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Question: Brachistochrone Time

Question:Brachistochrone Time

Dewwret 5
linearalgebra
December 07 2014
1

Hello,

I'm trying to calculate the time fro my brachistochrone problem.  An object travels from A(0,a) to B(b,0)

a=7 and b=10

I've already found the parametric version:

x(t)=0.5c(t-sin(t) 

y(t)=a-0.5c(1-cos(t))

c= 7.039837581

I cant get it right in maple:

 

restart; a := 7; b := 10; g := 9.81; eq1 := .5*r*(u-sin(u)) = a; eq2 := a-.5*r*(1-cos(u)) = b; sol := fsolve({eq1, eq2}, {r, u}); r0, u0 := op(subs(sol, [r, u])); x := proc (u) options operator, arrow; .5*r0*(u-sin(u)) end proc; y := proc (u) options operator, arrow; a+(-1)*.5*r0*(1-cos(u)) end proc; plot([x(u), y(u), u = 0 .. u0]); Int(sqrt((diff(x(u), u))^2+(diff(y(u), u))^2)/sqrt(-2*g*y(u)), u = 0 .. u0); evalf(%)

                     
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