# coaster2.ode
# this is a rather simple coaster
tab xx xcoast.tab
tab yy ycoast.tab
# numerically compute x',x'' etc
xp=(xx(s+h)-xx(s-h))/(2*h)
yp=(yy(s+h)-yy(s-h))/(2*h)
xpp=(xx(s+h)-2*xx(s)+xx(s-h))/(h*h)
ypp=(yy(s+h)-2*yy(s)+yy(s-h))/(h*h)
#  
vsq=xp*xp+yp*yp
aa=(xp*xpp+yp*ypp)/vsq
# now add a few parameters to scale time and gravity etc
s'=v
v'=-r*yp/vsq-q*aa*v*v
#v'=-yp/r
par r=175,h=.02,q=.1
# give it a little push!
init v=1e-5
# here is the coaster
aux x=xx(s)
aux y=yy(s)
@ bound=100000,total=40
@ xp=x,yp=y,xlo=0,ylo=0,xhi=12000,yhi=4500,lt=0
done