Dave LeCompte (really) (tsmaster) wrote,
Dave LeCompte (really)
tsmaster

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?


Hint:
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?
Subscribe

  • Living is Easy (With Eyes Closed)

    This is really primarily for Cassie, but I rarely post here, so it's also an exercise in "how does LJ work again? Or how does it work today?".…

  • No mudslides for me, thank you.

    Hey, is this thing on? I was just sending email to a mailing list (nothing exciting, don't feel insulted if you're not on it) that was thinking…

  • Trivial

    So, this past weekend, a bunch of my friends / acquaintences / teammates got together and competed in a local trivia competition. There are a few…

  • Post a new comment

    Error

    Comments allowed for friends only

    Anonymous comments are disabled in this journal

    default userpic

    Your reply will be screened

    Your IP address will be recorded 

  • 6 comments