Accession Number : ADA294025

Title :   Windable Quasi-Geodesic Paths on Surfaces of Revolution.

Descriptive Note : Final rept.,

Corporate Author : ARMY ARMAMENT RESEARCH DEVELOPMENT AND ENGINEERING CENTER WATERVLIET NY BENET LABS

Personal Author(s) : Soanes, Royce W.

PDF Url : ADA294025

Report Date : FEB 1995

Pagination or Media Count : 27

Abstract : If r is the profile or radius function for a surface of revolution and ro is the polar radius function, a quasi-geodesic path on the surface can be defined by the generalized Clairaut relation rSin(w)=ro, where w is the meridional angle. An inequality involving r,r',rn,ro,and ro', is derived. The global satisfaction of this inequality guarantees the windability of the path on a convex (rn<0) surface by a filament winding machine. If the surface is concave anywhere (rn>0) and a more well known clinging inequality is also satisfied, windability is also guaranteed. By windable, we mean that the winding data produced from the path represents a single-valued function and that the wound filament does not bridge. In addition to this new windability criterion, simplified methods for generating quasi-geodesic paths and properly scaled winding data are also presented. (AN)

Descriptors :   *DIFFERENTIAL GEOMETRY, *GEODESICS, ALGORITHMS, DATA MANAGEMENT, PATHS, MATHEMATICAL PROGRAMMING, SURFACES, COORDINATES, FILAMENTS, RADIUS(MEASURE), PERIODIC FUNCTIONS, WINDING, MONOTONE FUNCTIONS, BODIES OF REVOLUTION.

Subject Categories : Geodesy
      Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE