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#Hey, define your roller coaster track here!
#Use parametric equations in M.
xM(M) = sin(alpha*M)
zM(M) = gamma*cos(beta*M+delta)
#Now calculate and put the derivatives of your
#parametric equations here:
xMdM(M) = alpha*cos(alpha*M)
zMdM(M) = -gamma*beta*sin(beta*M+delta)
par alpha=3,beta=1,gamma=1,delta=0
param drag=.1
param mass=1
param g=8.3
# scale mouse velocity a little as it is too sensitive
par sv=.25
init M=0,X=0,Z=1
init L=0,Lalt=0.001
#Shouldn't need to modify too much below...
normM(M) = sqrt(xMdM(M)^2 + zMdM(M)^2)
mdt(M) = Lalt/normM(M)
dX/dt=xMdM(M)*mdt(M)
dZ/dt=zMdM(M)*mdt(M)
dM/dt=mdt(M)
dL/dt=Lalt
#Thanks to Newton!
dLalt/dt=(1/mass)*((-g*zMdM(M)/normM(M)) - drag*Lalt)
set Sun {g=274.13}
set Mercury {g=3.59}
set Venus {g=8.87}
set Earth {g=9.81}
set Moon {g=1.62}
set Mars {g=3.77}
set Jupiter {g=25.95}
set Saturn {g=11.08}
set Uranus {g=10.67}
set Neptune {g=14.07}
set Pluto {g=0.42}
@ XP=X,YP=Z,XLO=-1,XHI=1,YLO=-1,YHI=1
@ bounds=100000
@ dt=.01,nout=5
@ total=50
done
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