Can a Rotating Object in Space Curve its Trajectory?

In summary, if you throw a wrench with rotation around it's geometric center, it will curve in it's trajectory.
  • #1
pallidin
2,209
2
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?
 
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  • #2
The center of mass will move in a straight line (or parabolic if acted upon by gravity)

n2extc.gif
 
  • #3
dav2008 said:
The center of mass will move in a straight line (or parabolic if acted upon by gravity)

n2extc.gif

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
Look up on Eulerian wobbles.
 
  • #5
arildno said:
Look up on Eulerian wobbles.

OK, thanks, I will. Appreciate the suggestion.
 
  • #6
pallidin said:
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.

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
How interesting, thanks pervect.
 

1. What is trajectory curvature?

Trajectory curvature refers to the amount of curvature or bending in the path of an object as it moves through space. It is a measure of how much the direction of the object's motion changes at any given point along its path.

2. How is trajectory curvature calculated?

Trajectory curvature is typically calculated using mathematical equations, such as the curvature formula, which takes into account the object's velocity, acceleration, and position at different points along its path. It can also be calculated using calculus and vector calculus methods.

3. What factors can affect trajectory curvature?

There are several factors that can affect trajectory curvature, including the object's initial velocity and direction, external forces acting on the object such as gravity or air resistance, and the shape and composition of the object itself.

4. How does trajectory curvature impact an object's flight path?

The amount of curvature in an object's trajectory can significantly impact its flight path. Objects with a large curvature will have a more curved flight path, while objects with a smaller curvature will have a more straight-line flight path. Additionally, changes in curvature can affect the stability and predictability of an object's flight.

5. What are some real-world applications of understanding trajectory curvature?

Understanding trajectory curvature has many practical applications, such as in engineering and design of airplanes, rockets, and other vehicles. It is also important in fields such as astronomy, where the curvature of planetary orbits must be taken into account. Additionally, understanding trajectory curvature can help improve accuracy in sports such as golf, tennis, and baseball, where the trajectory of an object greatly affects its outcome.

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