Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
The classical Frenet frame is a moving frame on a smooth curve. Connecting a sequence of points in space by line segments makes a discrete curve. The reference frame consisting of tangent, normal and binormal vectors at each point is defined as discrete Frenet frame (DFF). The DFF is useful in studying shapes of long molecules such as proteins. In this dissertation, we provide a solid mathematics foundation for DFF by showing the limit of the Frenet formula for DFF is the classical Frenet formula. As part of a survey of various ways to compute rigid body motion, we show the Denavit-Hartenberg (D-H) conventions in robotics are a special case of the DFFs. Finally, we apply DFF to solve the kink angle problem in protein alpha helical structure using data from NMR experiments.
A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
John R. Quine, Professor Directing Dissertation; Fred W. Huffer, University Representative; Richard Bertram, Committee Member; Timothy A. Cross, Committee Member; Nick Cogan, Committee Member.
Florida State University
Use and Reproduction
This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them.