IDENTIFICATION DIVISION
PROGRAM-ID MassOnSphere
VERSION 20240124
COMMENT A mass m rests at the apex on a fixed sphere with radius a.
COMMENT With a slight displacement, it slides down the sphere without friction
COMMENT x'' = C1*x*y - C3*x
COMMENT y'' = C2*y*y - C4*y - g
COMMENT Scaling: measuring distances in da-m (10¹ m)
COMMENT Initial condition: slightly off the top of the sphere to get the mass rolling.
COMMENT    Note: x0 is a function of y0 with x0² + y0² = a²
COMMENT    Note: ICs have to be negative as the integrator is inverting

ENVIRONMENT DIVISION
ENGINE Anabrid-THAT
TIMEBASE 1ms
REQUIRES COEFFICIENT 7
REQUIRES INTEGRATOR 4
REQUIRES MULTIPLIER 2
REQUIRES INVERTER 4
REQUIRES SUMMER 2

DATA DIVISION
OUTPUT OUTPUT.X x
OUTPUT OUTPUT.Y y
# Example values based on a=1
COEFFICIENT.1 3g/a² for xy e.g. 2,943
COEFFICIENT.2 3g/a² for y² 
COEFFICIENT.3 2g/a  for x  e.g. 1,962
COEFFICIENT.4 2g/a  for y
COEFFICIENT.5 g            e.g. 0,981
COEFFICIENT.6 a initial condition y e.g. 0,957
COEFFICIENT.7 0 initial condition x, slightly above 0 to start motion, e.g. 0,290

PROGRAM DIVISION
-1 -> COEFFICIENT.5 -> -g
-1 -> COEFFICIENT.6 -> -y0
-1 -> COEFFICIENT.7 -> -x0

x'' -> INTEGRATOR -> -x'
-x', IC:-x0 -> INTEGRATOR -> x
y'' -> INTEGRATOR -> -y'
-y', IC:-y0 -> INTEGRATOR -> y
x,y -> MULTIPLIER -> x*y
y,y -> MULTIPLIER -> y^2
x*y -> COEFFICIENT.1 -> 3g/a²*x*y/10
y^2 -> COEFFICIENT.2 -> 3g/a²*y^2/10
x -> COEFFICIENT.3 -> 2g/a*x/10
y -> COEFFICIENT.4 -> 2g/a*y/10
2g/a*x/10 -> INVERTER -> -2g/a*x/10
2g/a*y/10 -> INVERTER -> -2g/a*y/10
10:3g/a²*x*y/10, 10:-2g/a*x/10 -> SUMMER -> -x''
-x'' -> INVERTER -> x''
10:3g/a²*y^2/10, 10:-2g/a*y/10, 1:-g -> SUMMER -> -y''
-y'' -> INVERTER -> y''

OPERATION DIVISION
MODE REPEAT
OP-TIME 24ms # after that, the mass would jump off the sphere, which is not included in this model