Expression 68: "X" equals left parenthesis, "x" minus "h" Subscript, "t" , Baseline , right parenthesis cosine phi Subscript, "t" , Baseline plus left parenthesis, "y" minus "k" Subscript, "t" , Baseline , right parenthesis sine phi Subscript, "t" , BaselineX=x−htcosϕt+y−ktsinϕt
68
Reflector Bottom
69
Full ellipse
70
Expression 71: StartFraction, "X" squared Over "c" squared , EndFraction plus StartFraction, "Y" squared Over "d" squared , EndFraction equals 1 left brace, "F" equals 1 , right braceX20c2l+Y20d2l=1F=1
71
Without constraints
72
Expression 73: StartFraction, "X" squared Over "c" squared , EndFraction plus StartFraction, "Y" squared Over "d" squared , EndFraction equals 1 left brace, "y" less than StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline plus "b" cos theta Subscript, 0 , Baseline plus "a" Over "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" minus "a" plus "O" , right brace left brace, "y" less than negative left parenthesis, tan theta Subscript, 0 , Baseline , right parenthesis to the negative 1st power "x" plus "z" Subscript, 0 , Baseline left parenthesis, tan theta Subscript, 0 , Baseline plus left parenthesis, tan theta Subscript, 0 , Baseline , right parenthesis to the negative 1st power , right parenthesis plus "O" , right brace left brace, "P" equals 1 , right braceX20c2l+Y20d2l=1y<z0tanθ0+bcosθ0+az0−bsinθ0x−a+Oy<−tanθ0−1x+z0tanθ0+tanθ0−1+OP=1
73
Expression 74: StartFraction, "X" squared Over "c" squared , EndFraction plus StartFraction, "Y" squared Over "d" squared , EndFraction equals 1 left brace, "y" less than StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline plus "b" cos theta Subscript, 0 , Baseline plus "a" Over "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" minus "a" plus "O" , right brace left brace, "y" less than negative "b" plus "O" , right brace left brace, "P" equals 1 , right brace left brace, tan theta Subscript, 0 , Baseline equals 0 , right braceX20c2l+Y20d2l=1y<z0tanθ0+bcosθ0+az0−bsinθ0x−a+Oy<−b+OP=1tanθ0=0
74
True Reflector
75
Expression 76: StartFraction, "X" squared Over "c" squared , EndFraction plus StartFraction, "Y" squared Over "d" squared , EndFraction equals 1 left brace, "y" greater than "A" , right brace left brace, "x" greater than "T" , right brace left brace, "y" less than StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline plus "b" cos theta Subscript, 0 , Baseline plus "a" Over "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" minus "a" plus "O" , right brace left brace, "y" less than negative left parenthesis, tan theta Subscript, 0 , Baseline , right parenthesis to the negative 1st power "x" plus "z" Subscript, 0 , Baseline left parenthesis, tan theta Subscript, 0 , Baseline plus left parenthesis, tan theta Subscript, 0 , Baseline , right parenthesis to the negative 1st power , right parenthesis plus "O" , right braceX20c2l+Y20d2l=1y>Ax>Ty<z0tanθ0+bcosθ0+az0−bsinθ0x−a+Oy<−tanθ0−1x+z0tanθ0+tanθ0−1+O
76
Expression 77: StartFraction, "X" squared Over "c" squared , EndFraction plus StartFraction, "Y" squared Over "d" squared , EndFraction equals 1 left brace, "y" greater than "A" , right brace left brace, "x" greater than "T" , right brace left brace, "y" less than StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline plus "b" cos theta Subscript, 0 , Baseline plus "a" Over "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" minus "a" plus "O" , right brace left brace, "y" less than negative "b" plus "O" , right brace left brace, tan theta Subscript, 0 , Baseline equals 0 , right braceX20c2l+Y20d2l=1y>Ax>Ty<z0tanθ0+bcosθ0+az0−bsinθ0x−a+Oy<−b+Otanθ0=0
77
Expression 78: "Y" Subscript, 0 , Baseline equals negative left parenthesis, "x" minus "h" Subscript, "l" , Baseline , right parenthesis sine phi Subscript, "l" , Baseline plus left parenthesis, "y" minus "k" Subscript, "l" , Baseline , right parenthesis cosine phi Subscript, "l" , BaselineY0=−x−hlsinϕl+y−klcosϕl
78
Expression 79: "X" Subscript, 0 , Baseline equals left parenthesis, "x" minus "h" Subscript, "l" , Baseline , right parenthesis cosine phi Subscript, "l" , Baseline plus left parenthesis, "y" minus "k" Subscript, "l" , Baseline , right parenthesis sine phi Subscript, "l" , BaselineX0=x−hlcosϕl+y−klsinϕl
79
Expression 80:
80
Visual help for possible Irradiance (not a physical representation)
81
Expression 82: negative 0.5 greater than "x" greater than negative 0.5 minus StartFraction, "p" Over StartRoot, 2 pi times "q" squared , EndRoot , EndFraction "e" Superscript, negative StartFraction, left parenthesis, "y" minus "O" , right parenthesis squared Over 2 "q" squared , EndFraction , Baseline left brace, negative 2 "a" plus "O" less than "y" less than 2 "a" plus "O" , right brace left brace, "V" equals 1 , right brace left brace, "P" equals 1 , right brace−0.5>x>−0.5−p2π·q2pe−y−O22q2p−2a+O<y<2a+OV=1P=1
82
Expression 83: "q" Subscript, "p" , Baseline equals StartFraction, "a" Over 2 , EndFractionqp=a2
equals=
0.9 30.93
83
Expression 84: negative 0.5 greater than "x" greater than negative 0.5 minus StartFraction, "p" Over StartRoot, 2 pi times "q" squared , EndRoot , EndFraction "e" Superscript, negative StartFraction, left parenthesis, "y" minus "O" , right parenthesis squared Over 2 "q" squared , EndFraction , Baseline left brace, "b" Subscript, "l" , Baseline minus "a" less than "y" less than "b" Subscript, "t" , Baseline plus "a" , right brace left brace, "V" equals 1 , right brace left brace, "P" equals 0 , right brace−0.5>x>−0.5−p2π·q2ce−y−O22q2cbl−a<y<bt+aV=1P=0
Expression 88: negative "l" less than "x" less than 0 left brace, StartAbsoluteValue, "y" , EndAbsoluteValue less than "r" , right brace left brace, "V" equals 1 , right brace−l<x<0y<rV=1
88
Expression 89: "r" equals 20.5r=20.5
00
100100
89
Expression 90: "l" equals 20l=20
00
100100
90
Expression 91:
91
True cutoff line including constraints
92
Expression 93: "y" equals "m" Subscript, "t" 1 , Baseline "x" plus "b" Subscript, "t" 1 , Baseline left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline plus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "t" 1 , Baseline greater than "b" Subscript, "t" 2 , Baseline , right brace left brace, "b" Subscript, "t" 1 , Baseline greater than "O" plus "a" , right bracey=mt1x+bt10<x<z0+bsinθ0P=0bt1>bt2bt1>O+a
93
Expression 94: "y" equals "m" Subscript, "t" 1 , Baseline "x" plus "b" Subscript, "t" 1 , Baseline left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline plus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "t" 1 , Baseline greater than "O" plus "a" , right brace left brace, "B" squared less than 4 times "N" Subscript, "T" , Baseline times "C" Subscript, "T" , Baseline , right bracey=mt1x+bt10<x<z0+bsinθ0P=0bt1>O+aB2T<4·NT·CT
94
Expression 95: "y" equals StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline minus "b" cos theta Subscript, 0 , Baseline minus "a" Over "z" Subscript, 0 , Baseline plus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" plus "a" plus "O" left brace, 0 less than or equal to "x" less than or equal to "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "t" 1 , Baseline greater than "b" Subscript, "t" 2 , Baseline , right brace left brace, "b" Subscript, "t" 1 , Baseline less than "O" plus "a" , right bracey=z0tanθ0−bcosθ0−az0+bsinθ0x+a+O0≤x≤z0−bsinθ0P=0bt1>bt2bt1<O+a
95
Expression 96: "y" equals StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline minus "b" cos theta Subscript, 0 , Baseline minus "a" Over "z" Subscript, 0 , Baseline plus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" plus "a" plus "O" left brace, 0 less than or equal to "x" less than or equal to "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "t" 1 , Baseline less than "O" plus "a" , right brace left brace, "B" squared less than 4 times "N" Subscript, "T" , Baseline times "C" Subscript, "T" , Baseline , right bracey=z0tanθ0−bcosθ0−az0+bsinθ0x+a+O0≤x≤z0−bsinθ0P=0bt1<O+aB2T<4·NT·CT
96
Expression 97: "m" Subscript, "t" 1 , Baseline equals StartFraction, "y" Subscript, "t" 0 , Baseline minus "y" Subscript, "t" 1 , Baseline Over "x" Subscript, "t" 0 , Baseline minus "x" Subscript, "t" 1 , Baseline , EndFractionmt1=yt0−yt1xt0−xt1
Expression 99: "y" equals "m" Subscript, "t" 2 , Baseline "x" plus "b" Subscript, "t" 2 , Baseline left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline plus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "t" 1 , Baseline less than "b" Subscript, "t" 2 , Baseline , right brace left brace, "b" Subscript, "t" 2 , Baseline greater than "O" plus "a" , right bracey=mt2x+bt20<x<z0+bsinθ0P=0bt1<bt2bt2>O+a
99
Expression 100: "y" equals StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline minus "b" cos theta Subscript, 0 , Baseline minus "a" Over "z" Subscript, 0 , Baseline plus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" plus "a" plus "O" left brace, 0 less than or equal to "x" less than or equal to "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "t" 1 , Baseline less than "b" Subscript, "t" 2 , Baseline , right brace left brace, "b" Subscript, "t" 2 , Baseline less than "O" plus "a" , right bracey=z0tanθ0−bcosθ0−az0+bsinθ0x+a+O0≤x≤z0−bsinθ0P=0bt1<bt2bt2<O+a
100
Expression 101: "m" Subscript, "t" 2 , Baseline equals StartFraction, "y" Subscript, "t" 0 , Baseline minus "y" Subscript, "t" 2 , Baseline Over "x" Subscript, "t" 0 , Baseline minus "x" Subscript, "t" 2 , Baseline , EndFractionmt2=yt0−yt2xt0−xt2
Expression 105: "x" Subscript, "t" 1 , Baseline equals "T"xt1=T
equals=
66
105
Expression 106: "y" Subscript, "t" 1 , Baseline equals StartFraction, negative "B" Subscript, "t" , Baseline plus StartRoot, "B" squared minus 4 times "N" Subscript, "t" , Baseline times "C" Subscript, "t" , Baseline , EndRoot Over 2 "N" Subscript, "t" , Baseline , EndFractionyt1=−Bt+B2t−4·Nt·Ct2Nt
equals=
19.2 5 7 9 8 1 6 0 9 819.2579816098
106
Expression 107: "N" Subscript, "t" , Baseline equals StartFraction, cos squared phi Subscript, "t" , Baseline Over "d" squared , EndFraction plus StartFraction, sin squared phi Subscript, "t" , Baseline Over "c" squared , EndFractionNt=cos2ϕtd2t+sin2ϕtc2t
equals=
0.0 9 2 9 0 2 9 9 0 2 7 3 30.0929029902733
107
Expression 108: "B" Subscript, "t" , Baseline equals 2 left parenthesis, "T" minus "h" Subscript, "t" , Baseline , right parenthesis left parenthesis, StartFraction, 1 Over "c" squared , EndFraction minus StartFraction, 1 Over "d" squared , EndFraction , right parenthesis cosine left parenthesis, phi Subscript, "t" , Baseline , right parenthesis sine left parenthesis, phi Subscript, "t" , Baseline , right parenthesis minus 2 "k" Subscript, "t" , Baseline left parenthesis, StartFraction, cos squared phi Subscript, "t" , Baseline Over "d" squared , EndFraction plus StartFraction, sin squared phi Subscript, "t" , Baseline Over "c" squared , EndFraction , right parenthesisBt=2T−ht1c2t−1d2tcosϕtsinϕt−2ktcos2ϕtd2t+sin2ϕtc2t
equals=
negative 3.0 0 9 8 2 3 5 2 5 6 3−3.00982352563
108
Expression 109: "C" Subscript, "t" , Baseline equals left parenthesis, "T" minus "h" Subscript, "t" , Baseline , right parenthesis squared left parenthesis, StartFraction, sin squared phi Subscript, "t" , Baseline Over "d" squared , EndFraction plus StartFraction, cos squared phi Subscript, "t" , Baseline Over "c" squared , EndFraction , right parenthesis minus 1 minus 2 "k" Subscript, "t" , Baseline left parenthesis, StartFraction, 1 Over "c" squared , EndFraction minus StartFraction, 1 Over "d" squared , EndFraction , right parenthesis cosine left parenthesis, phi Subscript, "t" , Baseline , right parenthesis sine left parenthesis, phi Subscript, "t" , Baseline , right parenthesis left parenthesis, "T" minus "h" Subscript, "t" , Baseline , right parenthesis plus "k" squared left parenthesis, StartFraction, cos squared phi Subscript, "t" , Baseline Over "d" squared , EndFraction plus StartFraction, sin squared phi Subscript, "t" , Baseline Over "c" squared , EndFraction , right parenthesisCt=T−ht2sin2ϕtd2t+cos2ϕtc2t−1−2kt1c2t−1d2tcosϕtsinϕtT−ht+k2tcos2ϕtd2t+sin2ϕtc2t
Expression 111: "x" Subscript, "t" 2 , Baseline equals StartFraction, negative "B" Subscript, "T" , Baseline minus StartRoot, "B" squared minus 4 times "N" Subscript, "T" , Baseline times "C" Subscript, "T" , Baseline , EndRoot Over 2 "N" Subscript, "T" , Baseline , EndFractionxt2=−BT−B2T−4·NT·CT2NT
equals=
3.1 8 3 8 6 1 0 5 8 0 63.18386105806
111
Expression 112: "N" Subscript, "T" , Baseline equals StartFraction, sin squared phi Subscript, "t" , Baseline Over "d" squared , EndFraction plus StartFraction, cos squared phi Subscript, "t" , Baseline Over "c" squared , EndFractionNT=sin2ϕtd2t+cos2ϕtc2t
equals=
0.0 7 7 8 5 0 0 3 3 1 4 0 30.0778500331403
112
Expression 113: "B" Subscript, "T" , Baseline equals 2 left parenthesis, "A" minus "k" Subscript, "t" , Baseline , right parenthesis left parenthesis, StartFraction, 1 Over "c" squared , EndFraction minus StartFraction, 1 Over "d" squared , EndFraction , right parenthesis cosine left parenthesis, phi Subscript, "t" , Baseline , right parenthesis sine left parenthesis, phi Subscript, "t" , Baseline , right parenthesis minus 2 "h" Subscript, "t" , Baseline left parenthesis, StartFraction, sin squared phi Subscript, "t" , Baseline Over "d" squared , EndFraction plus StartFraction, cos squared phi Subscript, "t" , Baseline Over "c" squared , EndFraction , right parenthesisBT=2A−kt1c2t−1d2tcosϕtsinϕt−2htsin2ϕtd2t+cos2ϕtc2t
equals=
negative 1.0 2 3 3 7 2 1 3 3 8 6−1.02337213386
113
Expression 114: "C" Subscript, "T" , Baseline equals left parenthesis, "A" minus "k" Subscript, "t" , Baseline , right parenthesis squared left parenthesis, StartFraction, cos squared phi Subscript, "t" , Baseline Over "d" squared , EndFraction plus StartFraction, sin squared phi Subscript, "t" , Baseline Over "c" squared , EndFraction , right parenthesis minus 1 minus 2 "h" Subscript, "t" , Baseline left parenthesis, StartFraction, 1 Over "c" squared , EndFraction minus StartFraction, 1 Over "d" squared , EndFraction , right parenthesis cosine left parenthesis, phi Subscript, "t" , Baseline , right parenthesis sine left parenthesis, phi Subscript, "t" , Baseline , right parenthesis left parenthesis, "A" minus "k" Subscript, "t" , Baseline , right parenthesis plus "h" squared left parenthesis, StartFraction, sin squared phi Subscript, "t" , Baseline Over "d" squared , EndFraction plus StartFraction, cos squared phi Subscript, "t" , Baseline Over "c" squared , EndFraction , right parenthesisCT=A−kt2cos2ϕtd2t+sin2ϕtc2t−1−2ht1c2t−1d2tcosϕtsinϕtA−kt+h2tsin2ϕtd2t+cos2ϕtc2t
equals=
2.4 6 9 1 1 1 1 3 8 1 62.46911113816
114
Expression 115: "y" equals "m" Subscript, "l" 1 , Baseline "x" plus "b" Subscript, "l" 1 , Baseline left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "l" 1 , Baseline less than "b" Subscript, "l" 2 , Baseline , right brace left brace, "b" Subscript, "l" 1 , Baseline less than "O" minus "a" , right bracey=ml1x+bl10<x<z0−bsinθ0P=0bl1<bl2bl1<O−a
115
Expression 116: "y" equals "m" Subscript, "l" 1 , Baseline "x" plus "b" Subscript, "l" 1 , Baseline left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "l" 1 , Baseline less than "O" minus "a" , right brace left brace, "B" squared less than 4 times "N" Subscript, "L" , Baseline times "C" Subscript, "L" , Baseline , right bracey=ml1x+bl10<x<z0−bsinθ0P=0bl1<O−aB2L<4·NL·CL
116
Expression 117: "f" Subscript, "l" , Baseline equals StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline plus "b" cos theta Subscript, 0 , Baseline plus "a" Over "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" minus "a" plus "O" left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "l" 1 , Baseline less than "b" Subscript, "l" 2 , Baseline , right brace left brace, "b" Subscript, "l" 1 , Baseline greater than "O" minus "a" , right bracefl=z0tanθ0+bcosθ0+az0−bsinθ0x−a+O0<x<z0−bsinθ0P=0bl1<bl2bl1>O−a
117
Expression 118: "f" Subscript, "l" , Baseline equals StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline plus "b" cos theta Subscript, 0 , Baseline plus "a" Over "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" minus "a" plus "O" left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "l" 1 , Baseline greater than "O" minus "a" , right brace left brace, "B" squared less than 4 times "N" Subscript, "L" , Baseline times "C" Subscript, "L" , Baseline , right bracefl=z0tanθ0+bcosθ0+az0−bsinθ0x−a+O0<x<z0−bsinθ0P=0bl1>O−aB2L<4·NL·CL
118
Expression 119: "m" Subscript, "l" 1 , Baseline equals StartFraction, "y" Subscript, "l" 0 , Baseline minus "y" Subscript, "l" 1 , Baseline Over "x" Subscript, "l" 0 , Baseline minus "x" Subscript, "l" 1 , Baseline , EndFractionml1=yl0−yl1xl0−xl1
Expression 121: "y" equals "m" Subscript, "l" 2 , Baseline "x" plus "b" Subscript, "l" 2 , Baseline left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "l" 1 , Baseline greater than "b" Subscript, "l" 2 , Baseline , right brace left brace, "b" Subscript, "l" 2 , Baseline less than "O" minus "a" , right bracey=ml2x+bl20<x<z0−bsinθ0P=0bl1>bl2bl2<O−a
121
Expression 122: "f" Subscript, "l" , Baseline equals StartFraction, "z" Subscript, 0 , Baseline tan theta Subscript, 0 , Baseline plus "b" cos theta Subscript, 0 , Baseline plus "a" Over "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , EndFraction "x" minus "a" plus "O" left brace, 0 less than "x" less than "z" Subscript, 0 , Baseline minus "b" sin theta Subscript, 0 , Baseline , right brace left brace, "P" equals 0 , right brace left brace, "b" Subscript, "l" 1 , Baseline greater than "b" Subscript, "l" 2 , Baseline , right brace left brace, "b" Subscript, "l" 2 , Baseline greater than "O" minus "a" , right bracefl=z0tanθ0+bcosθ0+az0−bsinθ0x−a+O0<x<z0−bsinθ0P=0bl1>bl2bl2>O−a
122
Expression 123: "m" Subscript, "l" 2 , Baseline equals StartFraction, "y" Subscript, "l" 0 , Baseline minus "y" Subscript, "l" 2 , Baseline Over "x" Subscript, "l" 0 , Baseline minus "x" Subscript, "l" 2 , Baseline , EndFractionml2=yl0−yl2xl0−xl2
Expression 127: "x" Subscript, "l" 1 , Baseline equals "T"xl1=T
equals=
66
127
Expression 128: "y" Subscript, "l" 1 , Baseline equals StartFraction, negative "B" Subscript, "l" , Baseline minus StartRoot, "B" squared minus 4 times "N" Subscript, "l" , Baseline times "C" Subscript, "l" , Baseline , EndRoot Over 2 "N" Subscript, "l" , Baseline , EndFractionyl1=−Bl−B2l−4·Nl·Cl2Nl
equals=
16.1 5 6 3 6 1 9 3 5 816.1563619358
128
Expression 129: "N" Subscript, "l" , Baseline equals StartFraction, cos squared phi Subscript, "l" , Baseline Over "d" squared , EndFraction plus StartFraction, sin squared phi Subscript, "l" , Baseline Over "c" squared , EndFractionNl=cos2ϕld2l+sin2ϕlc2l
equals=
0.1 1 8 6 8 0 1 9 5 5 0 60.118680195506
129
Expression 130: "B" Subscript, "l" , Baseline equals 2 left parenthesis, "T" minus "h" Subscript, "l" , Baseline , right parenthesis left parenthesis, StartFraction, 1 Over "c" squared , EndFraction minus StartFraction, 1 Over "d" squared , EndFraction , right parenthesis cosine left parenthesis, phi Subscript, "l" , Baseline , right parenthesis sine left parenthesis, phi Subscript, "l" , Baseline , right parenthesis minus 2 "k" Subscript, "l" , Baseline left parenthesis, StartFraction, cos squared phi Subscript, "l" , Baseline Over "d" squared , EndFraction plus StartFraction, sin squared phi Subscript, "l" , Baseline Over "c" squared , EndFraction , right parenthesisBl=2T−hl1c2l−1d2lcosϕlsinϕl−2klcos2ϕld2l+sin2ϕlc2l
equals=
negative 4.4 7 9 5 5 1 5 1 7 2−4.4795515172
130
Expression 131: "C" Subscript, "l" , Baseline equals left parenthesis, "T" minus "h" Subscript, "l" , Baseline , right parenthesis squared left parenthesis, StartFraction, sin squared phi Subscript, "l" , Baseline Over "d" squared , EndFraction plus StartFraction, cos squared phi Subscript, "l" , Baseline Over "c" squared , EndFraction , right parenthesis minus 1 minus 2 "k" Subscript, "l" , Baseline left parenthesis, StartFraction, 1 Over "c" squared , EndFraction minus StartFraction, 1 Over "d" squared , EndFraction , right parenthesis cosine left parenthesis, phi Subscript, "l" , Baseline , right parenthesis sine left parenthesis, phi Subscript, "l" , Baseline , right parenthesis left parenthesis, "T" minus "h" Subscript, "l" , Baseline , right parenthesis plus "k" squared left parenthesis, StartFraction, cos squared phi Subscript, "l" , Baseline Over "d" squared , EndFraction plus StartFraction, sin squared phi Subscript, "l" , Baseline Over "c" squared , EndFraction , right parenthesisCl=T−hl2sin2ϕld2l+cos2ϕlc2l−1−2kl1c2l−1d2lcosϕlsinϕlT−hl+k2lcos2ϕld2l+sin2ϕlc2l
equals=
41.3 9 4 3 9 7 8 7 0 141.3943978701
131
Expression 132: "x" Subscript, "l" 2 , Baseline equals StartFraction, negative "B" Subscript, "L" , Baseline plus StartRoot, "B" squared minus 4 times "N" Subscript, "L" , Baseline times "C" Subscript, "L" , Baseline , EndRoot Over 2 "N" Subscript, "L" , Baseline , EndFractionxl2=−BL+B2L−4·NL·CL2NL
Expression 134: "N" Subscript, "L" , Baseline equals StartFraction, sin squared phi Subscript, "l" , Baseline Over "d" squared , EndFraction plus StartFraction, cos squared phi Subscript, "l" , Baseline Over "c" squared , EndFractionNL=sin2ϕld2l+cos2ϕlc2l
equals=
0.0 6 8 7 6 6 4 6 8 0 6 60.068766468066
134
Expression 135: "B" Subscript, "L" , Baseline equals 2 left parenthesis, "A" minus "k" Subscript, "l" , Baseline , right parenthesis left parenthesis, StartFraction, 1 Over "c" squared , EndFraction minus StartFraction, 1 Over "d" squared , EndFraction , right parenthesis cosine left parenthesis, phi Subscript, "l" , Baseline , right parenthesis sine left parenthesis, phi Subscript, "l" , Baseline , right parenthesis minus 2 "h" Subscript, "l" , Baseline left parenthesis, StartFraction, sin squared phi Subscript, "l" , Baseline Over "d" squared , EndFraction plus StartFraction, cos squared phi Subscript, "l" , Baseline Over "c" squared , EndFraction , right parenthesisBL=2A−kl1c2l−1d2lcosϕlsinϕl−2hlsin2ϕld2l+cos2ϕlc2l
equals=
negative 0.4 7 0 3 1 2 5 4 0 5 8−0.47031254058
135
Expression 136: "C" Subscript, "L" , Baseline equals left parenthesis, "A" minus "k" Subscript, "l" , Baseline , right parenthesis squared left parenthesis, StartFraction, cos squared phi Subscript, "l" , Baseline Over "d" squared , EndFraction plus StartFraction, sin squared phi Subscript, "l" , Baseline Over "c" squared , EndFraction , right parenthesis minus 1 minus 2 "h" Subscript, "l" , Baseline left parenthesis, StartFraction, 1 Over "c" squared , EndFraction minus StartFraction, 1 Over "d" squared , EndFraction , right parenthesis cosine left parenthesis, phi Subscript, "l" , Baseline , right parenthesis sine left parenthesis, phi Subscript, "l" , Baseline , right parenthesis left parenthesis, "A" minus "k" Subscript, "l" , Baseline , right parenthesis plus "h" squared left parenthesis, StartFraction, sin squared phi Subscript, "l" , Baseline Over "d" squared , EndFraction plus StartFraction, cos squared phi Subscript, "l" , Baseline Over "c" squared , EndFraction , right parenthesisCL=A−kl2cos2ϕld2l+sin2ϕlc2l−1−2hl1c2l−1d2lcosϕlsinϕlA−kl+h2lsin2ϕld2l+cos2ϕlc2l