How many orthogonal spins can an object have?

[onethatyawns]

I'm not talking about particles with defined spins. Imagine something visible to the human eye. It can spin in one direction (obviously), it can spin in a perpendicular dimension (momentarily before these two spins begin to combine), and I'm wondering if more spins can be added on this system momentarily. I'm trying to imagine if every other spin should instantly reduce to a sort of (x,y) component of these two initial spins, or if they would reduce over a relatively short period of time. In other words, a virtually infinite amount of orthogonal instantaneous spins. I think the potential orthogonal directions for instantaneous spin would be limited to the interval of zero to pi or 180 degrees (because you can't spin in opposing directions at once), and it may even reduce to a 0-90 degree or 0-pi/2 interval. I'm trying to visualize it.

Obviously, with linear motion, any combination of moments of velocity will instantly reduce to a single vector on an x,y,z plane. An object cannot move in two separate directions on this plane.

However, spin seems to be different. It seems that it can have more than one spin at a time, even though multiple spins tend to quickly join into a single spin.

I'm just trying to understand radial motion, folks.

 

[onethatyawns]

I think the wobble of a planet, for instance, would be the result of two separate spin directions that have yet to combine. These would be spins within a few degrees of each other, so they'd definitely fit the zero to 90 degree interval concept.

 

[Drakkith]

However, spin seems to be different. It seems that it can have more than one spin at a time, even though multiple spins tend to quickly join into a single spin.

Do they really join into a single spin? Or would applying a momentary torque cause precession that never ends?

 

[onethatyawns]

Do they really join into a single spin? Or would applying a momentary torque cause precession that never ends?

Oh, I think you are right. I'm guessing that was a rhetorical question because you are a "mentor", anyway. I think my fixation on the unification of the spins is based upon using a model that requires friction to spin the object. (Friction would stop the original spin, then begin the new spin, which isn't even good enough to model an eventual "spin unification" like I was trying to imagine using a different model)

What are the limits on the amount of momentary torques that won't combine?

 

[onethatyawns]

Ok, I figured it out. If you have two moments, they will divide into two component spins. If one component is much stronger, you get a wobble. If you have more than two moments of torque, they will divide into 3 component spins (to easily see, imagine an x,y,z plane with each pole capable of spinning in two directions (only one at a time though, of course)) (you can think of clockwise/counterclockwise options for each pole, or you can think of end over end rotation for each pole, but no matter what, it's still two directions for each pole.) The third component will essentially be constantly accelerating the first two components in different directions, so if you chose a single moment on the object, it would have a two component vector (just like you only need two components to find any spot on a sphere if you know the radius), which will then combine to form a singular vector for each singular point on the object at a singular point in time of its rotations.

I'm going to guess that what happens in the real world, where things push back, is that this third component frequently relaxes into an elliptical motion, essentially orbiting around some point.

 

[onethatyawns]

My next question is if the same rule holds true for objects in orbit. Formally: how many components are necessarily to describe all possible orbital motions for an object around another object?

I have two initial thoughts.

1. Maybe the spin of the satellite itself has the same components as its orbit. Therefore, the number of components would not increase. However, maybe not. Maybe the orbital and spin components merely tend to exchange between one another depending upon external forces.

2. I don't think you can get three more components out of an orbit. Why not? An object has three dimensions (which allows for three components of spin), but an orbit is only a plane, a 2D object, which allows for only one component of spin (although now, with gravity, you have the added capability of spinning around something off center, creating an ellipse).

 

[onethatyawns]

Ok, orbits can only have two new components. One of the three components that the orbit would have is a spin along the axis between the satellite and the point it's orbiting around. That spin is going to be one of the original three components of spin that that satellite itself already potentially had.

The orbit direction itself is singular, but you might need two components to define it if there is more than one momentary torques applied to the satellite.

 

[Drakkith]

Oh, I think you are right. I'm guessing that was a rhetorical question because you are a "mentor", anyway.

No, it was a serious question. Mentor's are moderators here on PF, not 'experts'. (Though they can be both, depending on the mentor's background)