Consider a freely rotating body. Let the axis of rotation be the z-axis. For simplicity assume all the mass of the body is concentrated in the x-y-plane, i.e. the plane in which the body rotates.
I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine it with a torque to tilt the axis of rotation.
Suppose the above rotating body indeed has a solid axis, albeit of zero mass, sticking out at one end with length [itex]\gt l[/itex]. At [itex]z=l[/itex] we apply a force perpendicular to the axis for a distance of [itex]\Delta s[/itex] in the direction of [itex]-x[/itex].
What will happen to the to the overall rotation.
a) Will the axis tilt only a certain amount or does the force applied induce a rotation that keeps going and combines with the previous rotation.
b) What is the formula to get the tilt angle or the angular speed? I assume it somehow combines the inertia tensor and the force F or torque [itex]l\times F[/itex]?
Thanks,
Harald.
I have read about the moment of inertia tensor on wikipedia, but I don't see how I would combine it with a torque to tilt the axis of rotation.
Suppose the above rotating body indeed has a solid axis, albeit of zero mass, sticking out at one end with length [itex]\gt l[/itex]. At [itex]z=l[/itex] we apply a force perpendicular to the axis for a distance of [itex]\Delta s[/itex] in the direction of [itex]-x[/itex].
Code:
|<- apply force
|
|
===== <- x-y plane of rotationa) Will the axis tilt only a certain amount or does the force applied induce a rotation that keeps going and combines with the previous rotation.
b) What is the formula to get the tilt angle or the angular speed? I assume it somehow combines the inertia tensor and the force F or torque [itex]l\times F[/itex]?
Thanks,
Harald.