       • To: mathgroup at smc.vnet.net
• Subject: [mg95765] Re: A question about Mathematica
• From: dh <dh at metrohm.com>
• Date: Mon, 26 Jan 2009 06:49:20 -0500 (EST)
• References: <glc4sh$37c$1@smc.vnet.net>


Hi Mohammed,

You may e.g. use Eliminate to change variables.

Unfortunately I can not read your input. But here is another example:

Given: eq = {(x - 1)^2 + (y - 3)^2 == 1, y/x == 2 + x}

we ewant to change variables to r and v: r == x^2 + y^2, v == y/x. This

can e.g. be done by:

Eliminate[Join[eq, {r == x^2 + y^2, v == y/x}], {x, y}]

For more elaborate cases we have "GroebnerBasis", but this needs a bit

theory.

hope this helps, Daniel

> Hello,

>

> I found this email address from "www.mathematica-users.org" as the reference

> I have not used Mathematica yet. but for one of the tasks in my research I

> have been told that Mathematica can be useful.

> My question is following:

>

> *I have couple of first order differential equations,  and I  want to change

> some variables, which I know would  simplified the equations. I was

> wondering if you can help me with it.

>

> The equations are:

> m \dot U + mQW + mg \sin{\theta} + \dot Q (\lambda_a \eta_a + \lambda_f

> \eta_f ) + 2Q(\lambda_a \dot \eta_a + \lambda_f \dot \eta_f ) = F_x

> m \dot W - mQU - mg \cos{\theta} + \lambda_a \ddot \eta_a + \lambda_f \ddot

> \eta_f  - Q^2 (\lambda_a \eta_a + \lambda_f \eta_f ) = F_z

> (I_{yy} + \eta_a^2 + \eta_f^2)\dot Q + (\dot U + QW)(\lambda_a \eta_a +

> \lambda_f \eta_f ) + 2Q(\eta_a \dot \eta_a + \eta_f \dot \eta_f) -  \psi_a

> \ddot \eta_a - \psi_f \ddot \eta_f = M

> \ddot \eta_f + (\dot W - QU) \lambda_f -\dot Q \psi_f + 2\zeta \omega_f \dot

> \eta_f + (\omega_f^2 - Q^2) \eta_f = N_f

> \ddot \eta_a + (\dot W - QU) \lambda_a -\dot Q \psi_a + 2\zeta \omega_a \dot

> \eta_a + (\omega_a^2 - Q^2) \eta_a = N_a

>

> and my change of variable is:

>

> \tan{alpha} = W/U

> V_T^2 = U^2 + W^2

> *

> M. Shakiba.

>

>



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