The algorithm of the transformations of a system of linear differential equations to the standard form (Q1342158)

Many problems in the linear theory of shells lead to the algebro- differential system (1) \(A\dot X= BX\), where \(\dim(A)= \dim(B)=[n\times n]\), with \(n\) linear boundary conditions (2) \((\Gamma_ 1 \dot X+ \Gamma_ 2 X)(s_ i)= 0\) for \(i= 1\) or 2, where \(\Gamma_ 1\) and \(\Gamma_ 2\) are \([n\times n]\) matrices. The analytical solution of system (1) may be found only in special cases. In the general case one can apply the methods of numerical or asymptotic integration. For this purpose it is better to represent (1) in the standard form \(\dot X= CX\), with the boundary conditions \(x_ i(s_ j)= 0\), \(i= 1,\dots, n\), \(j= 1\) or 2. In the paper the algorithm of the transformation of a linear system of algebro-differential equations to the standard form is proposed. As an example the system of equations describing the vibrations of a thin shell of revolution is considered.