Christoffel Symbol in Mathematica. I'm starting with the formulas:
X[r_, theta_] := r*Cos[theta];
Y[r_, theta_] := r*Sin[theta];
R[x_, y_] := Sqrt[x^2 + y^2];
Theta[x_, y_] := ArcTan[x, y];
Now, without…
Quark Soup
- 1,610
- 9
- 14
0
votes
1 answer
How can I make a convex catenoid (minimum surface of revolution that closes on -1 and 1?
In Wolfram MathWorld I see the catenoid (minimum surface of revolution which is concave and open ended, but I want the one where the sides are convex and close on the long axis (say z) at -1 and 1.
I want to start with the "rope-hanging" catenary of…
0
votes
0 answers
How get Mathematica to recognize a simple trigonometric identity
I am experimenting with simple differential geometry problem, computing the Frenet apparatus.
beta = {-(4/5) Sin[s], -Cos[s], (3/5) Sin[s]}
{-((4 Sin[s])/5), -Cos[s], (3 Sin[s])/5}
myT = D[beta, s]
{-((4 Cos[s])/5), Sin[s], (3 Cos[s])/5}
kappa =…
Gene Naden
- 327
- 2
- 9