# Rotations of Earth and other Rigid Bodies

1. Aug 21, 2008

### Peaks Freak

Does anyone know of a good mathematical reference covering the use of one-parameter group actions to model rotations of planets and/or other rigid bodies?

2. Aug 21, 2008

### D H

Staff Emeritus
It's not that simple. The Earth is not a spherical body, so it undergoes nutation and precession as well as rotating.

That said, the International Earth Rotation and Reference System Service (IERS) is the official organization that defines reference frames used for navitation and astronomy. See http://www.iers.org/MainDisp.csl?pid=36-25787&prodversid=11221 [Broken].

I also suggest "Fundamentals of Astrodynamics and Applications", 3rd Edition, David Vallado.

Last edited by a moderator: May 3, 2017
3. Aug 21, 2008

### Peaks Freak

Since I'm mostly interested in the geometry and mathematics involved, I'm assuming that Earth is spherical. My main concern is the use of one-parameter group actions to model time-dependent rotations. As a mathematician, whose specialties are far afield from physics and astronomy, I'm not sure of the right search terms to use here. Kinematics? Dynamical Systems?

Any further help/insight would be appreciated!

Thanks.

4. Aug 21, 2008

### Peaks Freak

OK, I think I've formulated a better question, one closer to my actual confusion.

In geometric terms, we define a rotation to be an orientation-preserving isometry that fixes some point p. Thus, a rotation is a map with properties.

In everyday terms, however, a rotation is a time-dependent, physical process. We observe rotations over time, the rotating rigid body passing through a continuum of orientations in between its starting and ending positions.

Whereas the former definition is of a particular kind of map, the second surely involves an action of the real numbers (acting as the passage of time). I'd like to conclude that this action is simply a one-parameter action of SO(3), but don't have experience with this physical setting. Do you know of a reference that addresses this scenario?

Also, does this conversation better belong in a different forum?

Thanks!

5. Aug 21, 2008

### D H

Staff Emeritus
That is only true for a body that has a spherical mass distribution and no external torques -- Not a particularly interesting or realistic situation.