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Discrete mechanics and optimal control

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  • Design
  • Physics

Abstract

Discrete Mechanics and Optimal Control Von der Fakulta¨t fu¨r Elektrotechnik, Informatik und Mathematik der Universita¨t Paderborn zur Erlangung des akademischen Grades Doktor der Naturwissenschaften – Dr. rer. nat. – genehmigte Dissertation von Sina Ober-Blo¨baum Paderborn, 2008 Gutachter: Prof. Dr. Michael Dellnitz Prof. Dr. Oliver Junge Prof. Dr. Jerrold E. Marsden Tag der mu¨ndlichen Pru¨fung: 13.03.2008 THE FUNDAMENTAL VARIATIONAL PRINCIPLE Namely, because the shape of the whole universe is the most perfect and, in fact, designed by the wisest creator, nothing in all the world will occur in which no maximum or minimum rule is somehow shining forth... Leonhard Euler (1744) iii Acknowledgements To begin, I would like to thank my advisor Prof. Dr. Michael Dellnitz for his guidance, support, and motivation, and, in particular, for the great freedom he has given me during my PhD research. I would also like to thank Prof. Dr. Oliver Junge from the Technische Univer- sita¨t Mu¨nchen for his extensive supervision over the last years. Professor Jerrold E. Marsden from the California Institute of Technology has provided valuable guidance during my studies. He introduced me to the area of discrete variational mechanics and provided interesting ideas for application. Mutual visits and discussions contributed to the progress of my research as well. Special thanks goes to my co-workers Dr. Sigrid Leyendecker, Dr. Kathrin Padberg and Mirko Hessel-von Molo for many interesting and enlightening dis- cussions, exciting joint work, and their constant support. I gratefully acknowledge support under the DFG-sponsored research project SFB 376 on Massively Parallel Computation. My colleages in Paderborn participated in lengthy discusssions on scientific and unscientific topics and I appreciate their technical and administrative sup- port, including Alessandro Dell’Aere, Olaf Bonorden, Tanja Bu¨rger, Sebastian Hage-Packha¨user, Marianne Kalle, Stefan Klus,

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