Geometry, Kinematics, and Rigid Body Mechanics in Cayley-Klein Geometries [Elektronische Ressource] / Charles Gunn. Betreuer: Ulrich Pinkall

1Geometry, Kinematics, andRigid Body Mechanicsin Cayley-Klein Geometriesvorgelegt von\Master of Science" MathematikerCharles GunnPortsmouth, Virginia, USAVon der Fakult at II - Mathematik und Naturwisssenschaftender Technischen Universit at Berlinzur Erlangung des akademischen GradesDoktor der Naturwissenschaftengenehmigte DissertationPromotionsausschuss:Vorsitzender: Prof. Dr. Stefan FelsnerBerichter/Gutachter: Prof. Dr. Ulrich PinkallBerichtehter: Prof. Dr. Johannes WallnerTag der wissenschaftlichen Aussprache: 21 September, 2011Berlin 2011D 83v.PrefaceThis thesis arose out of a desire to understand and simulate rigid body motion in 2- and3-dimensional spaces of constant curvature.The results are arranged in a theoretical partand a practical part. The theoretical part rst constructs necessary tools { a family of realprojective Cli ord algebras { which represent the geometric relations within the above-mentioned spaces with remarkable delity. These tools are then applied to representkinematics and rigid body dynamics in these spaces, yielding a complete description ofrigid body motion there. The practical part describes simulation and visualization resultsbased on this theory.thHistorically, the contents of this work ow out of the stream of 19 century math-ematics due to Chasles, M obius, Pluc ker, Klein, and others, which successfully appliednew methods, mostly from projective geometry, to the problem of rigid body motion.