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Published online by Cambridge University Press: 05 July 2011
What in the Universe I know can give directions how to go?
W.H. AudenBecause the classical interaction between gravitating point masses is totally understood – the subject has had its Newton – it is possible to solve the clustering problem completely, in principle. All that is necessary is to integrate the equations of motion with the desired initial conditions and read off the answer. Non-linear regimes are dealt with as easily as linear ones. From the time fast computers became available, about 1960, to the present day, a considerable industry has grown up around these numerical solutions. Beginning with the earliest computations for a couple of dozen particles, the power of computers and techniques has improved by more than an order of magnitude each decade. Now it is possible to follow several thousand galaxies for tens of relaxation times with direct integrations.
New numerical techniques are always being developed. Their general goal is more information about increased numbers of particles for longer times. Compromises are often worked, usually sacrificing information for more particles. Since direct integrations retain the most information, and computers always get better, this approach will continue to flourish.
The direct integration method integrates the equations of motion explicitly to retain complete information about all the galaxy positions and velocities at any time.
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