Accession Number : AD0600737

Title :   MATRIX RICCATI DIFFERENTIAL EQUATIONS.

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Coles,W. J.

Report Date : MAR 1964

Pagination or Media Count : 16

Abstract : The scalar Riccati equation y' = p(t) Y to the second power + q(t) y+r(t) has the following well-known properties: (I) If one solution is known, the complete solution is obtainable by two quadratures; (II) If two solutions are known, the complete solution is obtainable by one quadrature; (III) The crossratio of any four distinct solutions is constant. The scalar Riccati equation has been generalized to systems. Adoption of one or the other of two particular viewpoints leads to the matrix equations u' = Au - u alpha u (u is n x 1) and Y' = KY + L - YMY - YN (Y is n x m). This paper shows that there is an expression for the complete solution of equations of the first type, and that an expression for the complete solution of equations of the second type can be obtained by quadratures from the complete solution of the first type. Following this, properties corresponding to (II) and (III) are established for the first equation. (Author)

Descriptors :   *DIFFERENTIAL EQUATIONS, *MATRICES(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE