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frame , with being the linear transformation such that and it is clear that is orthogonal, i.e., . We can define an anti-symmetric matrix with this,

:

where we can write the dual of as (and ), where is nothing but the time-dependent rotation of the rotating frame with respect to the inertial frame.

Without loss of generality, let us assume that the inertial frame and the moving frame coincide initially, i.e., . By definition, Dirichlet's problem is looking for

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