Accession Number : AD0666086

Title :   ON STABILITY OF MOTION WITH CONSTANTLY ACTING PERTURBATIONS,

Corporate Author : FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO

Personal Author(s) : Tikhonov,A. A.

Report Date : 24 AUG 1967

Pagination or Media Count : 25

Abstract : An analysis is made of the effect of constantly acting perturbations upon the motion of a body described by a system of differential equations of the form the derivative of X sub s with respect to t = summation from k = 1 to k = n of the quantity ((p sub (sk) X sub k) + X sub s (X sub 1, X sub 2,..., X sub n) + f sub s (t,X sub 1,...,X sub n)), where P sub sk are constant real coefficients, X sub s are functions which can be expanded in an absolutely convergent series in integer powers of x in the neighborhood of the origin of a phase space, and f sub s are functions representing constant perturbations which satisfy the inequality the absolute value of (f sub s (t,X sub 1, X sub 2,..., X sub n)) < f star sub s(t) where f star sub s are certain continuous functions.

Descriptors :   (*PERTURBATION THEORY, *CELESTIAL MECHANICS), LINEAR SYSTEMS, STABILITY, ORBITS, MATHEMATICAL ANALYSIS, USSR

Subject Categories : Celestial Mechanics
      Spacecraft Trajectories and Reentry

Distribution Statement : APPROVED FOR PUBLIC RELEASE