📄 program4.m
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(* Code Generated by Mathematica packages written by Brian L. Evans *)(* Copyright (c) 1993-1997 by the Regents of the University of California *)(* All Rights Reserved. *)(* See the copyright file for copyright notice, *)(* limitation of liability, and disclaimer of warranty provisions. *)(* Overall Cost Function *)InputForm[WQ*(-0.5 + ((Sqrt[a[1]^2 + b[1]^2]*Sqrt[a[2]^2 + b[2]^2]* Sqrt[a[3]^2 + b[3]^2]*Sqrt[a[4]^2 + b[4]^2])/ (a[1]*a[2]*a[3]*a[4]))^(1/4)/2) + (Wms*integrate[((a[1]^2 + b[1]^2)^2*(a[2]^2 + b[2]^2)^2* (a[3]^2 + b[3]^2)^2*(a[4]^2 + b[4]^2)^2* ((c[1]^2 + d[1]^2)^2 + w^2*(w^2 + 2*(c[1]^2 - d[1]^2)))* ((c[2]^2 + d[2]^2)^2 + w^2*(w^2 + 2*(c[2]^2 - d[2]^2)))* ((c[3]^2 + d[3]^2)^2 + w^2*(w^2 + 2*(c[3]^2 - d[3]^2)))* ((c[4]^2 + d[4]^2)^2 + w^2*(w^2 + 2*(c[4]^2 - d[4]^2))))/ (((a[1]^2 + b[1]^2)^2 + w^2*(w^2 + 2*(a[1]^2 - b[1]^2)))* ((a[2]^2 + b[2]^2)^2 + w^2*(w^2 + 2*(a[2]^2 - b[2]^2)))* ((a[3]^2 + b[3]^2)^2 + w^2*(w^2 + 2*(a[3]^2 - b[3]^2)))* ((a[4]^2 + b[4]^2)^2 + w^2*(w^2 + 2*(a[4]^2 - b[4]^2)))* (c[1]^2 + d[1]^2)^2*(c[2]^2 + d[2]^2)^2*(c[3]^2 + d[3]^2)^2* (c[4]^2 + d[4]^2)^2), {w, ws, 100*ws}])/(99*ws) + (Wmp*integrate[(-1 + ((a[1]^2 + b[1]^2)*(a[2]^2 + b[2]^2)* (a[3]^2 + b[3]^2)*(a[4]^2 + b[4]^2)* Sqrt[((c[1]^2 + d[1]^2)^2 + w^2*(w^2 + 2*(c[1]^2 - d[1]^2)))* ((c[2]^2 + d[2]^2)^2 + w^2*(w^2 + 2*(c[2]^2 - d[2]^2)))* ((c[3]^2 + d[3]^2)^2 + w^2*(w^2 + 2*(c[3]^2 - d[3]^2)))* ((c[4]^2 + d[4]^2)^2 + w^2*(w^2 + 2*(c[4]^2 - d[4]^2)))])/ (Sqrt[((a[1]^2 + b[1]^2)^2 + w^2*(w^2 + 2*(a[1]^2 - b[1]^2)))* ((a[2]^2 + b[2]^2)^2 + w^2*(w^2 + 2*(a[2]^2 - b[2]^2)))* ((a[3]^2 + b[3]^2)^2 + w^2*(w^2 + 2*(a[3]^2 - b[3]^2)))* ((a[4]^2 + b[4]^2)^2 + w^2*(w^2 + 2*(a[4]^2 - b[4]^2)))]* (c[1]^2 + d[1]^2)*(c[2]^2 + d[2]^2)*(c[3]^2 + d[3]^2)* (c[4]^2 + d[4]^2)))^2, {w, 0, wp}])/wp + (Wmt*integrate[(-(w/(wp - ws)) + ws/(wp - ws) + ((a[1]^2 + b[1]^2)*(a[2]^2 + b[2]^2)*(a[3]^2 + b[3]^2)* (a[4]^2 + b[4]^2)* Sqrt[((c[1]^2 + d[1]^2)^2 + w^2*(w^2 + 2*(c[1]^2 - d[1]^2)))* ((c[2]^2 + d[2]^2)^2 + w^2*(w^2 + 2*(c[2]^2 - d[2]^2)))* ((c[3]^2 + d[3]^2)^2 + w^2*(w^2 + 2*(c[3]^2 - d[3]^2)))* ((c[4]^2 + d[4]^2)^2 + w^2*(w^2 + 2*(c[4]^2 - d[4]^2)))])/ (Sqrt[((a[1]^2 + b[1]^2)^2 + w^2*(w^2 + 2*(a[1]^2 - b[1]^2)))* ((a[2]^2 + b[2]^2)^2 + w^2*(w^2 + 2*(a[2]^2 - b[2]^2)))* ((a[3]^2 + b[3]^2)^2 + w^2*(w^2 + 2*(a[3]^2 - b[3]^2)))* ((a[4]^2 + b[4]^2)^2 + w^2*(w^2 + 2*(a[4]^2 - b[4]^2)))]* (c[1]^2 + d[1]^2)*(c[2]^2 + d[2]^2)*(c[3]^2 + d[3]^2)* (c[4]^2 + d[4]^2)))^2, {w, wp, ws}])/(-wp + ws) + (Wph*integrate[(ArcTan[(w - b[1])/a[1]] + ArcTan[(w + b[1])/a[1]] + ArcTan[(w - b[2])/a[2]] + ArcTan[(w + b[2])/a[2]] + ArcTan[(w - b[3])/a[3]] + ArcTan[(w + b[3])/a[3]] + ArcTan[(w - b[4])/a[4]] + ArcTan[(w + b[4])/a[4]] - ArcTan[(w - d[1])/c[1]] - ArcTan[(w + d[1])/c[1]] - ArcTan[(w - d[2])/c[2]] - ArcTan[(w + d[2])/c[2]] - ArcTan[(w - d[3])/c[3]] - ArcTan[(w + d[3])/c[3]] - ArcTan[(w - d[4])/c[4]] - ArcTan[(w + d[4])/c[4]] - (3*w*((-2*wmax*a[1] - (ArcTan[(wmax - b[1])/a[1]] + ArcTan[(wmax + b[1])/a[1]])* (-wmax^2 - a[1]^2 + b[1]^2) - a[1]*b[1]*Log[1 + (wmax - b[1])^2/a[1]^2] + a[1]*b[1]*Log[1 + (wmax + b[1])^2/a[1]^2])/2 + (-2*wmax*a[2] - (ArcTan[(wmax - b[2])/a[2]] + ArcTan[(wmax + b[2])/a[2]])* (-wmax^2 - a[2]^2 + b[2]^2) - a[2]*b[2]*Log[1 + (wmax - b[2])^2/a[2]^2] + a[2]*b[2]*Log[1 + (wmax + b[2])^2/a[2]^2])/2 + (-2*wmax*a[3] - (ArcTan[(wmax - b[3])/a[3]] + ArcTan[(wmax + b[3])/a[3]])* (-wmax^2 - a[3]^2 + b[3]^2) - a[3]*b[3]*Log[1 + (wmax - b[3])^2/a[3]^2] + a[3]*b[3]*Log[1 + (wmax + b[3])^2/a[3]^2])/2 + (-2*wmax*a[4] - (ArcTan[(wmax - b[4])/a[4]] + ArcTan[(wmax + b[4])/a[4]])* (-wmax^2 - a[4]^2 + b[4]^2) - a[4]*b[4]*Log[1 + (wmax - b[4])^2/a[4]^2] + a[4]*b[4]*Log[1 + (wmax + b[4])^2/a[4]^2])/2 + (2*wmax*c[1] + (ArcTan[(wmax - d[1])/c[1]] + ArcTan[(wmax + d[1])/c[1]])* (-wmax^2 - c[1]^2 + d[1]^2) + c[1]*d[1]*Log[1 + (wmax - d[1])^2/c[1]^2] - c[1]*d[1]*Log[1 + (wmax + d[1])^2/c[1]^2])/2 + (2*wmax*c[2] + (ArcTan[(wmax - d[2])/c[2]] + ArcTan[(wmax + d[2])/c[2]])* (-wmax^2 - c[2]^2 + d[2]^2) + c[2]*d[2]*Log[1 + (wmax - d[2])^2/c[2]^2] - c[2]*d[2]*Log[1 + (wmax + d[2])^2/c[2]^2])/2 + (2*wmax*c[3] + (ArcTan[(wmax - d[3])/c[3]] + ArcTan[(wmax + d[3])/c[3]])* (-wmax^2 - c[3]^2 + d[3]^2) + c[3]*d[3]*Log[1 + (wmax - d[3])^2/c[3]^2] - c[3]*d[3]*Log[1 + (wmax + d[3])^2/c[3]^2])/2 + (2*wmax*c[4] + (ArcTan[(wmax - d[4])/c[4]] + ArcTan[(wmax + d[4])/c[4]])* (-wmax^2 - c[4]^2 + d[4]^2) + c[4]*d[4]*Log[1 + (wmax - d[4])^2/c[4]^2] - c[4]*d[4]*Log[1 + (wmax + d[4])^2/c[4]^2])/2))/wmax^3)^2, {w, 0, wmax}])/wmax + 100*WO* (-1 + ((a[2]^2 + b[2]^2)*(a[3]^2 + b[3]^2)*(a[4]^2 + b[4]^2)* Sqrt[((a[1] - c[1])^2 + (b[1] - d[1])^2)* ((a[1] - c[1])^2 + (b[1] + d[1])^2)* ((a[1] - c[2])^2 + (b[1] - d[2])^2)* ((a[1] - c[2])^2 + (b[1] + d[2])^2)* ((a[1] - c[3])^2 + (b[1] - d[3])^2)* ((a[1] - c[3])^2 + (b[1] + d[3])^2)* ((a[1] - c[4])^2 + (b[1] - d[4])^2)* ((a[1] - c[4])^2 + (b[1] + d[4])^2)]* (b[1]*Cos[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + ArcTan[(b[1] + b[2])/(a[1] - a[2])] + ArcTan[(b[1] - b[3])/(a[1] - a[3])] + ArcTan[(b[1] + b[3])/(a[1] - a[3])] + ArcTan[(b[1] - b[4])/(a[1] - a[4])] + ArcTan[(b[1] + b[4])/(a[1] - a[4])] - ArcTan[(b[1] - d[1])/(a[1] - c[1])] - ArcTan[(b[1] + d[1])/(a[1] - c[1])] - ArcTan[(b[1] - d[2])/(a[1] - c[2])] - ArcTan[(b[1] + d[2])/(a[1] - c[2])] - ArcTan[(b[1] - d[3])/(a[1] - c[3])] - ArcTan[(b[1] + d[3])/(a[1] - c[3])] - ArcTan[(b[1] - d[4])/(a[1] - c[4])] - ArcTan[(b[1] + d[4])/(a[1] - c[4])]] + a[1]*Sin[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + ArcTan[(b[1] + b[2])/(a[1] - a[2])] + ArcTan[(b[1] - b[3])/(a[1] - a[3])] + ArcTan[(b[1] + b[3])/(a[1] - a[3])] + ArcTan[(b[1] - b[4])/(a[1] - a[4])] + ArcTan[(b[1] + b[4])/(a[1] - a[4])] - ArcTan[(b[1] - d[1])/(a[1] - c[1])] - ArcTan[(b[1] + d[1])/(a[1] - c[1])] - ArcTan[(b[1] - d[2])/(a[1] - c[2])] - ArcTan[(b[1] + d[2])/(a[1] - c[2])] - ArcTan[(b[1] - d[3])/(a[1] - c[3])] - ArcTan[(b[1] + d[3])/(a[1] - c[3])] - ArcTan[(b[1] - d[4])/(a[1] - c[4])] - ArcTan[(b[1] + d[4])/(a[1] - c[4])]])* (1 - E^(tpeak1*a[1])* (Cos[tpeak1*b[1]] - ((a[1] - ((a[1]^2 + b[1]^2)* Sin[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + ArcTan[(b[1] + b[2])/(a[1] - a[2])] + ArcTan[(b[1] - b[3])/(a[1] - a[3])] + ArcTan[(b[1] + b[3])/(a[1] - a[3])] + ArcTan[(b[1] - b[4])/(a[1] - a[4])] + ArcTan[(b[1] + b[4])/(a[1] - a[4])] - ArcTan[(b[1] - d[1])/(a[1] - c[1])] - ArcTan[(b[1] + d[1])/(a[1] - c[1])] - ArcTan[(b[1] - d[2])/(a[1] - c[2])] - ArcTan[(b[1] + d[2])/(a[1] - c[2])] - ArcTan[(b[1] - d[3])/(a[1] - c[3])] - ArcTan[(b[1] + d[3])/(a[1] - c[3])] - ArcTan[(b[1] - d[4])/(a[1] - c[4])] - ArcTan[(b[1] + d[4])/(a[1] - c[4])]])/ (b[1]*Cos[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + ArcTan[(b[1] + b[2])/(a[1] - a[2])] + ArcTan[(b[1] - b[3])/(a[1] - a[3])] + ArcTan[(b[1] + b[3])/(a[1] - a[3])] + ArcTan[(b[1] - b[4])/(a[1] - a[4])] + ArcTan[(b[1] + b[4])/(a[1] - a[4])] - ArcTan[(b[1] - d[1])/(a[1] - c[1])] - ArcTan[(b[1] + d[1])/(a[1] - c[1])] - ArcTan[(b[1] - d[2])/(a[1] - c[2])] - ArcTan[(b[1] + d[2])/(a[1] - c[2])] - ArcTan[(b[1] - d[3])/(a[1] - c[3])] - ArcTan[(b[1] + d[3])/(a[1] - c[3])] - ArcTan[(b[1] - d[4])/(a[1] - c[4])] - ArcTan[(b[1] + d[4])/(a[1] - c[4])]] + a[1]*Sin[ArcTan[(b[1] - b[2])/(a[1] - a[2])] + ArcTan[(b[1] + b[2])/(a[1] - a[2])] + ArcTan[(b[1] - b[3])/(a[1] - a[3])] + ArcTan[(b[1] + b[3])/(a[1] - a[3])] + ArcTan[(b[1] - b[4])/(a[1] - a[4])] + ArcTan[(b[1] + b[4])/(a[1] - a[4])] - ArcTan[(b[1] - d[1])/(a[1] - c[1])] - ArcTan[(b[1] + d[1])/(a[1] - c[1])] - ArcTan[(b[1] - d[2])/(a[1] - c[2])] - ArcTan[(b[1] + d[2])/(a[1] - c[2])] - ArcTan[(b[1] - d[3])/(a[1] - c[3])] - ArcTan[(b[1] + d[3])/(a[1] - c[3])] - ArcTan[(b[1] - d[4])/(a[1] - c[4])] - ArcTan[(b[1] + d[4])/(a[1] - c[4])]]))* Sin[tpeak1*b[1]])/b[1])))/ (b[1]*Sqrt[((a[1] - a[2])^2 + (b[1] - b[2])^2)* ((a[1] - a[2])^2 + (b[1] + b[2])^2)* ((a[1] - a[3])^2 + (b[1] - b[3])^2)* ((a[1] - a[3])^2 + (b[1] + b[3])^2)* ((a[1] - a[4])^2 + (b[1] - b[4])^2)* ((a[1] - a[4])^2 + (b[1] + b[4])^2)]*(c[1]^2 + d[1]^2)* (c[2]^2 + d[2]^2)*(c[3]^2 + d[3]^2)*(c[4]^2 + d[4]^2)) + ((a[1]^2 + b[1]^2)*(a[3]^2 + b[3]^2)*(a[4]^2 + b[4]^2)* Sqrt[((a[2] - c[1])^2 + (b[2] - d[1])^2)* ((a[2] - c[1])^2 + (b[2] + d[1])^2)* ((a[2] - c[2])^2 + (b[2] - d[2])^2)* ((a[2] - c[2])^2 + (b[2] + d[2])^2)* ((a[2] - c[3])^2 + (b[2] - d[3])^2)* ((a[2] - c[3])^2 + (b[2] + d[3])^2)* ((a[2] - c[4])^2 + (b[2] - d[4])^2)* ((a[2] - c[4])^2 + (b[2] + d[4])^2)]* (b[2]*Cos[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[2] - b[3])/(a[2] - a[3])] + ArcTan[(b[2] + b[3])/(a[2] - a[3])] + ArcTan[(b[2] - b[4])/(a[2] - a[4])] + ArcTan[(b[2] + b[4])/(a[2] - a[4])] - ArcTan[(b[2] - d[1])/(a[2] - c[1])] - ArcTan[(b[2] + d[1])/(a[2] - c[1])] - ArcTan[(b[2] - d[2])/(a[2] - c[2])] - ArcTan[(b[2] + d[2])/(a[2] - c[2])] - ArcTan[(b[2] - d[3])/(a[2] - c[3])] - ArcTan[(b[2] + d[3])/(a[2] - c[3])] - ArcTan[(b[2] - d[4])/(a[2] - c[4])] - ArcTan[(b[2] + d[4])/(a[2] - c[4])]] + a[2]*Sin[ArcTan[(-b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[1] + b[2])/(-a[1] + a[2])] + ArcTan[(b[2] - b[3])/(a[2] - a[3])] + ArcTan[(b[2] + b[3])/(a[2] - a[3])] + ArcTan[(b[2] - b[4])/(a[2] - a[4])] + ArcTan[(b[2] + b[4])/(a[2] - a[4])] - ArcTan[(b[2] - d[1])/(a[2] - c[1])] - ArcTan[(b[2] + d[1])/(a[2] - c[1])] - ArcTan[(b[2] - d[2])/(a[2] - c[2])] - ArcTan[(b[2] + d[2])/(a[2] - c[2])] - ArcTan[(b[2] - d[3])/(a[2] - c[3])] - ArcTan[(b[2] + d[3])/(a[2] - c[3])] - ArcTan[(b[2] - d[4])/(a[2] - c[4])] - ArcTan[(b[2] + d[4])/(a[2] - c[4])]])* (1 - E^(tpeak1*a[2])* (Cos[tpeak1*b[2]] - 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