I'm particularly intrigued by the appearance of _asinh_ in your derivation.
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
Perhaps I could convince this teenager to find some closed-form solutions to this baseball problem! Too bad it isn't about cricket! :-)
At 07:26 AM 5/31/2012, Jaime Villate wrote:
>On 05/31/2012 02:58 PM, Henry Baker wrote:
>>Thanks very much for this posting. It sounds very interesting.
>>
>>Do you have a reference or link to this teenager's paper?
>
>Hi,
>as far as I know, there is no published paper yet. Of course, once you see the general solution
>of an ODE, in a simple form like the one shown in the press, it is very easy to find out what
>the ODE is and then link it to Newton's law for the projectile.
>
>I just saw this morning someone's derivation of the equation in
>http://math.stackexchange.com/questions/150242/teenager-solves-newton-dynamics-problem-where-is-the-paper
>and I wrote down this variant that I sent to the list, but I still have no idea what
>method has the teenager used to get it.
>
>After I sent the message I have also seen a reference to a 19th century book
>(http://books.google.pt/books?id=2C9LAAAAMAAJ&pg=PA209&redir_esc=y#v=onepage&q&f=false)
>where apparently the equation also appears.
>
>Cheers,
>Jaime