Some kinematic relations in the 3-dimensional Minkowski space

ABSTRACTPhD ThesisSOME KINEMATIC RELATIONS IN THE 3-DIMENSIONAL MINKOWSKI SPACEğMustafa YENEROGLUFirat UniversityGraduate School of science and TechnologyDepartments of Mathematics2007, Page: 57This study has been arranged in five chapters.In the first chapter; the fundemental definitions such as Minkowski metric, Lorentz manifold, Liegroup, Lie algebra, are given.The original parth of study is given in the second, thirth and fourth chapters. In the secondchapter; Sphrerical motions are examined in the 3-dimensional Minkowski space R3 . The coordi-1nate transformations in spherical motion, the characteristic vectors of rotation matrix, the Cayleyformula, the Rodrigues equation and Euler parameters are investigated. In additon, the coordinatetransformations and the screw axis are given for spatial motions in the 3-dimensional Minkowskispace R3 .1In the third chapter; the algebraic properties a motion are investigated . In addition, we havegiven the norm, the matrix groups, the derivative of a motion and tangent operators.In the fourth chapter; The Minkowski metric choice of Spatial motions is investigated. It isgiven Minkowski metric whose geodesics are screw motions. Minkowski metric compatible with thekinematic connection and the curvature of H1 (4) is obtained.In the fifth chapter; some examples in interest with the H1 (3) and H1 (4) are given.Keywords: Spatial motion, Screw motion, Tangent operator, Lie group, Lie algebra, Levi-Civataconnection, Curvature.