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I'm looking for a reference, journal article, paper, etc. that supports the idea that classical mechanics, in particular rigid body dynamics, is largely predictable.

A view coming from the background of computer physics simulations would be an added bonus.

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Classical mechanics by definition is predictable. Given a position and momentum, the particle's trajectory can be tracked exactly for all times. I'm confused by what exactly your question is... – Kitchi Nov 5 '12 at 15:31
Classical mechanics by definition is predictable I'm looking for a peer reviewed article that confirms this is the case. – user1423893 Nov 5 '12 at 15:39
I disagree. I have seen plenty of rigid body mechanisms where minute adjustments in the initial conditions have huge effects in the motion. Since we cannot specify anything with infinite precision chaos will always creep in mechanisms. – ja72 Nov 5 '12 at 16:25
This really all depends on whether you consider chaotic behavior to be predictable or not. It is well known that classical mechanics is chaotic for suitable systems. – David Z Nov 5 '12 at 16:39
What are you really interested in? How classical mechanics is deterministic as a theory but may still be sensitive to numerical errors in measurements/simulations for a given system? Or how classical mechanics differs from quantum, where even with arbitrary precision, outcomes of measurements are not determined wholly from a previous state? – Muphrid Nov 5 '12 at 19:53

Depending on OP's precise definition of predictability and determinism, the following fact, taken from Wikipedia, may be relevant:

In the history of science, Laplace's demon was the first published articulation of causal or scientific determinism by Pierre-Simon Laplace in 1814.

Pierre Simon Laplace 1814 article is apparently published in:

Pierre-Simon Laplace, A Philosophical Essay on Probabilities (1902), available here.

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up vote 0 down vote accepted

Thanks to the references in Jamie's link I have found a wealth of arguments in the following publication:

Is Classical Mechanics Really Time-Reversible and Deterministic?

The full article can be found on JSTOR here.

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Consider the simple problem of a block sliding on a rough surface, being pulled by a linear spring. The resulting motion is unpredictable and non-deterministic. In general rigid body dynamics problems involve friction and here is were determinism breaks down.

Ignoring friction things might seems look better, but then we enter the area of joint singularities (gymbal lock and knee locking) causing non-determinism in time evolution. The actual solution relies outside the realm of rigid bodies, as body deflections and joint compliance must be considered.

For example with thin slender structures, you may have buckling which is unstable and not always predictable which way it is going to deflect. Try compressing a ruler on its ends and see what happens.

So the question is, under what conditions/assumptions do you want to bound determinism, because general determinism does not exist.

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As the question is seeking a reference, I really don't think this is that useful... – David Z Nov 5 '12 at 16:39
So the futility of the reference is not relevant here? – ja72 Nov 5 '12 at 17:17
Well, if you had a strong case that nobody has ever published anything about this aspect of classical mechanics, then that would be a useful answer. But I don't think this answer provides that. – David Z Nov 5 '12 at 21:54

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