| 1 | #*--------------------------------------------------------------------- |
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| 2 | * This file is property of the author and cannot be used, copyed |
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| 3 | * or modified without permission. |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2005 the author |
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| 6 | *---------------------------------------------------------------------- |
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| 7 | * Author: Rafael de Pelegrini Soares |
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| 8 | * $Id: sample_car.mso 6 2005-01-11 17:06:06Z paula $ |
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| 9 | *---------------------------------------------------------------------- |
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| 10 | * |
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| 11 | * The car axis problem |
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| 12 | * |
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| 13 | * The problem is a stiff DAE of index 3, consisting of 8 |
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| 14 | * differential and 2 algebraic equations. |
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| 15 | * |
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| 16 | *--------------------------------------------------------------------*# |
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| 17 | |
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| 18 | FlowSheet CarAxis |
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| 19 | |
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| 20 | PARAMETERS |
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| 21 | l as Real(Default=1); |
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| 22 | l0 as Real(Default=1/2); |
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| 23 | eps as Real(Default=1e-2); |
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| 24 | M as Real(Default=10); |
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| 25 | h as Real(Default=1/5); |
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| 26 | tau as Real(Default=3.1514/5); |
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| 27 | w as Real(Default=10); |
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| 28 | r as Real(Default=0.1); |
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| 29 | |
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| 30 | |
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| 31 | VARIABLES |
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| 32 | xl as Real(Default = 0, Lower=-1, Upper = 1); |
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| 33 | yl as Real(Default = 0.5, Lower=-1, Upper = 1); |
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| 34 | xr as Real(Default = 1, Lower=-2, Upper = 2); |
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| 35 | yr as Real(Default = 0.5, Lower=-1, Upper = 1); |
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| 36 | q(4) as Real(Default = -1); |
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| 37 | lambda(2) as Real(Default = 0); |
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| 38 | xb as Real(Default = 1); |
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| 39 | yb as Real(Default = 0); |
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| 40 | ll as Real(Default = 0.5, Brief="Left spring length"); |
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| 41 | lr as Real(Default = 0.5, Brief="Right spring length"); |
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| 42 | |
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| 43 | EQUATIONS |
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| 44 | diff([xl, yl, xr, yr]) = q; |
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| 45 | |
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| 46 | eps^2*M/2 * diff(q(1)) = (l0-ll)*xl/ll |
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| 47 | +lambda(1)*xb +2*lambda(1)*(xl-xr); |
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| 48 | |
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| 49 | eps^2*M/2 * diff(q(2)) = (l0-ll)*yl/ll |
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| 50 | +lambda(1)*yb +2*lambda(2)*(yr-yl) - eps^2*M/2; |
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| 51 | |
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| 52 | |
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| 53 | eps^2*M/2 * diff(q(3)) = (l0-lr)*(xr-xb)/lr |
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| 54 | -2*lambda(2)*(xl-xr); |
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| 55 | |
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| 56 | eps^2*M/2 * diff(q(4)) = (l0-lr)*(yr-yb)/lr |
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| 57 | -2*lambda(2)*(yl-yr) - eps^2*M/2; |
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| 58 | |
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| 59 | xl*xb + yl*yb = 0; |
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| 60 | |
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| 61 | (xl-xr)^2 + (yl-yr)^2 = l^2; |
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| 62 | |
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| 63 | xb = sqrt(l^2-yb^2); |
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| 64 | |
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| 65 | yb = r*sin(w*time); |
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| 66 | |
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| 67 | ll = sqrt(xl^2 + yl^2); |
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| 68 | |
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| 69 | lr = sqrt((xr-xb)^2 + (yr-yb)^2); |
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| 70 | |
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| 71 | INITIAL |
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| 72 | yl = 0.5; |
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| 73 | xr = 1; |
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| 74 | q(3) = -0.5; |
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| 75 | q(4) = 0; |
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| 76 | |
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| 77 | OPTIONS |
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| 78 | time = [0:0.01:3]; |
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| 79 | integration = "index0"; # "original"; |
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| 80 | #DAESolver = "mebdf"; |
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| 81 | |
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| 82 | relativeAccuracy = 1e-5; |
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| 83 | absoluteAccuracy = 1e-5; |
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| 84 | indVarAccuracy = 1e-3; |
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| 85 | end |
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