system of non-linear differential equations I have the system 
$$u'=\sin(w-v), v'=\sin(u-w), w'=\sin(v-u)$$
and I'm not sure how to approach it. Mathematica can't seem to spit out a closed form solution. Any ideas?
 A: Looking back at old posts and thought I would add a fun geometric partial "answer" to this question, although I had originally hoped for a more.
There is a family of solutions to this differential equation that is easy to see geometrically, following the intuition from my comment above. Suppose we have three points on the unit circle described by their angle od deflection from the positive $x$-axis, $u,v,w$. The derivative of the angle corresponding to each point is the z-coordinate of the cross-product of the other two points (viewed as vectors in the x-y plane inside $\mathbb{R}^3$), keeping track of a cyclic ordering of the three points.  This differential equation has one obvious solution: if at the initial condition $u_0,v_0,w_0$ the three points are vertices of an equilateral triangle then the differential equation is 
$$u' = v' = w' = \pm\frac{\sqrt{3}}{2}.$$
(with a plus or minus depending on how the triangle is oriented).
The solution to this differential equation is
$$ u(t) = \frac{\sqrt{3}}{2}t + u_0$$
$$ v(t) = \frac{\sqrt{3}}{2}t + v_0$$
$$ w(t) = \frac{\sqrt{3}}{2}t + w_0$$
which just describes the points rotating at a constant speed so they stay in an equilateral triangle configuration.
