[Analog_Engine.git] / AESL / TP1 04.10 MassOnSphere.AESL

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
Commit	Line	Data
f25252dd P	1	IDENTIFICATION DIVISION
	2	PROGRAM-ID MassOnSphere
	3	VERSION 20240124
	4	COMMENT A mass m rests at the apex on a fixed sphere with radius a.
	5	COMMENT With a slight displacement, it slides down the sphere without friction
	6	COMMENT x'' = C1xy - C3*x
	7	COMMENT y'' = C2yy - C4*y - g
ae9d78b7	8	COMMENT Scaling: measuring distances in da-m (10¹ m)
f25252dd P	9	COMMENT Initial condition: slightly off the top of the sphere to get the mass rolling.
	10	COMMENT Note: x0 is a function of y0 with x0² + y0² = a²
	11	COMMENT Note: ICs have to be negative as the integrator is inverting
	12
	13	ENVIRONMENT DIVISION
	14	ENGINE Anabrid-THAT
	15	TIMEBASE 1ms
	16	REQUIRES COEFFICIENT 7
	17	REQUIRES INTEGRATOR 4
	18	REQUIRES MULTIPLIER 2
	19	REQUIRES INVERTER 4
	20	REQUIRES SUMMER 2
	21
	22	DATA DIVISION
	23	OUTPUT OUTPUT.X x
	24	OUTPUT OUTPUT.Y y
	25	# Example values based on a=1
	26	COEFFICIENT.1 3g/a² for xy e.g. 2,943
	27	COEFFICIENT.2 3g/a² for y²
	28	COEFFICIENT.3 2g/a for x e.g. 1,962
	29	COEFFICIENT.4 2g/a for y
	30	COEFFICIENT.5 g e.g. 0,981
	31	COEFFICIENT.6 a initial condition y e.g. 0,957
	32	COEFFICIENT.7 0 initial condition x, slightly above 0 to start motion, e.g. 0,290
	33
	34	PROGRAM DIVISION
	35	-1 -> COEFFICIENT.5 -> -g
	36	-1 -> COEFFICIENT.6 -> -y0
	37	-1 -> COEFFICIENT.7 -> -x0
	38
6e8a1392 P	39	x'' -> INTEGRATOR -> -x'
	40	-x', IC:-x0 -> INTEGRATOR -> x
	41	y'' -> INTEGRATOR -> -y'
	42	-y', IC:-y0 -> INTEGRATOR -> y
	43	x,y -> MULTIPLIER -> x*y
	44	y,y -> MULTIPLIER -> y^2
f25252dd P	45	xy -> COEFFICIENT.1 -> 3g/a²x*y/10
	46	y^2 -> COEFFICIENT.2 -> 3g/a²*y^2/10
	47	x -> COEFFICIENT.3 -> 2g/a*x/10
	48	y -> COEFFICIENT.4 -> 2g/a*y/10
6e8a1392 P	49	2g/ax/10 -> INVERTER -> -2g/ax/10
	50	2g/ay/10 -> INVERTER -> -2g/ay/10
	51	10:3g/a²xy/10, 10:-2g/a*x/10 -> SUMMER -> -x''
	52	-x'' -> INVERTER -> x''
	53	10:3g/a²y^2/10, 10:-2g/ay/10, 1:-g -> SUMMER -> -y''
	54	-y'' -> INVERTER -> y''
f25252dd P	55
	56	OPERATION DIVISION
	57	MODE REPEAT
ae9d78b7	58	OP-TIME 24ms # after that, the mass would jump off the sphere, which is not included in this model