February 25th, 2006


(no subject)

Haven't done enough second-order differential equations or classical mechanics recently?

Dad just emailed me to ask about a numerical integration technique that I had mentioned to him some 5 years ago. I'm cleaning up his notation, which does him a disservice - once the notation's clean, the problem's a lot simpler:

Equation 1 (stated without proof in the paper I showed Dad):
s(2) = 2*s(1) - s(0) + a * (delta(t))^2

Equation 2 (Dad's recollection of his high school calculus notes):
s(t) = 1/2 a * (delta(t))^2

Dad's Question:
The 2*s(1) - s(0) accounts for the velocity between steps, but where did the 1/2 go?

Equation 2 is wrong, it really ought to be
s(t) = 1/2 a t^2 + v(0) t + s(0)

So. Where did that 1/2 go?