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. > >