Accession Number : AD0687088

Title :   ELLIPSOIDAL BOUNDS FOR THE VECTOR SUM OF TWO ELLIPSOIDS.

Descriptive Note : Final scientific rept.,

Corporate Author : AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Guderley,Karl G. ; Keller,Charles L.

Report Date : JAN 1969

Pagination or Media Count : 56

Abstract : Given two sets of vectors E sub 1 and E sub 2 consisting of all vectors inside and on the boundary of two given ellipsoids, the vector sum of these two sets is defined as the set of all vectors that can be obtained by adding arbitrary vectors of each set. Ellipsoids bounding the vector sum are found by constructing an inhomogeneous initial value problem for a system of ordinary differential equation such that a well defined set of solutions for a certain value of the independent variable gives exactly the vectors of this vector sum. This set is then bounded by a suitable differential inequality. The result is verified by direct computation. The relations between the bounding ellipsoid and the vector sum are studied in detail. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, PROBLEM SOLVING), (*NUMERICAL INTEGRATION, NUMERICAL ANALYSIS), BOUNDARY VALUE PROBLEMS, VECTOR SPACES, ERRORS, ELLIPSOIDS, CONVEX SETS, INEQUALITIES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE