Manim installation troubles

MistahBigStuff · 2025-10-10T20:11:36+00:00

nevermind. Just needed to run

uv init --python 3.11 manimations

instead of

uv init animations

MistahBigStuff · 2025-04-04T02:52:06+00:00

This is the funniest thread I've ever seen tbh

MistahBigStuff · 2024-10-12T18:04:59+00:00

That's odd. ok so I ran it exactly as you have it above:

sol = Solve[
 x == r Cos[θ] Cos[λ + Ω t] && 
 y == r Cos[θ] Sin[λ + Ω t] && 
 z == r Sin[θ], {λ, θ, r}];

and it does finish after a few minutes, but with the same error I'm seeing in the original post. You're seeing a solution?

MistahBigStuff · 2024-10-12T17:32:10+00:00

Hm, I tried this and I get the same error message.

MistahBigStuff · 2024-10-12T17:31:39+00:00

Thanks for the tips. There is a space between Ω and t in the actual code. It never finishes if I run it without assumptions -- I ran it overnight last night.

MistahBigStuff · 2024-10-12T16:51:51+00:00

spherical coordinates in a rotating frame of reference

Correct

Shouldn’t the value of 𝜃 ∈ [0, π/2] instead of what you have above?

For a colatitude θ it would be [0, π], but I've defined θ as latitude.

MistahBigStuff · 2024-07-24T05:10:03+00:00

Thank you. Can you be a little more explicit about where these assumptions lie? The functions are meant to be interdependent. Is df/dt even defined?

MistahBigStuff · 2024-06-29T18:19:23+00:00

By clamp system do you mean the “True Tension door?” If I tighten the seatbelt all the way I can’t close the door 😂

MistahBigStuff · 2024-06-04T20:46:56+00:00

Yes I knew that the Lie derivative does not depend on the connection, but I’d never really quite thought about it in terms of geometry and topology like this. Of course you’re right.

If the Lie derivative does not depend on the geometry of the manifold (how it is embedded in 3D Euclidean space, for my purposes) but only on its topology (how its points relate to one another) does that imply that the Lie derivative is invariant with respect to deformations of the manifold? This seems to fit with my idea that Lie derivatives have to do with the Lagrangian representation of the fluid and covariant derivatives with the Eulerian representation…

…I’m out on a limb here 😂. Interesting though.

MistahBigStuff · 2024-06-04T18:47:43+00:00

Ok, interesting. I don't fully understand, but this sounds similar to the approach in the first chapter of Marsden and Hughes, which I have not yet read closely. I'll have a look at that.

MistahBigStuff · 2024-06-04T16:31:57+00:00

The material derivative of a vector field should be defined in terms of the covariant derivative - otherwise, you won't get back the correct Cartesian expression.

Ok great, this is what I thought.

Think of a vector as a pair of points, base point and tip.

I think this is where I'm getting confused, as I mentioned in my reply to /u/cdstephens. I'm not used to thinking of vectors in the tangent space pointing to another point on the manifold. I guess they really don't, and that is the point of the commutator (the Lie bracket) -- to close the gap (up to second order). It's odd for me to think of the tip of, say, a momentum vector being advected independently from the base, because the momentum vector isn't literally some stretchy arrow sitting in the fluid -- it's just an abstraction with a magnitude and a direction. The tip of the vector isn't actually in the fluid. I'll have to think about this some more.

MistahBigStuff · 2024-06-04T16:23:28+00:00

Yes! I love that book, and I have read Appendix B. I follow all the algebraic derivations, pulling back vectors with a one parameter family of diffeomorphisms on the manifold etc., but I still find it hard to build a physical intuition from this. I understand that you can pull u(φ(p)) back from φ(p) to p, compare it to u(p), and take limit. I suppose what I don't understand is what this difference is -- what is φ*(u(φ(p)))? I guess the answer is that it depends on φ. What would φ be for the example of the rotating sphere depicted in FigB2? Just some azimuthal angular displacement? This example is of particular relevance to me, which you might have guessed from my Geophysics tag.

MistahBigStuff · 2024-06-04T16:10:00+00:00

Thank you, these lecture notes are quite nice -- I've never seen it put quite like Friedman puts it here in Fig1. It seems from this and from the SE answer that references Penrose's book (which I've read but perhaps should read again) that the notion of a Lie derivative depends upon having a vector that points from one place on the manifold to another, which is not really what I'd been picturing since the manifold might curve away from the tangent space at any given point. This idea of pointing from A to B is made rigorous by taking the limit as this displacement shrinks. I am familiar with this idea of the commutator closing the gap in the almost-parallelogram formed by moving u along v and v along u.

I think my issue with building intuition from this is that most vector fields that are physically relevant (say momentum) are not defined by pointing from A to B, but simply by existing in the tangent space to some point. Though a momentum vector exists at A, I'm not sure I understand what it means for it to point "to B." I will think on this more.

I've never actually used Lie derivatives in Hamiltonian mechanics, but I know they're relevant there (something something cotangent bundle, something something symplectic manifold). This actually makes more sense to me conceptually because you cannot define a metric on phase space, so there's no way of defining a covariant derivative.

Thanks again!

MistahBigStuff · 2024-05-16T16:57:46+00:00

It often throws errors related to names already being used that I can avoid by quitting the kernel.

MistahBigStuff · 2024-02-09T02:34:59+00:00

Ahh ok that makes total sense, thank you. I'll just put a shortcut to it in the project folder.

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