On 05/31/2012 03:51 PM, Henry Baker wrote:
> I'm particularly intrigued by the appearance of _asinh_ in your derivation.
It appears in the calculation of the integral of sqrt(1+s^2).
Also, notice that integrate(1/sqrt(1+s^2),s)=asinh(s)
One could also obtain the result using log functions, since asinh(s) =
log(s+sqrt(1+s^2))
> Asinh also appears in problems of constant absolute value accelerations -- e.g.,
> a rocket capable of a fixed amount of acceleration, no matter what direction it
> is pointed. E.g., see:
>
> Carroza, Davide; Johnson, Stewart; Morgan, Frank. "Baserunner's Optimal Path". Math. Intelligencer 32, 1 (2010), 10-15.
>
> www.williams.edu/Mathematics/fmorgan/Baserunner.pdf
Very interesting; thanks for the reference.
> Perhaps I could convince this teenager to find some closed-form solutions to this baseball problem! Too bad it isn't about cricket! :-)
>
>
Well, I've never tried cricket, but baseball is definitely one of my
favorite sports.
Regards,
Jaime