Hi!
I would like to know how "AccuracyGoal" works. I know that "AccuracyGoal" is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result" so i tought that if I choose a bigger value the results should be more accurate, but if I put, for example AccuracyGoal->2 I obtain results that are completly different from the results I obtein with AccuracyGoal->4... It seems that a bigger value brings to a worse result and if I reach AccuracyGoal->10 the results disappear!
I also have another point: I plot the evolution of a function (displacement) in the time. I plot the displacement of a point in the x direction and y direction. In both the directions the situation is the same but the solicitation in direction y is 30% of that in x. So I expect that the displacements follow the same evolution but one is simply smaller than the other. This is true and I can see it in the output but just until a certain time (about 20 seconds, while the time history lasts more than 40 seconds). So, I don't understand...what happen from second 20?!
(*Record*)
dT = 0.02;
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0.0713, -0.032, -0.1001, -0.0048, 0.1375,
0.1713, -0.0174, -0.2902, -0.2388, -0.1289, -0.1109, -0.0805, 0.0152,
0.0294, -0.0821, -0.1841, -0.1935, -0.0633, -0.0376, 0.0176, 0.1738,
0.2059, 0.1181, -0.0075, -0.0048, 0.0453, 0.036, -0.0228, -0.077, -0.0463,
0.032, 0.037, -0.0419, -0.0616, 0.0408,
0.0488, -0.0412, -0.0802, -0.1253, -0.1554, -0.0747, 0.1319,
0.1144, -0.0087, 0.0306, 0.0349, 0.0539, 0.0728, 0.1098, 0.1196, 0.0885,
0.0782, 0.0463, -0.0031, -0.0259, 0.0055, 0.0414, 0.0739, 0.1158,
0.0768, -0.0657, -0.1661, -0.1212, 0.0084, 0.0208, 0.0041, 0.065, 0.0918,
0.0676, 0.0035, -0.0739, -0.1074, -0.0524, -0.0186, 0.0478, 0.1711, 0.2268,
0.1728, 0.0242, -0.0729, -0.1506, -0.0918, 0.0612,
0.024, -0.0857, -0.0656, 0.0263,
0.0366, -0.0201, -0.0145, -0.0391, -0.0776, -0.0525, -0.0976, -0.0682,
0.0213, -0.007, -0.0871, -0.0249, 0.0993, 0.1438,
0.0401, -0.2518, -0.332, -0.2115, -0.1179, -0.0065, 0.0788, 0.112, 0.171,
0.1447, 0.0003, -0.1357, -0.1396, -0.037, -0.0072, 0.0406, 0.0051, 0.0104,
0.071, 0.0497, 0.0548, 0.0749, -0.0083, -0.1041, -0.0016, 0.0607, 0.0394,
0.0292, 0.0021, -0.0814, -0.0733, 0.0041, -0.0277, -0.0298, 0.0302, 0.0407,
0.0027, -0.0144, -0.0371, -0.0425, 0.0197, 0.0958,
0.0866, -0.0267, -0.1093, -0.0693, 0.0367, 0.0922,
0.0586, -0.0221, -0.0759, -0.0386, 0.0597,
0.0594, -0.0063, -0.0638, -0.117, -0.0846, 0.0278, 0.121, 0.1123,
0.025, -0.0363, 0.0042, 0.0868, 0.1026, 0.0817,
0.0208, -0.0082, -0.0074, -0.0477, -0.0227, 0.0759, 0.0946,
0.0143, -0.0609, -0.0576, -0.0004, -0.0036, -0.1016, -0.097, 0.02, 0.0472,
0.0313, -0.0246, -0.0466, -0.0194, -0.0451, -0.0763, -0.1171, -0.0968,
-0.0221, 0.0412, 0.1433, 0.1995, 0.0717, -0.1602, -0.1421, 0.0641, 0.1797,
0.1541, 0.0208, -0.0657, -0.112, -0.0591, 0.1236,
0.0702, -0.1791, -0.2918, -0.1892, -0.0228, -0.0116, -0.0544, -0.0561,
0.066, 0.1739, 0.1398, 0.059, 0.0039, 0.0004, 0.074, 0.1403, 0.1916,
0.1674, 0.0762, 0.0027, -0.0426, 0.0223, 0.1027, 0.1614,
0.0867, -0.1322, -0.3131, -0.3139, -0.1517, -0.0406, 0.0133,
0.0396, -0.0301, -0.201, -0.2275, -0.0505, 0.0577, 0.1915, 0.3301, 0.2343,
0.1235, 0.0858, 0.1044, 0.1797, 0.195, 0.1886, 0.0196, -0.3086, -0.0761,
0.0692, -0.3487, -0.3312, -0.1134, 0.0917, 0.2933, 0.0735, -0.0173, 0.0624,
0.0476, 0.0941, -0.0325, 0.1203, 0.2663, 0.1367, -0.1176, -0.185, -0.0253,
0.0894, 0.1611, 0.0943, -0.141, -0.1633, 0.0378, 0.1362, 0.146,
0.0526, -0.0261, -0.0434, -0.0248, -0.0485, -0.0891, -0.1162, -0.1998, \
-0.2119, -0.1698, -0.0786, 0.0481, 0.1385, 0.248, 0.2966, 0.284, 0.203,
0.0184, -0.0996, -0.1382, -0.074, -0.0669, -0.0763, 0.0417, 0.1416, 0.2211,
0.1903, -0.0322, -0.1971, -0.2447, -0.2224, -0.1597, -0.142, -0.0905, \
-0.043, 0.003, 0.0536, 0.0562, 0.0782,
0.0735, -0.049, -0.119, -0.162, -0.181, -0.183, -0.1389, 0.0577, 0.1729,
0.0468, -0.2103, -0.2416, -0.0804, 0.0464, 0.1305,
0.0958, -0.0787, -0.0861, 0.0637, 0.0313, 0.0345, 0.0833,
0.0377, -0.0292, -0.1031, -0.1808, -0.1751, -0.0636, 0.0283, 0.1021,
0.0812, -0.0564, -0.1066, -0.0212, 0.0104, 0.0192,
0.0299, -0.0505, -0.0708, -0.0067, 0.0281, 0.044, 0.0749, 0.0654,
0.0082, -0.025, -0.0453, -0.029, 0.0256, 0.0103, -0.0592, -0.0304, 0.0623,
0.0886, 0.0691, -0.0023, -0.0709, -0.0306, 0.0737, 0.0915, 0.0636, 0.0577,
0.0069, -0.0572, -0.0434, 0.0381,
0.0183, -0.0349, -0.045, -0.1226, -0.0972, -0.0117, 0.0196, 0.076,
0.0149, -0.0341, 0.0021, -0.0338, -0.11, -0.1043, -0.0244, 0.0402, 0.0632,
0.0937, 0.0956, 0.0416, 0.0163, 0.0201, 0.061, 0.0726, 0.0492, 0.0688,
0.0776, 0.0792, 0.0981, 0.129,
0.0402, -0.1363, -0.2369, -0.2509, -0.1321, -0.0457, -0.0018, 0.0499,
0.0665, 0.0156, -0.0182, 0.0638, 0.1661, 0.1383, 0.0126, -0.002,
0.036, -0.0119, -0.0661, -0.0454, -0.0229, -0.0482, -0.0438, -0.0728,
-0.0127, 0.1641, 0.2442, 0.1557, -0.0216, -0.1065, -0.1029, -0.0245, 0.0465,
0.0964, 0.102, 0.0438, 0.0119, 0.0934, 0.1466, 0.0467, -0.029, -0.0497,
0.001, 0.0253, 0.0102, 0.0653, 0.1294, 0.1468,
0.0707, -0.0229, -0.0906, -0.1235, -0.1419, -0.1384, -0.0215, 0.0858,
0.1563, 0.1094, -0.051, -0.1494, -0.1197, 0.0192,
0.0329, -0.0384, -0.0544, -0.041, 0.0618, 0.1508,
0.1165, -0.0003, -0.1077, -0.1241, -0.0141, 0.0577, 0.0655,
0.0286, -0.0454, -0.0806, -0.0451, 0.0143, 0.0301, 0.0336, 0.0895,
0.0335, -0.1382, -0.1466, 0.0016, 0.0605, -0.0131, -0.0982, -0.0781,
0.0136, 0.074, 0.0639, -0.0522, -0.0731, 0.0422, 0.118, 0.1015,
0.0339, -0.023, -0.096, -0.1142, -0.1102, -0.126, -0.1351, -0.0968, 0.0461,
0.1305, 0.0775, -0.043, -0.1205, -0.1306, -0.0922, -0.0573, -0.0484,
-0.051, -0.0249, 0.0155, 0.0626, 0.1029, 0.0873,
0.0041, -0.0564, -0.074, -0.0759, 0.0116, 0.0696, 0.0687, 0.0501, 0.0657,
0.0801, 0.0341, 0.0279, 0.0505, -0.0131, -0.0513, 0.0086,
0.0051, -0.0389, -0.0071, 0.0352, 0.05, 0.0454, 0.084, 0.1018,
0.0298, -0.0338, -0.0464, 0.0151, 0.02, -0.0475, -0.076, -0.0573, 0.0258,
0.0617, -0.0251, -0.0794, -0.028, -0.0006, -0.0438, -0.0406, 0.0503,
0.1284, 0.0992, -0.017, -0.0658, 0.0087, 0.081,
0.0566, -0.0046, -0.0684, -0.0876, -0.0618, -0.0608, -0.035, -0.0344,
-0.0295, 0.0103, 0.0464, 0.0321, -0.0507, -0.0476, 0.0283, 0.0539, 0.0286,
0.0395, 0.0528, 0.0189, 0.0461, 0.0642, 0.0073, -0.0149, 0.0454,
0.0642, -0.0015, -0.0926, -0.1003, -0.0517, -0.0025, 0.0787, 0.154, 0.1576,
0.0478, -0.0144, -0.0547, -0.0719, -0.021, -0.0717, -0.0917, 0.0204,
0.1141, 0.0925, -0.0516, -0.1962, -0.1679, 0.0102, 0.1063, 0.1206,
0.0481, -0.1055, -0.094, 0.0355, 0.1127, 0.1146,
0.0063, -0.1312, -0.1669, -0.0411, 0.0274, 0.0688,
0.0535, -0.0507, -0.1143, -0.0981, -0.025, -0.019, 0.0236, 0.088,
0.0757, -0.0005, -0.0643, -0.0345, 0.0298, 0.0328, 0.0374, 0.0598, 0.0759,
0.007, -0.0096, 0.1016, 0.1252, 0.0045, -0.1357, -0.1571, -0.0613, 0.0031,
0.0383, 0.059, 0.024, -0.0912, -0.1004, 0.0711, 0.1007, -0.0042, -0.0404,
0.008, 0.0361, 0.0329,
0.0008, -0.0346, -0.0292, -0.0523, -0.069, -0.0321, -0.0239, -0.0367,
-0.057, -0.0688, -0.0139, 0.0211, 0.0082, -0.0609, -0.0537, 0.0507,
0.047, -0.0405, -0.0483, 0.0211, 0.0539, 0.0361, 0.0143, 0.0224,
0.0247, -0.0146, -0.0061, 0.0256, 0.0177, -0.0024, 0.0333, 0.0438, 0.039,
0.0165, -0.0987, -0.1258, -0.0493, -0.0044, 0.0354, 0.0224, -0.0306, 0.006,
0.0539, 0.0708, 0.1089, 0.1015, -0.0159, -0.0984, -0.0732, 0.0249, 0.1018,
0.1338, 0.1166, -0.0069, -0.0617, -0.0031, -0.0146, -0.012, 0.0895,
0.0974, -0.0407, -0.0827, -0.0336, -0.0405, -0.0307,
0.0035, -0.0196, -0.0857, -0.1136, -0.0982, -0.0403, 0.0115, 0.0514,
0.0316, -0.1217, -0.1382, 0.0584, 0.1369, 0.0837, 0.0393, -0.0575, -0.0834,
0.0247, 0.0787, 0.0886, 0.0613, 0.0198, -0.0069, -0.0389, -0.0392, -0.013,
0.0177, 0.0712, 0.0939, 0.0392, -0.0643, -0.0942, -0.0238, 0.0012, 0.0154,
0.0163, -0.0098, -0.0217, -0.0074, -0.0319, -0.0485, -0.0119, 0.0148,
0.0548, 0.0698, 0.0403, -0.0081, -0.0512, 0.0008, 0.104, 0.14,
0.0792, -0.0361, -0.0785, 0.0016, 0.0833, 0.1106,
0.0613, -0.027, -0.074, -0.0421, -0.0034, 0.0265,
0.0303, -0.0346, -0.0555, -0.0026, 0.0362, 0.0405, -0.0187, -0.0441,
0.0339, 0.0445, -0.011, 0.0014, 0.0367, -0.0166, -0.0451, 0.0082, 0.0519,
0.0345, -0.0639, -0.1447, -0.1122, 0.0216, 0.0888,
0.0691, -0.0185, -0.1361, -0.1281, -0.0137, 0.0331, 0.0196,
0.0294, -0.0276, -0.078, -0.0361, 0.0059,
0.0132, -0.0285, -0.0475, -0.0026, 0.031, 0.0308,
0.0123, -0.0012, -0.0104, -0.0101, 0.0015, 0.008, 0.0071, 0.0027, -0.0002,
0.0004, 0.002, 0.0023, 0.0017, 0.0012, 0.001, 0.001, 0.001, 0.0009, 0.0009,
0.0009, 0.0008, 0.0008, 0.0008, 0.0008, 0.0008, 0.0007, 0.0007, 0.0007,
0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0};
ListLinePlot[mList,
PlotRange -> {{0, Length[mList]}, {Min[mList], Max[mList]}}]
ListLinePlot[(0.3*mList),
PlotRange -> {{0, Length[mList]}, {0.3*Min[mList], 0.3*Max[mList]}}]
GetIndex[t_] := IntegerPart[t/dT] + 1;
mList[[GetIndex[0.04]]]
GetGroundAcceleration[t_] :=
mList[[GetIndex[
t]]] + (mList[[GetIndex[t] + 1]] - mList[[GetIndex[t]]]) FractionalPart[
t/dT];
GetGroundAcceleration[40]
( Force-Displacement)
\[Mu] = 0.033;
g = 9.81;
R = 3.7;
\[Omega] = Sqrt[g/R];
YP = 0.001;
W = 726992.03;
\[Gamma] = 0.5;
tTotal = 45;
n = 5;
ParametricPlot[
Evaluate[{x1[t], (1/R)*x1[t] + \[Mu]*x3[t]} /.
Quiet@NDSolve[
{x1'[t] == x5[t],
x2'[t] == x6[t],
x3'[t] ==
x5[t]/YP (1 -
Abs[x3[t]]^n* (\[Gamma] *Sign[x5[t]* x3[t]] + (1 - \[Gamma]))),
x4'[t] ==
x6[t]/YP (1 -
Abs[x3[t]]^n* (\[Gamma] *Sign[x6[t]* x4[t]] + (1 - \[Gamma]))),
x5'[t] == -(\[Omega]^2)*x1[t] - \[Mu]*9.81*x3[t] -
9.81*GetGroundAcceleration[t],
x6'[t] == -(\[Omega]^2)*x2[t] - \[Mu]*9.81*x4[t] -
9.81*0.3*GetGroundAcceleration[t],
x1[0] == 0,
x2[0] == 0,
x3[0] == 0,
x4[0] == 0,
x5[0] == 0,
x6[0] == 0},
{x1[t], x2[t], x3[t], x4[t], x5[t], x6[t]},
{t, 0, tTotal}, AccuracyGoal -> 2]],
{t, 0, tTotal},
ImageSize -> {500, 500}, PlotRange -> {{-0.5, 0.5}, {-0.2, 0.2}},
AspectRatio -> 1/1, AxesLabel -> {"ux", "F"}]
ParametricPlot[
Evaluate[{x2[t], (1/R)*x2[t] + \[Mu]*x4[t]} /.
Quiet@NDSolve[
{x1'[t] == x5[t],
x2'[t] == x6[t],
x3'[t] ==
x5[t]/YP (1 -
Abs[x3[t]]^n* (\[Gamma] *Sign[x5[t]* x3[t]] + (1 - \[Gamma]))),
x4'[t] ==
x6[t]/YP (1 -
Abs[x3[t]]^n* (\[Gamma] *Sign[x6[t]* x4[t]] + (1 - \[Gamma]))),
x5'[t] == -(\[Omega]^2)*x1[t] - \[Mu]*9.81*x3[t] -
9.81*GetGroundAcceleration[t],
x6'[t] == -(\[Omega]^2)*x2[t] - \[Mu]*9.81*x4[t] -
9.81*0.3*GetGroundAcceleration[t],
x1[0] == 0,
x2[0] == 0,
x3[0] == 0,
x4[0] == 0,
x5[0] == 0,
x6[0] == 0},
{x1[t], x2[t], x3[t], x4[t], x5[t], x6[t]},
{t, 0, tTotal}, AccuracyGoal -> 5]],
{t, 0, tTotal},
ImageSize -> {500, 500}, PlotRange -> {{-0.1, 0.1}, {-0.05, 0.05}},
AspectRatio -> 1/1, AxesLabel -> {"uy", "F"}]
(* Displacement (time)*)
ParametricPlot[
Evaluate[{t, x1[t]} /.
Quiet@NDSolve[
{x1'[t] == x5[t],
x2'[t] == x6[t],
x3'[t] ==
x5[t]/YP (1 -
Abs[x3[t]]^n* (\[Gamma] *Sign[x5[t]* x3[t]] + (1 - \[Gamma]))),
x4'[t] ==
x6[t]/YP (1 -
Abs[x3[t]]^n* (\[Gamma] *Sign[x6[t]* x4[t]] + (1 - \[Gamma]))),
x5'[t] == -(\[Omega]^2)*x1[t] - \[Mu]*9.81*x3[t] -
9.81*GetGroundAcceleration[t],
x6'[t] == -(\[Omega]^2)*x2[t] - \[Mu]*9.81*x4[t] -
9.81*0.3*GetGroundAcceleration[t],
x1[0] == 0,
x2[0] == 0,
x3[0] == 0,
x4[0] == 0,
x5[0] == 0,
x6[0] == 0},
{x1[t], x2[t], x3[t], x4[t], x5[t], x6[t]},
{t, 0, tTotal}, AccuracyGoal -> 2]],
{t, 0, tTotal},
ImageSize -> {500, 500}, PlotRange -> {{0, tTotal}, {-0.4, 0.4}},
AspectRatio -> 1/1, AxesLabel -> {"t", "ux"}]
ParametricPlot[
Evaluate[{t, x2[t]} /.
Quiet@NDSolve[
{x1'[t] == x5[t],
x2'[t] == x6[t],
x3'[t] ==
x5[t]/YP (1 -
Abs[x3[t]]^n* (\[Gamma] *Sign[x5[t]* x3[t]] + (1 - \[Gamma]))),
x4'[t] ==
x6[t]/YP (1 -
Abs[x3[t]]^n* (\[Gamma] *Sign[x6[t]* x4[t]] + (1 - \[Gamma]))),
x5'[t] == -(\[Omega]^2)*x1[t] - \[Mu]*9.81*x3[t] -
9.81*GetGroundAcceleration[t],
x6'[t] == -(\[Omega]^2)*x2[t] - \[Mu]*9.81*x4[t] -
9.81*0.3*GetGroundAcceleration[t],
x1[0] == 0,
x2[0] == 0,
x3[0] == 0,
x4[0] == 0,
x5[0] == 0,
x6[0] == 0},
{x1[t], x2[t], x3[t], x4[t], x5[t], x6[t]},
{t, 0, tTotal}, AccuracyGoal -> 2]],
{t, 0, tTotal},
ImageSize -> {500, 500}, PlotRange -> {{0, tTotal}, {-0.3, 0.3}},
AspectRatio -> 1/1, AxesLabel -> {"t", "uy"}]
Thanks!
