' x
' angle
' lean
' leanrate

dt = .0001
g = 9.8

x = 2
'lean = .1

tmax = 20
SCREEN 12
WINDOW (0, -2)-(tmax, 2)

LINE (0, 0)-(tmax, 0)

a = 2
b = 7
c = 20
d = 10

L = 1
h = 1
v = 2





DO
   
    angledem = -a * x / b
    IF angledem > .2 THEN angledem = .2
    IF angledem < -.2 THEN angledem = -.2
    leandem = -b * (angle - angledem) / c
    IF leandem > .1 THEN leandem = .1
    IF leandem < -.1 THEN leandem = -.1
   
   
    u = c * (lean - leandem) + d * leanrate
    IF u > .5 THEN u = .5
    IF u < -.5 THEN u = -.5
    dx = v * angle
    dangle = v * u / L
    dlean = leanrate
    dleanrate = (g * lean - u * v * v / L) / h

    x = x + dx * dt
    angle = angle + dangle * dt
    lean = lean + dlean * dt
    leanrate = leanrate + dleanrate * dt
    t = t + dt

    PSET (t, lean), 10
    PSET (t, x), 14
    PSET (t, u), 9
    PSET (t, angle), 12
LOOP UNTIL t > tmax