Disputation "Methoden zur Berechnung und Darstellung dynamischer Systeme auf reellen Untermannigfaltigkeiten"
Am 15.12.15 hat Herr Dipl.-Ing. Martin Gutschke seine Doktorarbeit: “Methoden zur Berechnung und Darstellung dynamischer Systeme auf reellen Untermannigfaltigkeiten” in einer Disputation im Welfenschloss im Raum F 335 / (Senatssitzungssaal) verteidigt.
Das Prüfungskollegium bestand aus:
- Prof. Dr. F.-E. Wolter, (LUH),
- Prof. Dr. N. Thalmann, Univ. Genf, NTU (Singapore)
- Prof. Dr. M. Rohs, (LUH)
- Vorsitz, Prof. Dr. R. Hanke-Rauschenbach (LUH)
This work develops new differential geometrically based methods used to trace vector fields on implicitly defined manifolds being embedded in high-dimensional Euclidean spaces. The aforementioned vector fields may be defined explicitly or implicitly. A particular effort is made ensuring that our computational methods introduced for tracing the latter vector fields can precisely observe jumps of those vector fields occurring on manifolds being folded with respect to predefined jump directions. Methods for tracing the respective jump- and hit-sets are introduced and tested as well. Here the jump- and hit-sets are one- or multidimensional sub manifolds of the initially given implicitly defined manifold. The results obtained by rendering the computed results describing the wanted manifolds - (e.g. the initially given implicitly defined manifold and their respective sub manifolds defined by jump and hit sets) - are appropriately visualised by projecting them in Euclidean - 3-Space using a proprietary GUI flexibly observing requirements of the respective user. This work also introduces an efficient numerical parametrisation method yielding generalised polar coordinates used to parametrise implicitly defined manifolds by employing geodesic polar coordinates. Finally, some example applications are presented and calculated using the methods mentioned above. These examples come from the fields of mechanics, theoretical electrical engineering, biology and physiology.