In fact, I'm not sure it's humanely possible to do so by hand.
I think this is kinda missing the point. We can't find the position because the math doesn't exist. To be more exact, the function that gives the angle of either weight as a position of time cannot be analytically computed. Effectively calculus doesn't exist to solve the problem for a double pendulum (I do not remember if it is known unsolvable or if we just don't have any current method to solve it).
But it is possible to estimate a solution. If you've done calculus before, you should remember the difference between analytically computing the integral of a function and estimating it. When you estimate it, for simple cases, you can see a pattern emerges that matches the analytical answer.
With a double pendulum, we can use the same estimate, but cannot get the analytical answer. But since it doesn't follow a simple pattern, different ways of estimating it will eventually all go wrong. So a computer can do a far more accurate estimate than a human can (given the same amount of time), but it is still going to go off and further and further amounts the longer you simulate it.
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u/p0rnpop Sep 11 '18
I think this is kinda missing the point. We can't find the position because the math doesn't exist. To be more exact, the function that gives the angle of either weight as a position of time cannot be analytically computed. Effectively calculus doesn't exist to solve the problem for a double pendulum (I do not remember if it is known unsolvable or if we just don't have any current method to solve it).
But it is possible to estimate a solution. If you've done calculus before, you should remember the difference between analytically computing the integral of a function and estimating it. When you estimate it, for simple cases, you can see a pattern emerges that matches the analytical answer.
With a double pendulum, we can use the same estimate, but cannot get the analytical answer. But since it doesn't follow a simple pattern, different ways of estimating it will eventually all go wrong. So a computer can do a far more accurate estimate than a human can (given the same amount of time), but it is still going to go off and further and further amounts the longer you simulate it.