consider a body rotating with a constant angular velocity 'w' along the z axis of the space reference frame.the centre of mass of the body is at the origin of the space system of coordinates.(adsbygoogle = window.adsbygoogle || []).push({});

now since 'w' is a vector, it must transorm according to the rotation matrix

R (in this case as given below), when we pass from the space frame to the body frame (rigidly fixed on the body and with its z' axis along the z axis of the space frame).

R = | cos(wt) Sin(wt) 0 |

| -Sin(wt) Cos(wt) 0 |

| 0 0 1 |

here i have used (wt) in the place of the angular seperation (theta) between the two reference frames, as the angular seperation increases linearly with time.

pardon me for using the symbol '|' for denoting the matrix.i have used this symbol because i couldn't find anything better on the keyboard.

even though it looks like a determinant, i mean a matrix.

when we use this matrix for transforming from the space frame to the body frame, we get theangular velocity as 'w' in the body frame also !

but,in the body frame, shouldn't the angular velocity bezero ?

(since the body frame is rotating with the body)

what is wrong? is the rotation matrix wrong, or can't the angular velocity be transformed according to the rotation matrix when we pass from space frame to body frame?

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# Rotation : angular velocity from body frame

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