Loxodromes and geodesics on rotational surfaces in pseudo-isotropic space

Loxodromes are special curves that cut all meridians on the Earth's surface at the same angle. Ships sailing and airplanes flying along a fixed magnetic compass course move along this curve. The Mercator projections of the loxodromes on the sphere correspond to lines and their stereographic projections to logarithmic spirals. In general, loxodromes are not great circular arcs (geodesics). Geodesics measure the shortest distance between two points on the Earth's surface. However, since loxodromes do not need to change course, they are often used in navigation. In this thesis, we will first define the concept of angle in pseudo-isotropic space. Also, time-like rotational surfaces in pseudo-isotropic space will be obtained. Then, parametrizations of space-like and time-like loxodromes and geodesics on time-like rotational surfaces will be given. Finally, examples will be given using the Wolfram Mathematica 7.0 program.