Existence, uniqueness, and angle computation for the loxodrome on an ellipsoid of revolution (Q1019322)

In a Euclidean \(3\)-space a \textit{loxodrome} on a surface of revolution is a curve that transverses all meridians along its way at a constant angle. The existence and uniqueness of a loxodrome on an ellipsoid \(\mathcal E\) of revolution and the formula for its angle are known results [cf. \textit{R. Williams}, Geometry of navigation, Horwood Publ.,West Sussex (1998)] proved usually with the help of a one-to-one conformal map and of ``infinitesimals''. Avoiding these two tools the author presents a rigorous proof of the mentioned results; he uses a diffeomorphism of an open connected half of \(\mathcal E\) and transforms the task into an initial value problem of an ordinary differential equation. Reviewer's remark: Fig. 1 does not satisfy the laws of descriptive geometry.