Re: A question about Mathematica
- 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
Mohammad Shakiba wrote:
> Hello,
>
> I found this email address from "www.mathematica-users.org" as the reference
> that I can ask my questions about mathematica.
> 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
> *
> Thanks for your help,
> M. Shakiba.
>
>