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StephenPrivitera

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- Thread starter StephenPrivitera
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StephenPrivitera

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mathman

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Ambitwistor

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StephenPrivitera

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Excellent! That's exactly what I suspected. I tried to solve the problem under the assumption that I knew the exact point of impact and I got a very complicated result (it was very tedious and I gave up after finding one of the final components of one of the masses). But I suspected that the unknown quantity was the direction of the impulse during the collision.Originally posted by mathman

By the way, what exactly is a degree of freedom?

My astronomy professor said once, "The three-body problem is unsolvable because there are too many degrees of freedom" (or hopefully something close to that). This "unsolvable" problem also bothers me, because nature ought to be predictable. What makes the three body problem so difficult? Is it similar to the 2D collision problem in that some unknown cannot be known precisely?

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Ambitwistor

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StephenPrivitera

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Would you say that this is due to a weakness of some sort in the manner of our mathematics? That is, is this problem difficult more due to the mathematics involved or more due to the physics? I have no idea what the solution looks like. It's just that I believe strongly in the power of math and it disappoints me when "numerical methods" have to be used.Originally posted by Ambitwistor

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Ambitwistor

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Originally posted by StephenPrivitera

Would you say that this is due to a weakness of some sort in the manner of our mathematics? That is, is this problem difficult more due to the mathematics involved or more due to the physics?

Neither. It's just that many -- in fact, most -- functions do not have closed-form formulas. For instance, many functions can only be expressed algebraically as infinite series. The 3-body problem happens to be an example of an equation whose general solution is not closed-form. There are infinitely many such equations; this one is just famous because a lot of people were interested in it. It's not a limitation of mathematics or anything; if anything, it's a limitation in what functions we consider to be "nice" (i.e., ones that we can write down simple formulas for).

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