What are the differential equations of motion for this system?

a good thread?
on my Veeky Forums?

>Ubuntu

Wait, when I said axis of rotation I meant angular velocity.

What course am I supposed to have learned this in?

600-level classical mechanics

If it's first-order then I can't specify all the initial conditions.

It's first order in angular velocity. The orientation itself doesn't play a role in the dynamics.

If you want to write it in terms of orientation than you can do:

[math] I \frac{d^2 \theta}{dt^2}=-\frac{d \theta}{dt} \times (I \frac{d \theta}{dt}) [/math]

Where theta is the orientation.

It almost feels like it's charging some kind of symmetry breaking energy and that when put over some kind of edge makes it switch.

That makes sense. Now it's just spinning in place though -- no flipping around.

Well it's probably perfectly stable. Add a small component of angular velocity along another axis as a perturbation.

Fug I don't think I'm gonna get there, my degree is too elettromagnetism/modern physics oriented. How do I look this up on my own?

This is the book I learned it from.

It wiggles a bit but no flipping.

Play with the initial velocities a bit. Try making the initial spin really high.

It's basically a pendulum under centrifugal artificial gravity.

?? What does this even mean?

It's spinning like a space station habitat that Isaac Arthur is always banging on about. The long bit in the middle is at the "high" point of the artificial gravity field and wants to fall outwards. A tiny perturbation and it will quickly wobble its way out, but it keeps going and finds itself at the other end. It's an inexact way to look at it, but gives some intuitive guidance.

Alternatively, it's a battle for stability between two coupled rotators, one of which is spinning about its long axis and wants to tumble about its short axis (this is the extended middle section) and the other which is already rotating about its short axis and is quite happy in this configuration (this is the handle bit).

It no work.

Here's the notebook file if anyone else wants to play with it.
my.mixtape.moe/qkuhmz.nb

take something rectangular like your remote and hold it like pic related. Now throw the top towards your and try to get it to do a backflip with no corkscrew. That's impossible unless you give it a reverse vector. It will always do a corkscrew.
think that's the same mechanics at work here

goes by Dzhanibekov effect

youtu.be/L2o9eBl_Gzw

en.wikipedia.org/wiki/Tennis_racket_theorem

Came to post this. Glad someone else is on the job.

[math]\color{#b5bd68}{>\text{we assume }I_1 > I_2 > I_3}[/math]
That doesn't seem to be true in the OP webm.

You're free to relabel any axes you want. No loss of generality.

The principal axes with the middle eigenvalue will be unstable.

What if the mid-valued principal axis is the one it's rotating on.

It tumbles

Somebody make a working simulation of this NOW!

It's an unstable equilibrium. So in theory if it's perfectly balanced it'll stay rotating that way, but any infinitesimal perturbation will blow up and make it tumble.

Do they use this here to add rotation midair?
youtube.com/watch?v=13mf5qkcv7U

Not really... I mean maybe, but the effect refers to rigid bodies, which humans are decidedly not.

Though it does look they are staying pretty stiff.

I'm this
guy, so assume I pretty much don't know shit about all this, but just to see if I have the right idea could I write an equation for the spinning of the object using a body-fixed frame of reference and then another one (or rather a set of other ones) for its ''change of direction'' using a different frame of reference?

>could I write an equation for the spinning of the object using a body-fixed frame of reference and then another one (or rather a set of other ones) for its ''change of direction'' using a different frame of reference?

You could, but one of those is a non-inertial reference frame. You'd have centrifugal and Coriolis forces.

Unlike linear velocities, angular velocity reference frames are not made equal.

The equations I showed about can be found here, where for a free body torque is zero.

en.wikipedia.org/wiki/Rigid_body_dynamics#Force-torque_equations

>Cross product
What if I want to model the rotation of an object in 4D space.

Shit gets weird. There are six axes of rotation in 4D.

en.wikipedia.org/wiki/Rotations_in_4-dimensional_Euclidean_space#Geometry_of_4D_rotations

You need to look at SU(n) my nigga.

t. pajeet windows shill

Still waiting on those differential equations.

good luck

You already have them itt, but what do you expect that we somehow find the initial conditions from just looking at the hands in your webm?