If the force is central, $\mathbf{F}=F(r)\hat{\mathbf{r}}$, then the torque vanishes: $\boldsymbol{\tau}=\mathbf{r}\times\mathbf{F}=\mathbf{0}$. Therefore $\mathbf{L}=\mathbf{r}\times m\mathbf{v}$ is conserved, and the motion is confined to a plane.

The radial dynamics can be reduced to one dimension by introducing $$V_{\mathrm{eff}}(r)=V(r)+\frac{L^2}{2mr^2}.$$ The second term is a centrifugal barrier, and equilibrium radii satisfy $dV_{\mathrm{eff}}/dr=0$.

Using the substitution $u(\theta)=1/r$, one obtains Binet's equation for the orbit under a central force. This form is especially powerful for perturbation analysis and for distinguishing closed from precessing trajectories.