2197 particles each of mass = (Mass of Sun/10000) were initialised in a roughly cubic 13x13x13 array with edge length = (Radius of Jupiter's oribt * 1.5).
The particles were also initialised to have a random velocity with an rms of 141ms^-1, and a net angular momentum about the z-axis.
2197 particles each of mass = (Mass of Sun/10000) were initialised in a roughly cubic 13x13x13 array with edge length = (Radius of Jupiter's oribt * 1.5).
The particles were also initialised to have a random velocity with an rms of 141ms^-1, but also a net angular momentum about the z-axis.
The numerical method used was a 2nd order 'Leap Frog', where newtonian gravitational interactions had to be computed 2*N(N-1) times for each of the N bodies - an N^2 problem.
Future refinements would be implementing a 4th order Hermite algorithm which would achieve greater precision while only computing gravitational interactions the same number of times as the 'Leap Frog' method.
The step size was chosen to be 10 days as the inevitablity of close approaches meant that iterations smaller than 10 days did not significantly improve upon the overall appearance of long-term evolution.
At an average rate of computation of 1.7 iterations per second, this simulation of 20000 iterations took about 3 hours to compute, and produced 1.7GB of data.
Current machine precision is fairly limited as particle quantities are stored as 8byte floating point numbers (a double) but as the algorithm used hardly approached machine precision, switching to 16byte floating point numbers (long double) would be relatively pointless.
Perhaps with higher order methods and/or smaller step sizes, this switch would be meaningful, although it will come with a significant drop in computational speed. On the other hand, using a 64bit system could resolve this without the same drop in performance.
The full simulation is not shown in this video, so each second corresponds to roughly 200 days.
The dominant axial symmetry, which superficially resemble jets, could be a result of initialisation with a net angular momentum, while the weaker three fold symmetry along the axes could have risen form the approximate cubic symmetry of initial state.
It is notable that the system is able to reach a stable dynamic equilibrium.
This simulation was run on a X61 Lenovo laptop with a
Core 2 Duo T7500 @ 2.2Ghz and 1.96 GB of ram running Windows XP
C++ was used to program the number cruncher.
FLTK was used with C++ for interfacing.
OpenGL was used for the graphics.
Future refinements would be implementing a 4th order Hermite algorithm which would achieve greater precision while only computing gravitational interactions the same number of times as the 'Leap Frog' method.
The step size was chosen to be 10 days as iterations smaller than 10 days were limited by machine precision. At an average rate of computation of 1.7 iterations per second, this simulation of 20000 iterations took about 3 hours to compute, and produced 1.7GB of data.
Current machine precision is fairly limited as particle quantities are stored as 8byte floating point numbers (a double), so switching to 16byte floating point numbers (long double) should be done, although this will come with a significant drop in computational speed. Switching to a 64bit system could resolve this without the same drop in performance.
The full simulation is not shown in this video, so each second corresponds to roughly 200 days.
The dominant axial symmetry could be a result of initialisation with a net angular momentum, while the weaker three fold symmetry along the axes could have risen form the approximate cubic symmetry of initial state.
It is notable that the system is able to reach a stable dynamic equilibrium.
This simulation was run on a X61 Lenovo laptop with a
Core 2 Duo T7500 @ 2.2Ghz and 1.96 GB of ram running Windows XP
C++ was used to program the number cruncher.
FLTK was used with C++ for interfacing.
OpenGL was used for the graphics.
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Restricted 3-Body Problem With Osculating Orbitsby vdoerr1,678 views
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