# Trajectory Curvature question

1. Apr 1, 2006

### pallidin

Can an object be constructed in such a way that, when thrown WITH rotation in space, causes the object to curve in it's trajectory.
Now, I'm not referring to "curve balls" in baseball, because a curve ball in space will not curve.

Rather, I'm thinking somewhere along the lines of a "dumbell" that has less mass on one side versus the other, and is thrown in space with a rotational moment. Under that condition, I assume the center of mass shifts in a cyclic fashion during rotation, causing the trajectory to trace a sinusodal path. Is that correct?

If that is correct, is there some arrangement of a differential rotating mass that will perform a sustained curve in space as opposed to the above sinusodal motion?

2. Apr 1, 2006

### dav2008

The center of mass will move in a straight line (or parabolic if acted upon by gravity)

3. Apr 1, 2006

### pallidin

You are right, and I can see that my question was not worded correctly and that my use of term center of mass was also used incorrectly.
If you draw a circle around the wrench in your above .gif and place a "dot" at the center of that circle, one can see that the dot takes on a sinusodal motion as it travels the trajectory.
Granted, the center of mass does not "shift" as I erroneously suggested, but the geometrical center does indeed shift during rotation.

So, if I take a metal jar lid, glue a heavy ball bearing to the inside lip, spin it rapidy about the geometric center of the lid(NOT the center of mass) and then force this lid into a linear push across the table, the lid will wobble left and right as it traverses across the table, forming a sinusudal trace about the geometric center.

Perhaps the above description makes more sense as opposed to my incorrect initial question.

4. Apr 2, 2006

### arildno

Look up on Eulerian wobbles.

5. Apr 2, 2006

### pallidin

OK, thanks, I will. Appreciate the suggestion.

6. Apr 2, 2006

### pervect

Staff Emeritus
This is probably not what you had in mind, but there is an extremely tiny effect in General relativity where spinning gyroscopes can experience a different force than a non-spining body of the same size and shape. Note that off-center motion has nothing at all to do with this tiny effect, it is caused by any sort of spin.

This effect is due to the coupling of the gravitomagnetic field to a spinning body, and is currently being tested (somewhat indirectly) by gravity probe B, and is described by the Papapetrou equations.

Wikipedia has only a stub on the topic :-(
http://en.wikipedia.org/wiki/Papapetrou-Dixon_equations

7. Apr 3, 2006

### pallidin

How interesting, thanks pervect.