Mathematics Commons^™

Quadrature-Based Gravity Models For The Homogeneous Polyhedron, Jason Pearl

Graduate College Dissertations and Theses

A number of missions to comets and asteroids have been undertaken by major space organizations driving a need to accurately characterize their gravitational fields. This is complicated however by their irregular shapes. To accurately and safely navigate spacecraft in these environments, a simple point-mass gravity model is insufficient and instead higher-fidelity models are required. Several such models exist for this purpose but all posess drawbacks. Moreover, there are some applications for which the currently available models are not particular well suited.

In this dissertation, numerical quadrature and curvilinear meshing techniques are applied to the small body gravity problem. The goal …

Gravity And Electromagnetism In Noncommutative Geometry, Giovanni Landi, Nguyen Ai Viet, Kameshwar C. Wali

Physics - All Scholarship

We present a unified description of gravity and electromagnetism in the framework of a Z 2 non-commutative differential calculus. It can be considered as a “discrete version” of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory.