extract coefficients
- To: mathgroup at smc.vnet.net
- Subject: [mg100978] extract coefficients
- From: Galina <Galina.Pilgun at gmail.com>
- Date: Fri, 19 Jun 2009 20:45:02 -0400 (EDT)
Hello all,
I have an expression that is nonlinear with respect to variables q
[i].
I need to transform it into equation with respect to unknown q[].
Multipliers near each of such combination of q[] are functions that
must be extracted for integration. I'm having problem with Coefficient
[] because it does not allow extract multipliers near q[i] of just 1-
order, combination of the type q[i]q[j] or near q[i]q[j]q[k]
Please, help
Below there is an example of the expression. I need to transform it
into equation with respect to unknown q[1], q[4] and q[7].
w1,v1,u1 are functions of polynomial type that must be integrated
numerically to perform a coefficients at q[].
Everything else is numbers in reality.
-((EE*h*q[7]*w1[x, y]*Derivative[0, 1][v1][x, y])/(b*R*(-1 + \[Nu]
^2))) - (EE*h*\[Nu]*q[4]*w1[x, y]*Derivative[1, 0][u1][x, y])/(b*R*(-1
+ \[Nu]^2)) -
(3*q[1]^2*(EE*h*w1[x, y]*Derivative[0, 1][w1][x, y]^2 + EE*h*\[Nu]*w1
[x, y]*Derivative[1, 0][w1][x, y]^2))/(2*b^2*R*(-1 + \[Nu]^2)) +
(q[1]^3*((-EE)*h*Derivative[0, 1][w1][x, y]^4 - 2*EE*h*Derivative[0,
1][w1][x, y]^2*Derivative[1, 0][w1][x, y]^2 - EE*h*Derivative[1, 0][w1]
[x, y]^4))/
(2*b^4*(-1 + \[Nu]^2)) + q[1]*((q[7]*((-EE)*h*Derivative[0, 1][v1]
[x, y]*Derivative[0, 1][w1][x, y]^2 - EE*h*Derivative[0, 1][w1][x, y]
*Derivative[1, 0][v1][x, y]*
Derivative[1, 0][w1][x, y] + EE*h*\[Nu]*Derivative[0, 1][w1]
[x, y]*Derivative[1, 0][v1][x, y]*Derivative[1, 0][w1][x, y] -
EE*h*\[Nu]*Derivative[0, 1][v1][x, y]*Derivative[1, 0][w1][x, y]
^2))/(b^3*(-1 + \[Nu]^2)) +
(q[4]*((-EE)*h*\[Nu]*Derivative[0, 1][w1][x, y]^2*Derivative[1, 0]
[u1][x, y] - EE*h*Derivative[0, 1][u1][x, y]*Derivative[0, 1][w1][x, y]
*Derivative[1, 0][w1][x, y] +
EE*h*\[Nu]*Derivative[0, 1][u1][x, y]*Derivative[0, 1][w1][x, y]
*Derivative[1, 0][w1][x, y] - EE*h*Derivative[1, 0][u1][x, y]
*Derivative[1, 0][w1][x, y]^2))/
(b^3*(-1 + \[Nu]^2)) + (-12*b^4*EE*h*w1[x, y]^2 -
EE*h^3*R^2*Derivative[0, 2][w1][x, y]^2 - 2*EE*h^3*R^2*Derivative[1, 1]
[w1][x, y]^2 +
2*EE*h^3*R^2*\[Nu]*Derivative[1, 1][w1][x, y]^2 - 2*EE*h^3*R^2*\
[Nu]*Derivative[0, 2][w1][x, y]*Derivative[2, 0][w1][x, y] -
EE*h^3*R^2*Derivative[2, 0][w1][x, y]^2)/
(12*b^4*R^2*(-1 + \[Nu]^2)))
Thanks you