Both equations reduce to the single linear equation .

However, Hamilton's equations usually don't reduce the difficulty of finding explicit solutions.

Thus, the equation reduces to a simple inner-product of the two vectors.

Dividing through by r, we get that all these equations reduce to the same thing:

The geodesic equation for the rotating frame therefore reduces to.

Ignoring the source term, the equation further reduces to:

This equation reduces to the one above it, at small (compared to c) speed.

Since cannot equal zero the equation reduces to the following.

If characteristic were not an obstruction, each equation would reduce to the previous ones by a suitable change of variables.

This equation reduces to Maxwell's Equations as a special case; see gauge theory.