1# ___________________________________________________________________________ 2# 3# Pyomo: Python Optimization Modeling Objects 4# Copyright 2017 National Technology and Engineering Solutions of Sandia, LLC 5# Under the terms of Contract DE-NA0003525 with National Technology and 6# Engineering Solutions of Sandia, LLC, the U.S. Government retains certain 7# rights in this software. 8# This software is distributed under the 3-clause BSD License. 9# ___________________________________________________________________________ 10 11# If a user doesn't have numpy the needed collocation values can be read from 12# the following dictionaries for up to 10 collocation points. 13 14radau_tau_dict = dict() 15radau_adot_dict = dict() 16radau_adotdot_dict = dict() 17 18radau_tau_dict[1] = [0.00000000000000000, 1.00000000000000000, ] 19radau_adot_dict[1] = [[-1.00000000000000000, -1.00000000000000000, ], 20 [1.00000000000000000, 1.00000000000000000, ]] 21radau_adotdot_dict[1] = [[0.00000000000000000, 0.00000000000000000, ], 22 [0.00000000000000000, 0.00000000000000000, ]] 23 24radau_tau_dict[2] = [0.00000000000000000, 0.33333333333333331, 25 1.00000000000000000, ] 26radau_adot_dict[2] = [[-4.00000000000000000, -2.00000000000000000, 27 2.00000000000000000, ], 28 [4.49999999999999911, 1.50000000000000000, 29 -4.49999999999999911, ], 30 [-0.49999999999999994, 0.49999999999999983, 31 2.49999999999999956, ]] 32radau_adotdot_dict[2] = [[6.00000000000000000, 6.00000000000000000, 33 6.00000000000000000, ], 34 [-8.99999999999999822, -8.99999999999999822, 35 -8.99999999999999822, ], 36 [2.99999999999999956, 2.99999999999999956, 37 2.99999999999999956, ]] 38 39radau_tau_dict[3] = [0.00000000000000000, 0.15505102572168220, 40 0.64494897427831788, 1.00000000000000000, ] 41radau_adot_dict[3] = [[-9.00000000000000000, -4.13938769133981310, 42 1.73938769133981630, -2.99999999999999289, ], 43 [10.04880939982741417, 3.22474487139158850, 44 -3.56784008469040437, 5.53197264742180472, ], 45 [-1.38214273316074876, 1.16784008469040512, 46 0.77525512860840951, -7.53197264742180739, ], 47 [0.33333333333333343, -0.25319726474218079, 48 1.05319726474218167, 5.00000000000000089, ]] 49radau_adotdot_dict[3] = [[36.00000000000000000, 26.69693845669907262, 50 -2.69693845669906551, -23.99999999999998579, ], 51 [-51.25918289415326967, -36.76428546632148908, 52 9.03367350481121889, 42.22550938934205078, ], 53 [20.59251622748660893, 12.29965982852211681, 54 -13.90238120034517166, -32.89217605600872218, ], 55 [-5.33333333333333393, -2.23231281889968969, 56 7.56564615223302539, 14.66666666666666963, ]] 57 58radau_tau_dict[4] = [0.00000000000000000, 0.08858795951270398, 59 0.40946686444073388, 0.78765946176084856, 60 1.00000000000000000, ] 61radau_adot_dict[4] = [[-16.00000000000000000, -7.15559202347522572, 62 2.50822508194848126, -1.96487795643240304, 63 4.00000000000000000, ], 64 [17.80758523451450515, 5.64410787595007868, 65 -5.04921463839143314, 3.49246615862542953, 66 -6.92348825644540966, ], 67 [-2.37791303706810631, 1.92350727705471236, 68 1.22110002889472469, -3.98451789578249116, 69 6.59523766962805347, ], 70 [0.82032780255359539, -0.58590148210381310, 71 1.75468098876082568, 0.63479209515516966, 72 -12.17174941318265979, ], 73 [-0.25000000000000150, 0.17387835257424678, 74 -0.43479146121258294, 1.82213759843428735, 75 8.50000000000003375, ]] 76radau_adotdot_dict[4] = [[120.00000000000002842, 80.77386659356440646, 77 -6.12558744008319422, 2.49457798937631026, 78 59.99999999999991473, ], 79 [-167.81099920936088665, -108.53014807707648970, 80 19.13996123354024803, -5.55774820017956017, 81 -102.50641734094637059, ], 82 [64.47853847308765296, 33.70195692546346322, 83 -24.04456776658558681, 16.01268812735257541, 84 89.78248626844741409, ], 85 [-24.16753926372676275, -8.29000996475936880, 86 13.56458045001081913, -32.42528415633811534, 87 -92.27606892750115719, ], 88 [7.50000000000004352, 2.34433452280806431, 89 -2.53438647688229590, 19.47576623978871879, 90 45.00000000000021316, ]] 91 92radau_tau_dict[5] = [0.00000000000000000, 0.05710419611451772, 93 0.27684301363812430, 0.58359043236891450, 94 0.86024013565621971, 1.00000000000000000, ] 95radau_adot_dict[5] = [[-24.99999999999998934, -11.03867924120895161, 96 3.58306852250104768, -2.34417155790386644, 97 2.28263550020568218, -4.99999999999998934, ], 98 [27.78093394406463190, 8.75592397793835531, 99 -7.16138072014532057, 4.12216524624339797, 100 -3.87866321972407846, 8.41242422359434627, ], 101 [-3.64147849804922608, 2.89194261538012576, 102 1.80607772408358258, -4.49601712581350110, 103 3.39315191806494454, -6.97025611665680067, ], 104 [1.25254772116912538, -0.87518639620026994, 105 2.36379717606862361, 0.85676524539728360, 106 -5.18834090640715306, 8.77711420415049659, ], 107 [-0.59200316718453727, 0.39970520793996167, 108 -0.86590078028312090, 2.51832094921101479, 109 0.58123305258075575, -18.21928231108803686, ], 110 [0.19999999999999910, -0.13370616384921521, 111 0.27433807777519198, -0.65706275713435502, 112 2.80998365527971972, 12.99999999999998046, ]] 113radau_adotdot_dict[5] = [[299.99999999999988631, 193.30767250574382388, 114 -12.94260048470914626, 4.01680944012088048, 115 -2.65348639942789077, -120.00000000000011369, ], 116 [-416.05571460180254917, -256.99169401863719031, 117 39.31282295335989829, -8.59570089776997293, 118 5.14998177149959702, 200.87922525110633387, ], 119 [155.76675211023618317, 76.96489565450156078, 120 -45.97406446951362113, 21.61006933401930041, 121 -7.68796759900843085, -161.94936171559132276, ], 122 [-58.33482863565966170, -18.65076273063174028, 123 23.95041306691950922, -35.27049804403287681, 124 31.47710816272410739, 186.04880918852478544, ], 125 [28.22379112722612859, 7.99493810747577882, 126 -6.09624628722275475, 22.52106574808429329, 127 -69.76374346781608438, -212.97867272403951233, ], 128 [-9.59999999999995346, -2.62504951845222578, 129 1.74967522116616792, -4.28174558042124787, 130 43.47810753202831080, 107.99999999999987210, ]] 131 132radau_tau_dict[6] = [0.00000000000000000, 0.03980985705146874, 133 0.19801341787360807, 0.43797481024738633, 134 0.69546427335363914, 0.90146491420116948, 135 1.00000000000000000, ] 136radau_adot_dict[6] = [[-36.00000000000000711, -15.78653932217885725, 137 4.92210694074628208, -2.96075238465032697, 138 2.43407205775748992, -2.63456859759603645, 139 6.00000000000010658, ], 140 [39.96978645997430846, 12.55970347629152073, 141 -9.80283871256804673, 5.18215783855881540, 142 -4.10823909345830174, 4.38578506340130758, 143 -9.94297742192795653, ], 144 [-5.18155025366218513, 4.07582598887629377, 145 2.52508140796374825, -5.54452290952744065, 146 3.49150290911372618, -3.46400504745112281, 147 7.67606215723310026, ], 148 [1.76075790144825750, -1.21720380846425580, 149 3.13222586264732650, 1.14161816684750228, 150 -5.06987875099333429, 3.95154245658764758, 151 -8.23273712821850268, ], 152 [-0.84940911985935841, 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6.00595681392809411, 175 264.87167990774685222, ], 176 [-118.73411607342019636, -36.68950585393311314, 177 41.92433232904805607, -50.48791488764605617, 178 32.08939067396651978, -12.66778060664290706, 179 -275.31458997144886780, ], 180 [58.71474561680227566, 15.95063527339483755, 181 -10.49847307491926074, 29.90013111545132318, 182 -57.34807867927669633, 58.56656747411289388, 183 354.19642620195918425, ], 184 [-32.59360830764193651, -8.42709970780833828, 185 4.60480310763264100, -7.77295210269013381, 186 38.56768819963112804, -135.50588398238815557, 187 -428.24045246523792230, ], 188 [11.66666666666629837, 2.96739341632510722, 189 -1.52801378606603855, 2.24641791473642805, 190 -7.41642014213210032, 85.99333233918015651, 191 221.66666666666105812, ]] 192 193radau_tau_dict[7] = [0.00000000000000000, 0.02931642715978489, 194 0.14807859966848425, 0.33698469028114536, 195 0.55867151877159871, 0.76923386202996824, 196 0.92694567131978900, 1.00000000000000000, ] 197radau_adot_dict[7] = [[-49.00000000000001421, -21.39849085856454991, 198 6.51502179852680996, -3.73823715601904638, 199 2.82962981889280485, -2.61247344089161970, 200 3.00318659221646556, -6.99999999999705835, ], 201 [54.37443689412862113, 17.05528430442161181, 202 -12.94898869881147618, 6.52679743370207177, 203 -4.76041564316764010, 4.32945101663698750, 204 -4.94362383351764834, 11.49545520510287133, ], 205 [-7.00002400425923099, 5.47529951218552391, 206 3.37658514545231903, -6.91230492548291586, 207 3.99086031809394370, -3.35352800168034548, 208 3.70480267602441060, -8.51707242305759848, ], 209 [2.35566109198741191, -1.61858110519068976, 210 4.05401350392539683, 1.48374693100539568, 211 -5.66068833365461455, 3.69061793186311915, 212 -3.74572843137643474, 8.38103130196178014, ], 213 [-1.13228906610625679, 0.74965412823858335, 214 -1.48631397600665593, 3.59460335445588974, 215 0.89498029378042587, -6.03730918727312726, 216 4.78166562576183818, -10.03344165195551696, ], 217 [0.64689132676740668, 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1.19387569800088045, 598 -1.29555622403296056, 1.87654198775976155, 599 -3.60884808750712338, 9.79809219080568994, 600 -44.97321472272450649, 620.42461854547525490, 601 1683.00000001738249011, ]] 602 603 604legendre_tau_dict = dict() 605legendre_adot_dict = dict() 606legendre_adotdot_dict = dict() 607legendre_afinal_dict = dict() 608 609legendre_tau_dict[1] = [0.00000000000000000, 0.50000000000000000, ] 610legendre_adot_dict[1] = [[-2.00000000000000000, -2.00000000000000000, ], 611 [2.00000000000000000, 2.00000000000000000, ]] 612legendre_adotdot_dict[1] = [[0.00000000000000000, 0.00000000000000000, ], 613 [0.00000000000000000, 0.00000000000000000, ]] 614legendre_afinal_dict[1] = [-1.00000000000000000, 2.00000000000000000, ] 615 616legendre_tau_dict[2] = [0.00000000000000000, 0.21132486540518713, 617 0.78867513459481287, ] 618legendre_adot_dict[2] = [[-6.00000000000000000, -3.46410161513775439, 619 3.46410161513775350, ], 620 [6.46410161513775350, 2.99999999999999867, 621 -6.46410161513775527, ], 622 [-0.46410161513775472, 0.46410161513775461, 623 3.00000000000000000, ]] 624legendre_adotdot_dict[2] = [[12.00000000000000000, 12.00000000000000000, 625 12.00000000000000000, ], 626 [-16.39230484541326405, -16.39230484541326405, 627 -16.39230484541326405, ], 628 [4.39230484541326405, 4.39230484541326405, 629 4.39230484541326405, ]] 630legendre_afinal_dict[2] = [1.00000000000000000, -1.73205080756887853, 631 1.73205080756887719, ] 632 633legendre_tau_dict[3] = [0.00000000000000000, 0.11270166537925834, 634 0.49999999999999989, 0.88729833462074226, ] 635legendre_adot_dict[3] = [[-11.99999999999999645, -5.99999999999999822, 636 3.00000000000000000, -6.00000000000001421, ], 637 [13.12163891034569119, 4.99999999999999645, 638 -5.72748612183952233, 10.16397779494323395, ], 639 [-1.33333333333333304, 1.16397779494322196, 640 2.00000000000000533, -9.16397779494322151, ], 641 [0.21169442298763785, -0.16397779494322201, 642 0.72748612183951156, 4.99999999999999289, ]] 643legendre_adotdot_dict[3] = [[59.99999999999997158, 46.47580015448897939, 644 0.00000000000002842, -46.47580015448902202, ], 645 [-82.06316679540748282, -62.06316679540748993, 646 6.66666666666661456, 75.39650012874085405, ], 647 [26.66666666666665009, 17.65053343632599336, 648 -13.33333333333329307, -44.31720010299263635, ], 649 [-4.60349987125914950, -2.06316679540749437, 650 6.66666666666664476, 15.39650012874080076, ]] 651legendre_afinal_dict[3] = [-0.99999999999999645, 1.66666666666665364, 652 -1.33333333333332416, 1.66666666666666163, ] 653 654legendre_tau_dict[4] = [0.00000000000000000, 0.06943184420297367, 655 0.33000947820757198, 0.66999052179243102, 656 0.93056815579702290, ] 657legendre_adot_dict[4] = [[-20.00000000000000355, -9.43327565893721243, 658 3.72430573391146424, -3.72430573391140385, 659 9.43327565893692110, ], 660 [21.98973890127313524, 7.73861278752584170, 661 -7.20134099970690400, 6.34362221862489939, 662 -15.56386959855438334, ], 663 [-2.46548206404896098, 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39.88281996479484093, ]] 687legendre_afinal_dict[4] = [1.00000000000005329, -1.64070532173932548, 688 1.21439396979861636, -1.21439396979864811, 689 1.64070532173930372, ] 690 691legendre_tau_dict[5] = [0.00000000000000000, 0.04691007703066801, 692 0.23076534494715878, 0.49999999999999767, 693 0.76923465505284816, 0.95308992296932671, ] 694legendre_adot_dict[5] = [[-29.99999999999999645, -13.74066696148972966, 695 4.85177807260082616, -3.75000000000000355, 696 4.85177807260098248, -13.74066696148843292, ], 697 [33.07195697163451342, 11.18330013267038581, 698 -9.44759960151609590, 6.42011650355944496, 699 -8.01592078481075987, 22.42091502590413299, ], 700 [-3.87041820427842742, 3.13131216201181450, 701 2.81669986732958266, -6.22012045466986141, 702 6.19052235495304970, -16.19339023999791749, ], 703 [1.06666666666666399, -0.75873179598080620, 704 2.21788633227481746, 2.00000000000017453, 705 -7.39311627638205326, 15.41544322156842561, ], 706 [-0.34832238831592910, 0.23910122335368422, 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