Here are the best pictures I have made. The C code uses fourth order Runge-Kutta with variable Δt. See Weisstein's note on Runge-Kutta for what you need to know to write the code. (See at least the pictures in this for clues as to why it works..) Here are comments on the accuracy of the method. About one million steps were used. The Java code that plots the pictures on the screen reads files, one per image. This was computed with the Pentium's 64 significant bits. I use the Mac utility "grab" to capture the screen image in a .tiff file and then Adobe's Photoshop lite to crop and label the pictures with timestamps. Photoshop then produces the .png files that your browser reads.
Each picture is for 8 time units. White dots on the curve are where the time has an integral value. I have labeled some to avoid ambiguities. Labels for times 35 thru 40 are confusing. At t = 37 and t = 38 the 5 mass (yellow) lands on the track of the 3 mass (turquois). At t = 47 the 5 mass is just back to where it was at about t = 40.6. The greatest numerical distress occurs about 15.7 which event is notable in the picture. The 3 mass is off screen between t = 49 and t = 57 after which it makes its last encounter with the other two which have already begun their final perpetual pas de deux. It passes between the other two in such a phase so as to extract enough of their potential energy to be ejected from the system.
Legend:
| mass | color |
| 3 | turqouis |
| 4 | magenta |
| 5 | yellow |
| 0<=t<8 |
| at t = 1.8793 ke = 2057 Δt = 6*10-8 at t = 3.8 at t = 6.898 |
| 8<=t<16 |
| at t = 8.76 ke = 2344 Δt = 1.6*10-8 at t = 15.82992 |
| 16<=t<24 |
| at t = 22.965 ke = 1136 Δt = 2.5*10-7 |
| 24<=t<32 |
| at t = 29.8015 ke = 7100 Δt = 7.8*10-9 |
| 32<=t<40 |
| at t = 33.6715 ke = 213 Δt = 2*10-6 |
| 40<=t<48 |
| at t = 41.209 ke = 620 Δt = 5*10-7 at t = 46.015 at t = 47.371 |
| 48<=t<56 |
| at t = 52.116 ke = 1509 Δt = 1.2*10-7 etc. |
| 56<=t<62 |
| at t = 59.777 ke = 2662 Δt = 6.2*10-8 at t = 60.6335 at t = 61.494 |
See the effects of some perturbations of the initial conditions