Solution of Cermelo navigational problem for free axial field of velocities

The paper contains the solution of the Cermelo navigational problem for a free axial field of velocities obtained in analytical and integral form by means of the principle of the Pontryagin maximum. As an example the results of concrete solutions of problems with different forms of the velocities' profile and given correlation of its base velocity and velocities of the moving object have been given. The management function has been received analytically, trajectory solutions have been built as integrals using MathCad software package. Some examples have been shown when the maximum principle does not give the optimum decision.