One case of analytic integrability of a nonstationary matrix ordinary differential equation

被引：0

作者：

Fokin, L. A. ^{[1
]}

Shchipitsyn, A. G. ^{[1
]}

机构：

[1] S Ural State Univ, Chelyabinsk, Russia

来源：

DIFFERENTIAL EQUATIONS | 2008年 / 44卷 / 09期

关键词：

Angular Velocity; Euler Angle; Approximate Formula; Direction Cosine; Orientation Error;

D O I：

10.1134/S0012266108090140

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find the general solution of the equation for the error in the matrix of direction cosines of the form. (x) over dot = alpha x+beta, where alpha(t) is a skew- symmetric matrix with zero main diagonal, beta(t) is the product of a skew- symmetric matrix by a matrix exponential, and alpha(t) and beta(t) are functions of direction cosines, the angular velocity of the moving trihedral, and the error in the determination of the angular velocity. We point out the possibility of using the general solution to construct approximate formulas for the analysis of the orientation error.

引用

页码：1343 / 1346

页数：4

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