A question about Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg95631] A question about Mathematica
- From: Mohammad Shakiba <m.shakiba at gmail.com>
- Date: Fri, 23 Jan 2009 05:07:22 -0500 (EST)
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.