I've derived a system of ODE's, but there is a problem. Basically I have a set of three coupled ODE's $\lbrace\dot{\rho},\dot{\phi}_1,\dot{\phi}_2 \rbrace$ Now $\rho$ is in [0,1], but the two others are both in [0,2$\pi$]. Can I still consider them as spherical coordinates in $\mathbb{R^3}$. Isn't the system overdetermined? And what can I do about it.
Thanks