!
! An object begins a fall from position (1000,0), sliding along a frictionless
! guide to position (px,py). It then slides along another guide
! from (px,py) to position (0,1000).  Find px and py that minimize descent time.
! The minimum value of the function found by Nonlin is the descent time in
! seconds.  All coordinates are in centimeters.
!
Title Two segment path for fastest descent
Register			! Please register your use of Nonlin
Constant G=980			! Acceleration of gravity = 980 cm/sec^2
Constant h=1000			! Height from which object falls (cm.)
Constant d=1000			! Horizontal distance traveled during fall (cm.)
Parameter px			! X coordinate of bend
Parameter py			! Y coordinate of bend
Constrain px=.1,999		! px must be in range 0 < px < d
Constrain py=.1,999		! py must be in range 0 < py < h
Function ;			! Function to be minimized (what a monster)
(sqrt(2*(sqrt(px^2+(py-h)^2))/(G*(h-py)/(sqrt(px^2+(py-h)^2))))) + ;
((sqrt(((G*(h-py)/(sqrt(px^2+(py-h)^2)))* ;
(sqrt(2*(sqrt(px^2+(py-h)^2))/(G*(h-py)/(sqrt(px^2+(py-h)^2))))))^2+ ;
2*(G*py/(sqrt((px-d)^2+py^2)))*(sqrt((px-d)^2+py^2)))- ;
((G*(h-py)/(sqrt(px^2+(py-h)^2)))* ;
(sqrt(2*(sqrt(px^2+(py-h)^2))/(G*(h-py)/ ;
(sqrt(px^2+(py-h)^2)))))))/(G*py/(sqrt((px-d)^2+py^2))))
Data