Does the equation dr/dr = w(t)xr(t) hold true for a changing axis vector?

[yetar]

In a motion about a fixed axis, where the position is r(t) and the angular velocity is w(t), we know that dr/dr = w(t)xr(t).
My question, does this equation remains true if the axis vector is changing by the time t? Why so?
Thank you.

 

[Mentz114]

dr/dr = w(t)xr(t).

Do you mean dr/dt ? I'm not clear about the description.

 

[yetar]

Do you mean dr/dt ? I'm not clear about the description.

Yes, dr/dt.
r(t) = r0*R+h0*D
Where r0 is a constant distance scalar, and h0 is the distance from the plane that D is normal to.
D is a unit vector, the axis of rotation, so the particle rotates around the axis D. And R is a unit vector, which is the radial vector. R is the opposite direction of the centerpital accelaration.
R is dependent of t, the time.
On a motion around a fixed axis, D is a constant vector, and in this case:
dr/dt = r0*dR/dt = wxr
My question is, what happens when D is not a constant, but instead D(t) is a vector dependent of the time t?
Is it still true that dr/dt = wxr?
Where w is the angular velocity.

 

[Mentz114]

Yetar, I'm sorry I can't answer your question. Maybe someone else can help.