Surface Navigation and Geodesy, A Parametric Approach
Abstract
This document covers the area of minimum distance theory and its application to geodesic measurement and surface navigation. The purpose is to develop a new approach to solving the problem of getting from point a to point b on well behaved surfaces. The study is confined to the use of curvilinear coordinates (u1, u2, u3) and to surfaces which can be represented by a function, k, such that: u3 = k(u1, u2), (ie, surfaces where one coordinate can be written as a function of the remaining two). In rederiving the relations which determine the geodesics or curves of minimum distance, we shall see how using parametric separation of variables, along with the above coordinate variables and surface restrictions, greatly simplifies the problem, thus giving manageable solutions. The paper addresses the development of solutions not just from the point of theoretical interest, but in terms of product useability, for eventual software implementation. By product useability, I mean we need to know more than just the relations between u2 and u3 for an arbitrary minima curve, we need explicit relations for distance traveled and direction (measured normally on the surface) of the minima curve.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1988
- Accession Number
- ADA227907
Entities
Organizations
- Air Force Space Command