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We consider a problem on maximizing the height of vertical flight of amaterial point ("meteorological rocket") in the presence of a nonlinearfriction and a constant flat gravity field under a bounded thrust and fuelexpenditure. The original Goddard problem is simplified by removing thedependence on the rocket mass from the equations of motion. Using the maximumprinciple we find all possible types of Pontryagin extremals and classify themw.r.t. problem parameters. Since the velocity of the point can be negative, weobtain some new types of extremals with two or three switching points, whichoptimality should be further investigated.

Classification of extremals in a simplified Goddard model on the maximal height of rocket flight