Date of Award
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The Frenet-Serret formalism for both time-like and space-like curves is studied. The Frenet-Serret vectors and the Frenet-Serret coefficients in both three and four dimensions are expressed in terms of "world" quantities. The conversion from the three dimensional Frenet-Serret formalism to the four dimensional Frenet-Serret formalism and vice versa is described. Indicators of the four dimensional Frenet-Serret vector are investigated. The Frenet-Serret equations in both three and four dimensions are solved for constant Frenet-Serret coefficients with arbitrary initial conditions. Nulltetrads, spinors, bispinors, spinor adjoint and bispinor adjoint are then defined. The Frenet-Serret equations for the nulltetrads, the spinors, the bispinors and the bispinor adjoints are introduced. Darboux bivector forms of the Frenet-Serret equations for the orthonormal tetrads and the nulltetrads are derived. Darboux bispinor forms of the Frenet-Serret equations for the spinors and the bispinor adjoints are derived. Solutions for the nulltetrads and the Darboux bivectors and the Darboux dispinors are discussed. Motion of a point charge in electromagnetic field and motion of a freely spinning particle are briefly discussed. Most of the foregoing are duplicated for the skew-symmetrized descriptions. Examples of the above analysis are given for the time-like curve and the space-like curve with indicators ((epsilon)(,2) = -1, (epsilon)(,0) = (epsilon)(,1) = (epsilon)(,3) = 1). The former is picked in order to compare with the existing literature and the latter is chosen as the simplest case of space-like curves.Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1985 .I345. Source: Dissertation Abstracts International, Volume: 46-09, Section: B, page: 3086. Thesis (Ph.D.)--University of Windsor (Canada), 1985.
ICHIMURA, HIDEO., "TIME-LIKE AND SPACE-LIKE CURVES IN FRENET-SERRET FORMALISMS." (1985). Electronic Theses and Dissertations. 4392.