Shortest Curves for Vehicles on Surfaces of Celestial Bodies
L. Bittner · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2001
Abstract The classical problem, to find the shortest line connecting two given points of a given surface, does not take account of 1) obstacles, i. e. forbidden regions (islands, icebergs, foreign territories a. s. o.) through which the curve must not run, 2) alterations of the shape of the surface in the course of time (tides, tectonic displacements a. s. o.), 3) the fact that the length of the curve, described by a vehicle moving on the surface, has eventually to be measured with respect to a primary inertial coordinate system emitting the control signals. The surface system may change its position relating to the primary system.