Application Gravity

[Analog_Engine.git] / scripts / TP1 06.18 Mass in Tube.AESL

IDENTIFICATION DIVISION
PROGRAM-ID MassInTube
VERSION 20240214
COMMENT A thin tube rotates at a constant angular velocity perpendicular to gravity 
COMMENT A mass point moves frictionless in this tube. The differential equation gives the position of this mass point.
COMMENT r''=omega^2*r -g*sin(omega*t+phi0)

ENVIRONMENT DIVISION
ENGINE Anabrid-THAT
TIMEBASE 1ms
REQUIRES COEFFICIENT 8, INTEGRATOR 4, INVERTER 1, MULTIPLIER 2

DATA DIVISION
OUTPUT OUTPUT.X x
OUTPUT OUTPUT.Y y
COEFFICIENT.1 ICw'    
COEFFICIENT.2 ICw     
COEFFICIENT.3 OMEGAC
COEFFICIENT.4 OMEGAS  # same as OMEGAC
COEFFICIENT.5 G
COEFFICIENT.6 R0      # r(0)
COEFFICIENT.7 V0      # r'(0)
COEFFICIENT.8 OMEGA^2 # = OMEGAC*OMEGAS

PROGRAM DIVISION
### Generating sin(omega*t+phi0) ###
+1 -> COEFFICIENT.ICw’ -> icw’
-1 -> COEFFICIENT.ICw  -> -icw 
w’’, IC:icw’ -> INTEGRATOR -> -w’=-cos
-w' -> COEFFICIENT.OMEGAC -> -omega*w'
-omega*w', IC:-icw -> INTEGRATOR -> w=sin
w  -> INVERTER -> -w=-sin
-w -> COEFFICIENT.OMEGAS -> -omega^2*w=w’’

### the actual problem ###
-sin -> COEFFICIENT.G  -> -g*sin
-1   -> COEFFICIENT.R0 -> -r0
+1   -> COEFFICIENT.V0 -> v0
omega^2*r, -g*sin,IC:v0  -> INTEGRATOR -> -r' # input is r''
-r',IC:-r0 -> INTEGRATOR -> r
r -> COEFFICIENT.OMEGA^2 -> omega^2*r

### Converting r, phi to x,y coordinates for display ###
r, sin  -> MULTIPLIER -> x
r, -cos -> MULTIPLIER -> y # y-axis shall go down according to gravity, thus negativ input

OPERATION DIVISION
MODE REPEAT
OP-TIME 17,5ms