Re: Help with Solve
- To: mathgroup at smc.vnet.net
- Subject: [mg112337] Re: Help with Solve
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Fri, 10 Sep 2010 04:47:24 -0400 (EDT)
Use Reduce
eq1 = n*Sin[x] == (m*v^2)/r;
eq2 = n*Cos[x] == m*g;
cons = {m > 0, g > 0, r > 0, v > 0};
sys = Join[{eq1, eq2}, cons];
FullSimplify[Reduce[sys, x, Reals], cons] // ToRadicals
Element[C[1], Integers] &&
v == -((n^2*r^2 - g^2*m^2*r^2)^(1/4)/Sqrt[m]) &&
((x == 2*(Pi*C[1] + ArcTan[
Sqrt[1 - (2*g*m)/(g*m + n)]]) && n > g*m) ||
(2*ArcTan[Sqrt[1 - (2*g*m)/(g*m + n)]] + x ==
2*Pi*C[1] && g*m + n < 0))
Bob Hanlon
---- Eduardo Cavazos <wayo.cavazos at gmail.com> wrote:
=============
Hello!
A newb question I'm sure... :-)
Here's a couple of equations:
eq1 = n*Sin[x] == (m*v^2)/r;
eq2 = n*Cos[x] == m*g;
The goal is to solve for 'x'.
I can do this in a roundabout way via:
Solve[eq1 /. Solve[eq2, n], x]
I.e. solve eq2 for 'n', substitute this into eq1, and solve the result
for 'x'. But this approach seems too "manual".
Is there a more straightforward way to carry out the problem? I tried
this:
Solve[{eq1, eq2}, x]
but it doesn't seem to work. What's a good way to go about this?
Thanks!
Ed