Why is rotation not a vector

Well, suppose that vector describes the small rotation that a given object executes in the infinitesimal time interval between and. We can then define the quantity Suppose, for example, that a rigid body rotates at constant angular velocity. Let us now combine this motion with rotation about a different axis at constant angular velocity. What is the subsequent motion of the body?

Since we know that angular velocity is a vector, we can be certain that the combined motion simply corresponds to rotation about a third axis at constant angular velocity The axis of the wheel has thus moved perpendicular to the forces exerted on it, instead of in the expected direction.

Gyroscopic Effect : In figure a , a person holding the spinning bike wheel lifts it with her right hand and pushes down with her left hand in an attempt to rotate the wheel. This action creates a torque directly toward her. The wheel moves toward the person, perpendicular to the forces she exerts on it. Gyroscope: This same logic explains the behavior of gyroscopes see. There are two forces acting on a spinning gyroscope. The torque produced is perpendicular to the angular momentum, thus the direction of the angular momentum is changed, but not its magnitude.

The gyroscope precesses around a vertical axis, since the torque is always horizontal and perpendicular to L. Gyroscopes : As seen in figure a , the forces on a spinning gyroscope are its weight and the supporting force from the stand. Gyroscopes serve as rotational sensors.

For this reason, applications of gyroscopes include inertial navigation systems where magnetic compasses would not work as in the Hubble telescope or would not be precise enough as in ICBMs. Another application is the stabilization of flying vehicles, such as radio-controlled helicopters or unmanned aerial vehicles. Privacy Policy.

But that's typically not going to be the expected result of rotating a vector whose tail doesn't start at the origin, as illustrated by my example. So how do you use Rodrigues' formula in such cases and what's the "fix" for the general case? Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Tail of rotated vector not properly defined using Rodrigues' rotation formula Ask Question.

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Add a comment. Active Oldest Votes. Improve this answer. Frobenius Frobenius Diracology Diracology Passive rotation is totally clear to me but in passive rotation how exactly did the vector changed.

Only its components do.