IDENTIFICATION DIVISION
PROGRAM-ID HollowCylinder
VERSION 20240312
COMMENT A homogeneous hollow cylinder (mass m, ration inner to outer radius epsilon) is connected to a massless spring (constant lambda). 
COMMENT The system is deflected from its rest position by the distance a. 
COMMENT The cylinder rolls without sliding. 
COMMENT x'' = - 2*lambda * 1/m * 1/(3+epsilon²) * x

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

DATA DIVISION
OUTPUT OUTPUT.X x
COEFFICIENT.1 2*lambda
COEFFICIENT.2 1/m
COEFFICIENT.3 1/(3+epsilon²) # = 1/3 (0,333) for epsilon=0 and 1/4 (0,25) for epsiolon=1 or anything in between
COEFFICIENT.4 a 

PROGRAM DIVISION
+1 -> COEFFICIENT.A -> a

x'' -> INTEGRATOR -> -x'
-x', IC:a -> INTEGRATOR -> x
x -> COEFFICIENT.2*lambda -> 2*lambda*x
2*lambda*x -> COEFFICIENT.1/m -> 2*lambda*1/m*x
2*lambda*1/m*x -> COEFFICIENT.1/(3+epsilon²) -> 2*lambda*1/m*1/(3+epsilon²)*x
2*lambda*1/m*1/(3+epsilon²)*x -> INVERTER -> -2*lambda*1/m*1/(3+epsilon²)*x = x''

OPERATION DIVISION
MODE REPEAT
OP-TIME 52ms