For a 2D potential (or any image) on a grid, this program will list the local minima, maxima and saddle points. In rotating potentials these are the L1, L2, L3, L4 and L5 lagrangian points.
For a barred galaxy (see e.g. Sellwood & Wilkinson, 1993) L3 (center), L4 and L5 (along minor axis) are stable, whereas L1,L2 (along major axis) are unstable.
For a two-body system L4,L5 are stable (as long as the mass ratio > 24.96), and L1,L2,L3 are all unstable!
% potccd 2body_0.2 potname=twobody potpars=-1,0.2,1,0.05 x=-2:2:0.01 y=-2:2:0.01
% ccdl2 2body_0.2
### Warning [ccdl2]: Draft program
### nemo Debug Info: Dx,Dy= 0.01 0.01
###: IX0 IY0 X Y Potential
L00: 240 112 0.4 -0.88 -1.59263
L00: 241 113 0.41 -0.87 -1.59264
L01: 85 200 -1.15 0 -1.80542
L11: 180 200 -0.2 0 -20.1865
L01: 257 200 0.57 0 -1.92043
L11: 300 200 1 0 -5.33261
L01: 343 200 1.43 0 -2.09766
L00: 241 287 0.41 0.87 -1.59264
L00: 240 288 0.4 0.88 -1.59263
% ccdplot 2body_0.2 contour=-3.5,-2.09766,-1.92043,-1.80542,-1.7,-1.6
Where L00 is a local maximum, L11 a local minimum, and L01/L10 are saddle points. The contour plot can thus use the potential values of the critical saddle points L1, L2 and L3.
1980s CYBER version for my thesis PJT 9-jan-22 V0.1 drafted from scratch PJT