The 'knocking over on their sides' of Uranus was caused, it is proposed, by collisions by some other objects.

If this were so, by Newton's laws, would not the two planets continue to revolve, not only equatorily, but(I can't think of a proper word) also pole over pole?

The only thing I can think of is perhaps a gyroscopic effect would stop this pole over pole motion. Could this be correct? or can someone enlighten me please!

Andy

Actually, what you're describing is impossible. A sphere can only rotate in one way. If you don't believe me, try it with a ball.

In fact, if it is rotating "polarly" (there wouldn't be a word for it), then the poles would become points along the equator and the new poles would be somewhere along the former equator.

If you take a ball and add a polar rotational motion to it, what will happen is, the new equator will be a line going diagonal. But either way, a ball can only spin on one axis.

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In fact, any body, not just a sphere, can only rotate about one axis.

How does that relate to precession? Is that not a rotation? Or am I confused about the actual axis?

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Well, yes & no. Precession is a motion of the rotational axis. So, Earth rotates around its axis, while the axis (taking Earth along for the ride), executes a motion around a conic section (not a real "rotation"), that we see as the precession of the equinoxes. Any further motion of the axis, that is not on the conic section surface, is called nutation.

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Hardly. See: http://www.tcnj.edu/~rgraham/ron/TrimProblem.html

Scroll down to "Extending to Three Dimensions". This gives equations for a body rotating on three mutually perpendicular axes.

While that is exceedingly unlikely in nature, at least one asteroid in the Solar System has been found to rotate on two axes: http://abob.libs.uga.edu/bobk/ccc/cc111400.html

Which means, among other things, that no point on Toutatis' surface ever passes directly under the same star twice.

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And what, exactly, is it that prevents us from calculating a net rotation vector by adding the three orthogonal rotation vectors? It looks to me, from that page, that they's simply reduced this net vector into its components. Why can't we work backwards?

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You can't take the sky from me.

You can, but you will find no definable plane of rotation. A line drawn from Earth's center to any point on Earth's surface draws a circle every 24 hours on the imaginary "sphere of stars". A similar line on Toutatis draws a chaotic curve which never completely repeats. There is no "equator".

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I asked a similar question on a related thread last year and received this reply:

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Interesting. I stand corrected. Why is it, though, that the plane of rotation isn't simply the plane normal to the sum of those vectors?

Simple Answer:

It's Shaped, Like a POTATO!!!

Long Answer:

It Has, an Uneven Mass Distribution, That is Very Vulnerable to Tidal Forces, Which Tends, to Make It Tumble, More or Less Chaotically, through Space!!!

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Because the two periods are not the same.

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