Defining related charts

[Joel Feske]

Hi,

I'm wondering if there is a way to define charts whose scalar functions are explicitly defined in terms of one another. A very simple case would be two spherical coordinate charts where one is fixed and the other is rotating with angular velocity \Omega. I can define two spherical charts this way:

DefManifold[M3, 3, {a, b, c, d, e, f, g, h, i, j, k, l, m, n}]

DefChart[sph, M3, {1, 2, 3}, {\[Phi][], \[Theta][], r[]}]

DefChart[sph, M3, {1, 2, 3}, {\[Lambda][], \[Theta][], r[]}]

But xAct doesn't yet know about any particular relationship between them. I'd like to set it up so that 

\lambda = \phi - \Omega t

If you were sitting on the surface of the Earth, you would have a fixed longitude 

lambda, but a changing \phi = \lambda + \Omega t. 

Is there a way to set this up so that xAct is aware of these functional relationships between the coordinates in different charts?

Thank you!

Joel