1.3 Modifying of given system of equations to type, this can be calculated by eller method

To calculate

To transform the initial system of equations to the form suitable for numerical solution, we must make the matrix RX, RY, KX, KY.

, , H=(Hx , Hy)T.

Matrix RX, RY, KX, KY relevant parameters R and K in its diagonal elements in the circuit, respectively, matrices X and Y.

Matrix RX:

R	X1	X2	X3	X4	X5
R2 (Q2)	2.53	0	0	0	0
R3 (Q3)	0	3.34	0	0	0
R6 (Q6)	0	0	1.52	0	0
R7 (Q7)	0	0	0	1.36	0
R9 (Q9)	0	0	0	0	1.53

Matrix RY:

R	Y1	Y2	Y3	Y4	Y5	Y6
R4 (Q4)	2.87	0	0	0	0	0
R5 (Q5)	0	3.35	0	0	0	0
R10 (Q10)	0	0	2.13	0	0	0
R1 (Q1)	0	0	0	1.35	0	0
R8 (Q8)	0	0	0	0	1.25	0
R11 (Q11)	0	0	0	0	0	1.34

Matrix KX:

K	X1	X2	X3	X4	X5
K2 (Q2)	94	0	0	0	0
K3 (Q3)	0	84	0	0	0
K6 (Q6)	0	0	69	0	0
K7 (Q7)	0	0	0	68	0
K9 (Q9)	0	0	0	0	55

Matrix KY:

K	Y1	Y2	Y3	Y4	Y5	Y6
K4 (Q4)	75	0	0	0	0	0
K5 (Q5)	0	72	0	0	0	0
K10 (Q10)	0	0	89	0	0	0
K1 (Q1)	0	0	0	135	0	0
K8 (Q8)	0	0	0	0	57	0
K11 (Q11)	0	0	0	0	0	93

Convenient form of equations aerodynamic network can be written as

,

where:

TP=(SyKy – SxKx)^-1S,

RU=(SyKy – SxKx)^-1SR,

W=Ax^-1Ay.

Components of vectors H (Hx Hy) are functions of dynamic processes that are computed in the iterative cycle of equation solver. So the result is the generation of topological matrix:

TP = (SyKy – SxKxW)^-1S,

RU = TPR = (SyKy – SxKxW)^-1SR

Thus, the generation of equations is reduced to matrix operations.

Addition \ matrices subtraction.

May need to add the result to calculate the matrix C = A + B, where A, B, C - matrix of size n x n. Elements of matrix S calculated by the formula

, where i = j =1,…,n.

Multiplication of matrices.

Let to calculate the product matrix C = A x B, where A, B, C - matrix of size n*n. Elements of matrix S calculated by the formula

,

Where i = j =1,…,n.