Date of Award:
5-1999
Document Type:
Thesis
Degree Name:
Master of Science (MS)
Department:
Mathematics and Statistics
Committee Chair(s)
Ian M. Anderson
Committee
Ian M. Anderson
Committee
Mark Fels
Committee
Charles Torre
Abstract
The Maple V package Vessiot is an extensive set of procedures for performing computations in variational and tensor calculus. Vessiot is an extension of a previous package, Helmholtz, which was written by Cinnamon Hillyard for performing operations in the calculus of variations. The original set of commands included standard operators on differential forms, Euler-Lagrange operators, the Lie bracket operator, Lie derivatives, and homotopy operators. These capabilities are preserved in Vessiot, and enhanced so as to function in a multiple coordinate frame context. In addition, a substantial number of general tensor operations have been added to the package. These include standard algebraic operations such as the tensor product, contraction, raising and lowering of indices, as well covariant and Lie differentiation. Objects such as connections, the Riemannian curvature tensor, and Ricci tensor and scalar may also be easily computed. A synopsis of the command syntax appears in Appendix A on pages 194 through 225, and a complete listing of the Maple procedural code is given in Appendix B, beginning on page 222.
Checksum
60b0cdf6fc20914188dfeafd41930292
Recommended Citation
Miller, Charles E., "Vessiot: A Maple Package for Varational and Tensor Calculus in Multiple Coordinate Frames" (1999). All Graduate Theses and Dissertations, Spring 1920 to Summer 2023. 7115.
https://digitalcommons.usu.edu/etd/7115
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