For a medium whose motion is described by v˙+B×v=0, where B is perpendicular to the two‐dimensional velocity v, the trajectory of each element of the medium is a circle that is determined by the initial value of v. Through a transformation of coordinates the differential equation for the (transformed) velocity derivative matrix is U˙+U2=−I, a special Ricatti equation for which the solution is known. This allows the determination of ∇⋅v, ∇×v, and other functions of the velocity derivatives until the time of formation of a shock.