Talk:Zermelo's navigation problem
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There is an easier derivation of the Zermelo equation. Just observe that the vector (cosphi, sinphi) is parallel to (lx,ly) and take the time derivative of the third EL.
Did Zermelo consider the curvature of the earth in his original optimum solution of simply heading to B? This is a start of a thought made the Portuguese and Italians experts, and why they and not Germans discovered the world nautically outside Europe, because of the incidence of not natural variables, but the space itself.