Radially symmetric planar dynamical system

For

\overset{x}{˙} = y + h (r^{2}) x, \overset{y}{˙} = - x + h (r^{2}) y, r^{2} = x^{2} + y^{2},

polar coordinates give

\overset{r}{˙} = h (r^{2}) r, \dot{θ} = - 1.

The trajectories rotate clockwise, while the sign of the radial equation determines stability.

 Ancestors (4)