rotating frame

From Physics wiki

Infinitesimal rotations

The components of a vector in some fixed frame are related to the components in a rotating frame through some rotation:

.

An infinitesimal change in this vector is found by the product rule:

,

but an infinitesimal rotation takes the form

,

so we may write

.

More specifically,

,

where we have defined . This can be written as

,

where is the rate of change of a vector quantity due solely to the changes in the rotating frame.

Example: rigid body

For instance, suppose a particle is at rest in the rotating frame , and let us fix an instant in time so that the separation between the particle and some point on the rotating body is in both frames. Then

,

or

(rigid body).

References

Further reading:^{[1] [2]}

1. ↑ Landau, L.D.; Lifshitz, E.M. (1997). Mechanics (3rd ed). Butterworth-Heinemann. ISBN 0-750-62896-0. 
2. ↑ Herbert Goldstein, Charles P. Poole, John L. Safko (1980). Classical Mechanics (3rd ed). Addison Wesley. ISBN 978-0201657029.