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1IDENTIFICATION DIVISION
2PROGRAM-ID HollowCylinder
3VERSION 20240312
4COMMENT A homogeneous hollow cylinder (mass m, ration inner to outer radius epsilon) is connected to a massless spring (constant lambda).
5COMMENT The system is deflected from its rest position by the distance a.
6COMMENT The cylinder rolls without sliding.
7COMMENT x'' = - 2*lambda * 1/m * 1/(3+epsilon²) * x
8
9ENVIRONMENT DIVISION
10ENGINE Anabrid-THAT
11TIMEBASE 1ms
12REQUIRES COEFFICIENT 4, INTEGRATOR 2, INVERTER 1
13
14DATA DIVISION
15OUTPUT OUTPUT.X x
16COEFFICIENT.1 2*lambda
17COEFFICIENT.2 1/m
18COEFFICIENT.3 1/(3+epsilon²) # = 1/3 (0,333) for epsilon=0 and 1/4 (0,25) for epsiolon=1 or anything in between
19COEFFICIENT.4 a
20
21PROGRAM DIVISION
22+1 -> COEFFICIENT.A -> a
23
24x'' -> INTEGRATOR -> -x'
25-x', IC:a -> INTEGRATOR -> x
26x -> COEFFICIENT.2*lambda -> 2*lambda*x
272*lambda*x -> COEFFICIENT.1/m -> 2*lambda*1/m*x
282*lambda*1/m*x -> COEFFICIENT.1/(3+epsilon²) -> 2*lambda*1/m*1/(3+epsilon²)*x
292*lambda*1/m*1/(3+epsilon²)*x -> INVERTER -> -2*lambda*1/m*1/(3+epsilon²)*x = x''
30
31OPERATION DIVISION
32MODE REPEAT
33OP-TIME 52ms