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alTmp.010
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(1) degrees off
(2) autoz on
(3) Newtonian N
(4) Bodies DiskA, DiskB
(5) bodies FakeA, FakeB
(6) points ahat,bhat
(7) points fakeahat, fakebhat
(8) motionvariables' u', fakeu{6}'
(9) variables e{4}',posa{3}',posb{3}',ke,pe,cahat{3}',cbhat{3}', q{3}'
(10) variables u{6}
(11) variables aforce{3},bforce{3}
(12) variables fakee{4}'
(13) constants l,rad,a,qq{3}, gamma
(14) l = sqrt(2) * rad * gamma
-> (15) l = 1.414214*gamma*rad
(16) a = pi/2
-> (17) a = 1.570796
(18) mass diska = m
(19) mass diskb = m
(20) inertia diska,m*rad*rad/4,m*rad*rad/4,m*rad*rad/2
-> (21) Z1 = m*rad^2
-> (22) I_diska_diskaO>> = 0.25*Z1*DiskA1>*DiskA1> + 0.25*Z1*DiskA2>*DiskA2> +
0.5*Z1*DiskA3>*DiskA3>
(23) inertia diskb,m*rad*rad/4,m*rad*rad/4,m*rad*rad/2
-> (24) I_diskb_diskbO>> = 0.25*Z1*DiskB1>*DiskB1> + 0.25*Z1*DiskB2>*DiskB2> +
0.5*Z1*DiskB3>*DiskB3>
(25) mass fakea = m
(26) mass fakeb = m
(27) inertia fakea,m*rad*rad/4,m*rad*rad/4,m*rad*rad/2
-> (28) I_fakea_fakeaO>> = 0.25*Z1*FakeA1>*FakeA1> + 0.25*Z1*FakeA2>*FakeA2> +
0.5*Z1*FakeA3>*FakeA3>
(29) inertia fakeb,m*rad*rad/4,m*rad*rad/4,m*rad*rad/2
-> (30) I_fakeb_fakebO>> = 0.25*Z1*FakeB1>*FakeB1> + 0.25*Z1*FakeB2>*FakeB2> +
0.5*Z1*FakeB3>*FakeB3>
(31) dircos(N,DiskA,Euler,e1,e2,e3,e4)
-> (32) Z2 = 1 - 2*e2^2 - 2*e3^2
-> (33) Z3 = 2*e1*e2 - 2*e3*e4
-> (34) Z4 = 2*e1*e3 + 2*e2*e4
-> (35) Z5 = 2*e1*e2 + 2*e3*e4
-> (36) Z6 = 1 - 2*e1^2 - 2*e3^2
-> (37) Z7 = 2*e2*e3 - 2*e1*e4
-> (38) Z8 = 2*e1*e3 - 2*e2*e4
-> (39) Z9 = 2*e1*e4 + 2*e2*e3
-> (40) Z10 = 1 - 2*e1^2 - 2*e2^2
-> (41) N_DiskA = [Z2, Z3, Z4; Z5, Z6, Z7; Z8, Z9, Z10]
(42) dircos(DiskA,DiskB,body123,pi/2,0,0)
-> (43) DiskA_DiskB = [1, 0, 0; 0, 0, -1; 0, 1, 0]
(44) dircos(N,fakeA,Euler,fakee1,fakee2,fakee3,fakee4)
-> (45) Z11 = 1 - 2*fakee2^2 - 2*fakee3^2
-> (46) Z12 = 2*fakee1*fakee2 - 2*fakee3*fakee4
-> (47) Z13 = 2*fakee1*fakee3 + 2*fakee2*fakee4
-> (48) Z14 = 2*fakee1*fakee2 + 2*fakee3*fakee4
-> (49) Z15 = 1 - 2*fakee1^2 - 2*fakee3^2
-> (50) Z16 = 2*fakee2*fakee3 - 2*fakee1*fakee4
-> (51) Z17 = 2*fakee1*fakee3 - 2*fakee2*fakee4
-> (52) Z18 = 2*fakee1*fakee4 + 2*fakee2*fakee3
-> (53) Z19 = 1 - 2*fakee1^2 - 2*fakee2^2
-> (54) N_fakeA = [Z11, Z12, Z13; Z14, Z15, Z16; Z17, Z18, Z19]
(55) dircos(fakeA,fakeB,body123,pi/2,0,0)
-> (56) fakeA_fakeB = [1, 0, 0; 0, 0, -1; 0, 1, 0]
(57) %gamma is l/sqrt(2)/r
(58) p_diskao_ahat> = rad * unitvec(dot(diska3>,n3>)*diska3>-n3>)
-> (59) Z20 = 1 - Z10^2
-> (60) Z21 = Z20^0.5
-> (61) Z22 = Z10/Z21
-> (62) Z23 = 1/Z21
-> (63) Z24 = rad*Z22
-> (64) Z25 = rad*Z23
-> (65) p_diskao_ahat> = Z24*DiskA3> - Z25*N3>
(66) p_diskbo_bhat> = rad * unitvec(dot(diskb3>,n3>)*diskb3>-n3>)
-> (67) DiskB_N = [Z2, Z5, Z8; Z4, Z7, Z10; -Z3, -Z6, -Z9]
-> (68) Z26 = 1 - Z9^2
-> (69) Z27 = Z26^0.5
-> (70) Z28 = Z9/Z27
-> (71) Z29 = 1/Z27
-> (72) Z30 = rad*Z28
-> (73) Z31 = rad*Z29
-> (74) p_diskbo_bhat> = -Z30*DiskB3> - Z31*N3>
(75) p_diskao_diskbo> = -l * diska1>
-> (76) p_diskao_diskbo> = -l*DiskA1>
(77) p_fakeao_fakeahat> = rad * unitvec(dot(fakea3>,n3>)*fakea3>-n3>)
-> (78) Z32 = 1 - Z19^2
-> (79) Z33 = Z32^0.5
-> (80) Z34 = Z19/Z33
-> (81) Z35 = 1/Z33
-> (82) Z36 = rad*Z34
-> (83) Z37 = rad*Z35
-> (84) p_fakeao_fakeahat> = Z36*FakeA3> - Z37*N3>
(85) p_fakebo_fakebhat> = rad * unitvec(dot(fakeb3>,n3>)*fakeb3>-n3>)
-> (86) FakeB_N = [Z11, Z14, Z17; Z13, Z16, Z19; -Z12, -Z15, -Z18]
-> (87) Z38 = 1 - Z18^2
-> (88) Z39 = Z38^0.5
-> (89) Z40 = Z18/Z39
-> (90) Z41 = 1/Z39
-> (91) Z42 = rad*Z40
-> (92) Z43 = rad*Z41
-> (93) p_fakebo_fakebhat> = -Z42*FakeB3> - Z43*N3>
(94) p_fakeao_fakebo> = -l * fakea1>
-> (95) p_fakeao_fakebo> = -l*FakeA1>
(96) w_diska_n> = u * unitvec(p_ahat_bhat>)
-> (97) Z44 = Z25 - Z31
-> (98) Z45 = l^2
-> (99) Z46 = Z45 + Z24^2 + Z30^2 + Z44^2 + 2*Z9*Z30*Z44 - 2*l*Z8*Z44 - 2*Z10*
Z24*Z44
-> (100) Z47 = Z46^0.5
-> (101) Z48 = Z24/Z47
-> (102) Z49 = Z44/Z47
-> (103) Z50 = l/Z47
-> (104) Z51 = Z30/Z47
-> (105) Z52 = Z8*Z49 - Z50
-> (106) Z53 = Z51 + Z9*Z49
-> (107) Z54 = Z10*Z49 - Z48
-> (108) w_diska_n> = Z52*u*DiskA1> + Z53*u*DiskA2> + Z54*u*DiskA3>
(109) w_diskb_diska> = 0>
-> (110) w_diskb_diska> = 0>
(111) w_fakea_n> = fakeu1 * fakea1> + fakeu2 * fakea2> + fakeu3 * fakea3>
-> (112) w_fakea_n> = fakeu1*FakeA1> + fakeu2*FakeA2> + fakeu3*FakeA3>
(113) w_fakeb_fakea> = 0>
-> (114) w_fakeb_fakea> = 0>
(115) kindiffs(N,DiskA,Euler,e1,e2,e3,e4)
-> (116) Z55 = e2*Z54 + e4*Z52 - e3*Z53
-> (117) e1' = 0.5*Z55*u
-> (118) Z56 = e3*Z52 + e4*Z53 - e1*Z54
-> (119) e2' = 0.5*Z56*u
-> (120) Z57 = e1*Z53 + e4*Z54 - e2*Z52
-> (121) e3' = 0.5*Z57*u
-> (122) Z58 = e1*Z52 + e2*Z53 + e3*Z54
-> (123) e4' = -0.5*Z58*u
(124) kindiffs(N,FakeA,Euler,fakee1,fakee2,fakee3,fakee4)
-> (125) fakee1' = 0.5*fakee2*fakeu3 + 0.5*fakee4*fakeu1 - 0.5*fakee3*fakeu2
-> (126) fakee2' = 0.5*fakee3*fakeu1 + 0.5*fakee4*fakeu2 - 0.5*fakee1*fakeu3
-> (127) fakee3' = 0.5*fakee1*fakeu2 + 0.5*fakee4*fakeu3 - 0.5*fakee2*fakeu1
-> (128) fakee4' = -0.5*fakee1*fakeu1 - 0.5*fakee2*fakeu2 - 0.5*fakee3*fakeu3
(129) v_ahat_n> = 0>
-> (130) v_ahat_n> = 0>
(131) v_diskao_n> = v_ahat_n> + cross(w_diska_n>,p_ahat_diskao>)
-> (132) Z59 = Z24*Z53
-> (133) Z60 = Z24*Z52
-> (134) Z61 = Z25*(Z5*Z52+Z6*Z53+Z7*Z54)
-> (135) Z62 = Z25*(Z2*Z52+Z3*Z53+Z4*Z54)
-> (136) v_diskao_n> = -Z59*u*DiskA1> + Z60*u*DiskA2> + Z61*u*N1> - Z62*u*N2>
(137) v_diskbo_n> = v_diskao_n> + cross(w_diska_n>,p_diskao_diskbo>)
-> (138) Z63 = Z60 - l*Z54
-> (139) Z64 = l*Z53
-> (140) v_diskbo_n> = -Z59*u*DiskA1> + Z63*u*DiskA2> + Z64*u*DiskA3> + Z61*u*
N1> - Z62*u*N2>
(141) v_bhat_n> = 0>
-> (142) v_bhat_n> = 0>
(143) v_fakeao_n> = fakeu4 * n1> + fakeu5 * n2> + fakeu6 * n3>
-> (144) v_fakeao_n> = fakeu4*N1> + fakeu5*N2> + fakeu6*N3>
(145) v_fakebo_n> = v_fakeao_n> + cross(w_fakea_n>,p_fakeao_fakebo>)
-> (146) v_fakebo_n> = -l*fakeu3*FakeA2> + l*fakeu2*FakeA3> + fakeu4*N1> + fak
eu5*N2> + fakeu6*N3>
(147) v_fakeahat_n> = v_fakeao_n> + cross(w_fakea_n>,p_fakeao_fakeahat>)
-> (148) Z65 = Z14*Z37
-> (149) Z66 = Z15*Z37
-> (150) Z67 = Z16*Z37
-> (151) Z68 = Z11*Z37
-> (152) Z69 = Z12*Z37
-> (153) Z70 = Z13*Z37
-> (154) v_fakeahat_n> = Z36*fakeu2*FakeA1> - Z36*fakeu1*FakeA2> + (fakeu4-Z65*
fakeu1-Z66*fakeu2-Z67*fakeu3)*N1> + (fakeu5+Z68*fakeu1+Z69*fakeu2+Z70*
fakeu3)*N2> + fakeu6*N3>
(155) v_fakebhat_n> = v_fakebo_n> + cross(w_fakea_n>,p_fakebo_fakebhat>)
-> (156) Z71 = Z14*Z43
-> (157) Z72 = Z15*Z43
-> (158) Z73 = Z16*Z43
-> (159) Z74 = Z11*Z43
-> (160) Z75 = Z12*Z43
-> (161) Z76 = Z13*Z43
-> (162) v_fakebhat_n> = -l*fakeu3*FakeA2> + l*fakeu2*FakeA3> - Z42*fakeu3*Fak
eB1> + Z42*fakeu1*FakeB2> + (fakeu4-Z71*fakeu1-Z72*fakeu2-Z73*fakeu3)*
N1> + (fakeu5+Z74*fakeu1+Z75*fakeu2+Z76*fakeu3)*N2> + fakeu6*N3>
(163) u1 = dot(w_diska_n>,diska1>)
-> (164) u1 = Z52*u
(165) u2 = dot(w_diska_n>,diska2>)
-> (166) u2 = Z53*u
(167) u3 = dot(w_diska_n>,diska3>)
-> (168) u3 = Z54*u
(169) u4 = dot(v_diskao_n>, n1>)
-> (170) u4 = -(Z2*Z59-Z61-Z3*Z60)*u
(171) u5 = dot(v_diskao_n>, n2>)
-> (172) u5 = -(Z62+Z5*Z59-Z6*Z60)*u
(173) u6 = dot(v_diskao_n>, n3>)
-> (174) u6 = -(Z8*Z59-Z9*Z60)*u
(175) gravity(-9.81*n3>)
-> (176) FORCE_DiskAO> = -9.81*m*N3>
-> (177) FORCE_DiskBO> = -9.81*m*N3>
-> (178) FORCE_FakeAO> = -9.81*m*N3>
-> (179) FORCE_FakeBO> = -9.81*m*N3>
(180) force_fakeahat> = aforce1 * n1> + aforce2 * n2> + aforce3 * n3>
-> (181) force_fakeahat> = aforce1*N1> + aforce2*N2> + aforce3*N3>
(182) force_fakebhat> = bforce1 * n1> + bforce2 * n2> + bforce3 * n3>
-> (183) force_fakebhat> = bforce1*N1> + bforce2*N2> + bforce3*N3>
(184) %autoz on
(185) zee_not=[aforce1,aforce2,aforce3,bforce1,bforce2,bforce3]
-> (186) zee_not = [aforce1, aforce2, aforce3, bforce1, bforce2, bforce3]
(187) zero = fr() + frstar()
-> (188) Z77 = m*(2*Z8*Z59-Z9*Z60-Z9*Z63-Z10*Z64)
-> (189) Z78 = Z68 - Z15*Z36
-> (190) Z79 = -Z65 - Z12*Z36
-> (191) Z80 = Z18*Z36
-> (192) Z81 = Z74 + Z16*Z42
-> (193) Z82 = Z13*Z42 - Z71
-> (194) Z83 = Z19*Z42
-> (195) Z84 = Z69 + Z14*Z36
-> (196) Z85 = Z11*Z36 - Z66
-> (197) Z86 = Z17*Z36
-> (198) Z87 = Z75 + l*Z16
-> (199) Z88 = l*Z13 - Z72
-> (200) Z89 = l*Z19
-> (201) Z90 = l*m
-> (202) Z91 = Z90*Z19
-> (203) Z92 = Z76 - l*Z15 - Z14*Z42
-> (204) Z93 = -Z73 - l*Z12 - Z11*Z42
-> (205) Z94 = -l*Z18 - Z17*Z42
-> (206) Z95 = Z90*Z18
-> (207) Z96 = Z52*u
-> (208) Z97 = Z53*u
-> (209) Z98 = Z54*u
-> (210) Z99 = (e1*Z57+e2*Z58+e3*Z55-e4*Z56)*u
-> (211) Z100 = (e1*Z55+e2*Z56)*u
-> (212) Z101 = Z10*Z100/Z20^0.5
-> (213) Z102 = rad*Z101/Z21^2
-> (214) Z103 = (e1*Z58-e2*Z57-e3*Z56-e4*Z55)*u
-> (215) Z104 = Z9*Z103/Z26^0.5
-> (216) Z105 = rad*Z104/Z27^2
-> (217) Z106 = (Z10*Z101+Z21*Z100)/Z21^2
-> (218) Z107 = (Z9*Z104+Z27*Z103)/Z27^2
-> (219) Z108 = 4*Z24*Z44*Z100 + 4*rad*Z10*Z44*Z106 + 2*l*Z8*(2*Z102-Z105) + 2*
Z10*Z24*(2*Z102-Z105) - 4*rad*Z24*Z106 - 2*l*Z44*Z99 - 2*rad*Z30*Z107
- 2*Z30*Z44*Z103 - 2*rad*Z9*Z44*Z107 - 2*Z44*(2*Z102-Z105) - 2*Z9*Z30*
(2*Z102-Z105)
-> (220) Z109 = (Z44*Z108/Z46^0.5+2*Z47*(2*Z102-Z105))/Z47^2
-> (221) Z110 = l*Z108/(Z46^0.5*Z47^2)
-> (222) Z111 = 0.5*Z110 + Z49*Z99 - 0.5*Z8*Z109
-> (223) Z112 = u*Z111
-> (224) Z113 = (2*rad*Z47*Z107+Z30*Z108/Z46^0.5)/Z47^2
-> (225) Z114 = -0.5*Z113 - Z49*Z103 - 0.5*Z9*Z109
-> (226) Z115 = u*Z114
-> (227) Z116 = (4*rad*Z47*Z106+Z24*Z108/Z46^0.5)/Z47^2
-> (228) Z117 = 0.5*Z116 - 2*Z49*Z100 - 0.5*Z10*Z109
-> (229) Z118 = u*Z117
-> (230) Z119 = Z1*Z96
-> (231) Z120 = Z1*Z97
-> (232) Z121 = Z1*Z98
-> (233) Z122 = Z1*Z52
-> (234) Z123 = Z1*Z112
-> (235) Z124 = Z1*Z53
-> (236) Z125 = Z1*Z115
-> (237) Z126 = Z1*Z54
-> (238) Z127 = Z1*Z118
-> (239) Z128 = 0.25*Z96*Z120 - 0.25*Z97*Z119
-> (240) Z129 = 0.25*Z98*Z119 - 0.5*Z96*Z121
-> (241) Z130 = 0.5*Z97*Z121 - 0.25*Z98*Z120
-> (242) Z131 = 0.5*Z96*Z120 - 0.25*Z97*Z119
-> (243) Z132 = 0.25*Z96*Z121 - 0.25*Z98*Z119
-> (244) Z133 = 0.25*Z97*Z121 - 0.5*Z98*Z120
-> (245) Z134 = Z1*fakeu1
-> (246) Z135 = Z1*fakeu2
-> (247) Z136 = Z1*fakeu3
-> (248) Z137 = 0.25*fakeu1*Z135 - 0.25*fakeu2*Z134
-> (249) Z138 = 0.25*fakeu3*Z134 - 0.5*fakeu1*Z136
-> (250) Z139 = 0.5*fakeu2*Z136 - 0.25*fakeu3*Z135
-> (251) Z140 = 0.5*fakeu1*Z135 - 0.25*fakeu2*Z134
-> (252) Z141 = 0.25*fakeu1*Z136 - 0.25*fakeu3*Z134
-> (253) Z142 = 0.25*fakeu2*Z136 - 0.5*fakeu3*Z135
-> (254) Z143 = Z59*u
-> (255) Z144 = Z60*u
-> (256) Z145 = Z61*u
-> (257) Z146 = Z62*u
-> (258) Z147 = Z24*Z114 - 2*rad*Z53*Z106
-> (259) Z148 = u*Z147
-> (260) Z149 = Z24*Z111 - 2*rad*Z52*Z106
-> (261) Z150 = u*Z149
-> (262) Z151 = (e3*Z58-e1*Z56-e2*Z55-e4*Z57)*u
-> (263) Z152 = (e1*Z55+e3*Z57)*u
-> (264) Z153 = (e1*Z58+e2*Z57+e3*Z56-e4*Z55)*u
-> (265) Z154 = -2*(Z5*Z52+Z6*Z53+Z7*Z54)*Z102 - Z25*(Z52*Z151+2*Z53*Z152-Z5*
Z111-Z6*Z114-Z7*Z117-Z54*Z153)
-> (266) Z155 = u*Z154
-> (267) Z156 = (e2*Z56+e3*Z57)*u
-> (268) Z157 = (e1*Z56+e2*Z55+e3*Z58-e4*Z57)*u
-> (269) Z158 = (e2*Z58-e1*Z57-e3*Z55-e4*Z56)*u
-> (270) Z159 = Z25*(Z2*Z111+Z3*Z114+Z4*Z117+Z53*Z157-2*Z52*Z156-Z54*Z158) - 2*
(Z2*Z52+Z3*Z53+Z4*Z54)*Z102
-> (271) Z160 = u*Z159
-> (272) Z161 = -Z148 - Z98*Z144
-> (273) Z162 = Z96*Z144 + Z97*Z143
-> (274) Z163 = Z150 - Z98*Z143
-> (275) Z164 = Z63*u
-> (276) Z165 = Z64*u
-> (277) Z166 = Z149 - l*Z117
-> (278) Z167 = u*Z166
-> (279) Z168 = l*u*Z114
-> (280) Z169 = Z97*Z165 - Z148 - Z98*Z164
-> (281) Z170 = Z168 + Z96*Z164 + Z97*Z143
-> (282) Z171 = Z167 - Z96*Z165 - Z98*Z143
-> (283) Z172 = l*fakeu3
-> (284) Z173 = l*fakeu2
-> (285) Z174 = fakeu1*Z173
-> (286) Z175 = fakeu1*Z172
-> (287) Z176 = fakeu2*Z173 + fakeu3*Z172
-> (288) Z177 = 0.5*Z52*Z122 + 0.75*Z53*Z124 + 0.75*Z54*Z126 + m*(Z60^2+2*Z59^2
+2*Z61^2+2*Z62^2+2*Z3*Z60*Z61+4*Z5*Z59*Z62-2*Z6*Z60*Z62) + m*(Z63^2+
Z64^2+2*Z3*Z61*Z63+2*Z4*Z61*Z64-4*Z2*Z59*Z61-2*Z6*Z62*Z63-2*Z7*Z62*Z64
)
-> (289) Z178 = Z52*Z130 + Z52*Z133 + Z53*Z129 + Z54*Z128 + Z54*Z131 + 0.5*Z52*
Z123 + 0.75*Z53*Z125 + 0.75*Z54*Z127 + m*(Z60*Z163+2*Z61*Z155+2*Z62*
Z160+Z2*Z61*Z161+Z3*Z60*Z155+Z3*Z61*Z163+Z4*Z61*Z162+2*Z5*Z59*Z160-Z59
*Z161-Z5*Z62*Z161-Z6*Z60*Z160-Z6*Z62*Z163-Z7*Z62*Z162) + m*(Z63*Z171+
Z64*Z170+Z2*Z61*Z169+Z3*Z61*Z171+Z3*Z63*Z155+Z4*Z61*Z170+Z4*Z64*Z155-
Z59*Z169-2*Z2*Z59*Z155-Z5*Z62*Z169-Z6*Z62*Z171-Z6*Z63*Z160-Z7*Z62*Z170
-Z7*Z64*Z160) - Z53*Z132
-> (290) Z179 = Z139 + Z142
-> (291) Z180 = m*l^2 + 0.75*Z1
-> (292) Z181 = Z90*Z13
-> (293) Z182 = Z90*Z16
-> (294) Z183 = Z138 - Z141 - Z90*Z175
-> (295) Z184 = Z90*Z12
-> (296) Z185 = Z90*Z15
-> (297) Z186 = Z137 + Z140 + Z90*Z174
-> (298) Z187 = m*(Z11*Z176-Z12*Z174-Z13*Z175)
-> (299) Z188 = m*(Z14*Z176-Z15*Z174-Z16*Z175)
-> (300) Z189 = m*(Z17*Z176-Z18*Z174-Z19*Z175)
-> (301) zero[1] = 9.81*Z77 - Z178 - Z177*u'
-> (302) zero[2] = aforce1*Z79 + aforce2*Z78 + bforce1*Z82 + bforce2*Z81 + bfo
rce3*Z83 - aforce3*Z80 - Z179 - 0.5*Z1*fakeu1'
-> (303) zero[3] = aforce1*Z85 + aforce2*Z84 + aforce3*Z86 + bforce1*Z88 + bfo
rce2*Z87 + bforce3*Z89 - 9.81*Z91 - Z183 - Z180*fakeu2' - Z91*fakeu6'
- Z181*fakeu4' - Z182*fakeu5'
-> (304) zero[4] = 9.81*Z95 + aforce2*Z70 + bforce1*Z93 + bforce2*Z92 + bforce3
*Z94 + Z95*fakeu6' + Z184*fakeu4' + Z185*fakeu5' - aforce1*Z67 - Z186
- Z180*fakeu3'
-> (305) zero[5] = aforce1 + bforce1 + Z184*fakeu3' - Z187 - 2*m*fakeu4' - Z181
*fakeu2'
-> (306) zero[6] = aforce2 + bforce2 + Z185*fakeu3' - Z188 - 2*m*fakeu5' - Z182
*fakeu2'
-> (307) zero[7] = aforce3 + bforce3 + Z95*fakeu3' - 19.62*m - Z189 - 2*m*fake
u6' - Z91*fakeu2'
(308) newzero = zero[1]
-> (309) newzero = 9.81*Z77 - Z178 - Z177*u'
(310) solve(newzero,u')
-> (311) Z190 = Z178 - 9.81*Z77
-> (312) Z191 = Z190/Z177
-> (313) u' = -Z191
(314) %'
(315) forcezero = [zero[2],zero[3],zero[4],zero[5],zero[6],zero[7]]
-> (316) forcezero[1,1] = aforce1*Z79 + aforce2*Z78 + bforce1*Z82 + bforce2*Z81
+ bforce3*Z83 - aforce3*Z80 - Z179 - 0.5*Z1*fakeu1'
-> (317) forcezero[1,2] = aforce1*Z85 + aforce2*Z84 + aforce3*Z86 + bforce1*Z88
+ bforce2*Z87 + bforce3*Z89 - 9.81*Z91 - Z183 - Z180*fakeu2' - Z91*fa
keu6' - Z181*fakeu4' - Z182*fakeu5'
-> (318) forcezero[1,3] = 9.81*Z95 + aforce2*Z70 + bforce1*Z93 + bforce2*Z92 +
bforce3*Z94 + Z95*fakeu6' + Z184*fakeu4' + Z185*fakeu5' - aforce1*Z67
- Z186 - Z180*fakeu3'
-> (319) forcezero[1,4] = aforce1 + bforce1 + Z184*fakeu3' - Z187 - 2*m*fakeu4'
- Z181*fakeu2'
-> (320) forcezero[1,5] = aforce2 + bforce2 + Z185*fakeu3' - Z188 - 2*m*fakeu5'
- Z182*fakeu2'
-> (321) forcezero[1,6] = aforce3 + bforce3 + Z95*fakeu3' - 19.62*m - Z189 - 2*
m*fakeu6' - Z91*fakeu2'
(322) %explicit(forcezero)
(323) forces = [aforce1,aforce2,aforce3,bforce1,bforce2,bforce3]
-> (324) forces = [aforce1, aforce2, aforce3, bforce1, bforce2, bforce3]
(325) %forcezero = replace(forcezero,fakeu1=u1,fakeu2=u2,fakeu3=u3,fakeu4=u4, &
(326) % fakeu5=u5,fakeu6=u6,fakee1=e1,fakee2=e2,fakee3=e3,fakee4=e4, &
(327) % fakeu1'=Dt(u1),fakeu2'=Dt(u2),fakeu3'=Dt(u3),fakeu4'=Dt(u4), &
(328) % fakeu5'=Dt(u5),fakeu6'=Dt(u6))
(329) solve(forcezero,forces)
-> (330) Z192 = Z179 + 0.5*Z1*fakeu1'
-> (331) Z193 = 9.81*Z91 + Z183 + Z180*fakeu2' + Z91*fakeu6' + Z181*fakeu4' +
Z182*fakeu5'
-> (332) Z194 = Z186 + Z180*fakeu3' - 9.81*Z95 - Z95*fakeu6' - Z184*fakeu4' -
Z185*fakeu5'
-> (333) Z195 = Z187 + Z181*fakeu2' + 2*m*fakeu4' - Z184*fakeu3'
-> (334) Z196 = Z188 + Z182*fakeu2' + 2*m*fakeu5' - Z185*fakeu3'
-> (335) Z197 = 19.62*m + Z189 + Z91*fakeu2' + 2*m*fakeu6' - Z95*fakeu3'
-> (336) Z198 = Z79*Z84 - Z78*Z85
-> (337) Z199 = Z79*Z86 + Z80*Z85
-> (338) Z200 = Z70 - Z92
-> (339) Z201 = Z79*Z88 - Z82*Z85
-> (340) Z202 = Z79*Z87 - Z81*Z85
-> (341) Z203 = Z79*Z89 - Z83*Z85
-> (342) Z204 = Z78*Z86 + Z80*Z84
-> (343) Z205 = -Z67 - Z93
-> (344) Z206 = Z78*Z88 - Z82*Z84
-> (345) Z207 = Z78*Z87 - Z81*Z84
-> (346) Z208 = Z78*Z89 - Z83*Z84
-> (347) Z209 = -Z80*Z88 - Z82*Z86
-> (348) Z210 = Z92 - Z70
-> (349) Z211 = -Z80*Z87 - Z81*Z86
-> (350) Z212 = -Z80*Z89 - Z83*Z86
-> (351) Z213 = Z82*Z87 - Z81*Z88
-> (352) Z214 = Z82*Z89 - Z83*Z88
-> (353) Z215 = Z81*Z89 - Z83*Z87
-> (354) Z216 = Z94*Z202 + Z200*Z203 + Z204*Z205 + Z205*Z211 + Z205*Z215 + Z209
*Z210 - Z94*Z198 - Z94*Z206 - Z94*Z213 - Z199*Z200 - Z200*Z214 - Z205*
Z208
-> (355) Z217 = Z70*Z86
-> (356) Z218 = Z84*Z93 - Z70*Z88
-> (357) Z219 = Z84*Z92 - Z70*Z87
-> (358) Z220 = Z84*Z94 - Z70*Z89
-> (359) Z221 = Z86*Z93
-> (360) Z222 = Z86*Z92
-> (361) Z223 = Z86*Z94
-> (362) Z224 = Z88*Z92 - Z87*Z93
-> (363) Z225 = Z88*Z94 - Z89*Z93
-> (364) Z226 = Z87*Z94 - Z89*Z92
-> (365) Z227 = Z222 + Z226 - Z217 - Z220
-> (366) Z228 = Z67*Z86
-> (367) Z229 = Z67*Z88 + Z85*Z93
-> (368) Z230 = Z67*Z87 + Z85*Z92
-> (369) Z231 = Z67*Z89 + Z85*Z94
-> (370) Z232 = Z221 + Z225 + Z228 - Z231
-> (371) Z233 = Z67*Z84 + Z70*Z85
-> (372) Z234 = Z218 + Z224 + Z233 - Z230
-> (373) Z235 = Z70*Z80
-> (374) Z236 = Z78*Z93 - Z70*Z82
-> (375) Z237 = Z78*Z92 - Z70*Z81
-> (376) Z238 = Z78*Z94 - Z70*Z83
-> (377) Z239 = Z80*Z93
-> (378) Z240 = Z80*Z92
-> (379) Z241 = Z80*Z94
-> (380) Z242 = Z82*Z92 - Z81*Z93
-> (381) Z243 = Z82*Z94 - Z83*Z93
-> (382) Z244 = Z81*Z94 - Z83*Z92
-> (383) Z245 = Z235 + Z244 - Z238 - Z240
-> (384) Z246 = Z67*Z80
-> (385) Z247 = Z67*Z82 + Z79*Z93
-> (386) Z248 = Z67*Z81 + Z79*Z92
-> (387) Z249 = Z67*Z83 + Z79*Z94
-> (388) Z250 = Z243 - Z239 - Z246 - Z249
-> (389) Z251 = Z67*Z78 + Z70*Z79
-> (390) Z252 = Z236 + Z242 + Z251 - Z248
-> (391) Z253 = Z204 + Z211 + Z215 - Z208
-> (392) Z254 = Z199 + Z209 + Z214 - Z203
-> (393) Z255 = Z198 + Z206 + Z213 - Z202
-> (394) Z256 = Z93*Z204 + Z93*Z211 + Z93*Z215 + Z94*Z206 + Z94*Z213 + Z200*Z2
09 + Z200*Z214 - Z93*Z208
-> (395) Z257 = Z93*Z199 + Z94*Z201 - Z67*Z209 - Z67*Z214 - Z93*Z203
-> (396) Z258 = Z93*Z198 - Z67*Z206 - Z67*Z213 - Z93*Z202 - Z200*Z201
-> (397) Z259 = Z67*Z208 + Z94*Z202 + Z200*Z203 - Z67*Z204 - Z67*Z211 - Z67*Z2
15 - Z94*Z198 - Z199*Z200
-> (398) Z260 = Z92*Z208 - Z70*Z211 - Z70*Z215 - Z92*Z204 - Z94*Z207
-> (399) Z261 = Z92*Z203 + Z94*Z213 - Z92*Z199 - Z92*Z209 - Z92*Z214 - Z94*Z202
- Z205*Z211 - Z205*Z215
-> (400) Z262 = Z70*Z202 - Z70*Z213 - Z92*Z198 - Z92*Z206 - Z205*Z207
-> (401) Z263 = Z70*Z203 + Z204*Z205 - Z70*Z199 - Z70*Z209 - Z70*Z214 - Z94*Z1
98 - Z94*Z206 - Z205*Z208
-> (402) Z264 = Z94*Z204 + Z94*Z211 + Z200*Z212
-> (403) Z265 = Z94*Z199 + Z94*Z209 + Z205*Z212
-> (404) Z266 = Z94*Z198 + Z94*Z206 + Z94*Z213 + Z205*Z208 - Z94*Z202 - Z200*
Z203 - Z205*Z215 - Z210*Z214
-> (405) Z267 = Z94*Z204 + Z94*Z211 - Z210*Z212
-> (406) Z268 = Z204*Z205 + Z205*Z211 + Z209*Z210 - Z199*Z200
-> (407) Z269 = (Z227*Z192+Z253*Z194+Z260*Z196-Z245*Z193-Z256*Z195-Z264*Z197)/
Z216
-> (408) Z270 = (Z232*Z192+Z254*Z194+Z261*Z196-Z250*Z193-Z257*Z195-Z265*Z197)/
Z216
-> (409) Z271 = (Z234*Z192+Z255*Z194+Z262*Z196-Z252*Z193-Z258*Z195-Z266*Z197)/
Z216
-> (410) Z272 = (Z227*Z192+Z253*Z194+Z260*Z196-Z245*Z193-Z259*Z195-Z267*Z197)/
Z216
-> (411) Z273 = (Z232*Z192+Z254*Z194+Z263*Z196-Z250*Z193-Z257*Z195-Z265*Z197)/
Z216
-> (412) Z274 = (Z234*Z192+Z255*Z194+Z262*Z196-Z252*Z193-Z258*Z195-Z268*Z197)/
Z216
-> (413) aforce1 = Z269
-> (414) aforce2 = -Z270
-> (415) aforce3 = Z271
-> (416) bforce1 = -Z272
-> (417) bforce2 = Z273
-> (418) bforce3 = -Z274
(419) fakee1 = e1
-> (420) fakee1 = e1
(421) fakee2 = e2
-> (422) fakee2 = e2
(423) fakee3 = e3
-> (424) fakee3 = e3
(425) fakee4 = e4
-> (426) fakee4 = e4
(427) fakee1' = e1'
-> (428) fakee1' = 0.5*Z55*u
(429) fakee2' = e2'
-> (430) fakee2' = 0.5*Z56*u
(431) fakee3' = e3'
-> (432) fakee3' = 0.5*Z57*u
(433) fakee4' = e4'
-> (434) fakee4' = -0.5*Z58*u
(435) fakeu1 = u1
-> (436) fakeu1 = u1
(437) fakeu2 = u2
-> (438) fakeu2 = u2
(439) fakeu3 = u3
-> (440) fakeu3 = u3
(441) fakeu4 = u4
-> (442) fakeu4 = u4
(443) fakeu5 = u5
-> (444) fakeu5 = u5
(445) fakeu6 = u6
-> (446) fakeu6 = u6
(447) fakeu1' = Dt(u1)
-> (448) fakeu1' = u*Z111 + Z52*u'
(449) fakeu2' = Dt(u2)
-> (450) fakeu2' = u*Z114 + Z53*u'
(451) fakeu3' = Dt(u3)
-> (452) fakeu3' = u*Z117 + Z54*u'
(453) fakeu4' = Dt(u4)
-> (454) Z275 = Z154 + Z3*Z149 + Z60*Z157 + 2*Z59*Z156 - Z2*Z147
-> (455) Z276 = Z61 + Z3*Z60 - Z2*Z59
-> (456) fakeu4' = u*Z275 + Z276*u'
(457) fakeu5' = Dt(u5)
-> (458) Z277 = Z6*Z149 + Z59*Z151 - Z159 - 2*Z60*Z152 - Z5*Z147
-> (459) Z278 = Z6*Z60 - Z62 - Z5*Z59
-> (460) fakeu5' = u*Z277 + Z278*u'
(461) fakeu6' = Dt(u6)
-> (462) Z279 = Z9*Z149 - Z8*Z147 - Z59*Z99 - Z60*Z103
-> (463) Z280 = Z9*Z60 - Z8*Z59
-> (464) fakeu6' = u*Z279 + Z280*u'
(465) posa1' = dot(v_diskao_n>,n1>)
-> (466) posa1' = -(Z2*Z59-Z61-Z3*Z60)*u
(467) posa2' = dot(v_diskao_n>,n2>)
-> (468) posa2' = -(Z62+Z5*Z59-Z6*Z60)*u
(469) posa3' = dot(v_diskao_n>,n3>)
-> (470) posa3' = -(Z8*Z59-Z9*Z60)*u
(471) posb1' = dot(v_diskbo_n>,n1>)
-> (472) posb1' = -(Z2*Z59-Z61-Z3*Z63-Z4*Z64)*u
(473) posb2' = dot(v_diskbo_n>,n2>)
-> (474) posb2' = -(Z62+Z5*Z59-Z6*Z63-Z7*Z64)*u
(475) posb3' = dot(v_diskbo_n>,n3>)
-> (476) posb3' = -(Z8*Z59-Z9*Z63-Z10*Z64)*u
(477) cahat1' = dot((v_diskao_n>+cross(w_diska_n>-u3*diska3>,p_diskao_ahat>)) ,n1>)
-> (478) cahat1' = Z61*u + Z3*(Z60-Z24*Z52)*u + Z7*Z25*(u3-Z54*u) - Z5*Z25*Z52*
u - Z6*Z25*Z53*u - Z2*(Z59-Z24*Z53)*u
(479) cahat2' = dot((v_diskao_n>+cross(w_diska_n>-u3*diska3>,p_diskao_ahat>)) ,n2>)
-> (480) cahat2' = Z2*Z25*Z52*u + Z3*Z25*Z53*u + Z6*(Z60-Z24*Z52)*u - Z62*u -
Z4*Z25*(u3-Z54*u) - Z5*(Z59-Z24*Z53)*u
(481) cahat3' = 0
-> (482) cahat3' = 0
(483) cbhat1' = dot((v_diskbo_n>+cross(w_diskb_n>-dot(w_diskb_n>,diskb3>)*diskb3>,p_diskbo_bhat>)) ,n1>)
-> (484) cbhat1' = (Z61+Z3*Z63+Z4*Z64+Z4*Z30*Z52-Z2*Z59-Z2*Z30*Z54-Z5*Z31*Z52-
Z7*Z31*Z54)*u
(485) cbhat2' = dot((v_diskbo_n>+cross(w_diskb_n>-dot(w_diskb_n>,diskb3>)*diskb3>,p_diskbo_bhat>)) ,n2>)
-> (486) cbhat2' = -(Z62+Z5*Z59+Z5*Z30*Z54-Z6*Z63-Z7*Z64-Z2*Z31*Z52-Z4*Z31*Z54-
Z7*Z30*Z52)*u
(487) cbhat3' = 0
-> (488) cbhat3' = 0
(489) ke = m/2*dot(v_diskao_n>,v_diskao_n>)+m/2*dot(v_diskbo_n>,v_diskbo_n>) + &
dot(w_diska_n>,dot(I_diska_diskao>>,w_diska_n>))/2 + &
dot(w_diskb_n>,dot(I_diskb_diskbo>>,w_diskb_n>))/2
-> (490) ke = 0.25*(1.5*Z1*Z54^2+Z1*(Z52^2+1.5*Z53^2)+2*m*(Z60^2+2*Z59^2+2*Z61^
2+2*Z62^2+2*Z3*Z60*Z61+4*Z5*Z59*Z62-2*Z6*Z60*Z62)+2*m*(Z63^2+Z64^2+2*
Z3*Z61*Z63+2*Z4*Z61*Z64-4*Z2*Z59*Z61-2*Z6*Z62*Z63-2*Z7*Z62*Z64))*u^2
(491) pe = 9.81*m*posa3 + 9.81*m*posb3
-> (492) pe = 9.81*m*(posa3+posb3)
(493) qq1 = pi/4
-> (494) qq1 = 0.7853982
(495) qq2 = 0
-> (496) qq2 = 0
(497) qq3 = 0
-> (498) qq3 = 0
(499) %qq1 = 0
(500) %qq2 = asin(rad/(rad+l))
(501) %qq3 = 0
(502) q1' = u1
-> (503) q1' = u1
(504) q2' = u2
-> (505) q2' = u2
(506) q3' = u3
-> (507) q3' = u3
(508) %'
(509) input rad = .1, m = 2
(510) input gamma = 1
(511) input e4 = cos(qq1/2)*cos(qq2/2)*cos(qq3/2)+sin(qq1/2)*sin(qq2/2)*sin(qq3/2)
(512) input e1 = sin(qq1/2)*cos(qq2/2)*cos(qq3/2)-cos(qq1/2)*sin(qq2/2)*sin(qq3/2)
(513) input e2 = cos(qq1/2)*sin(qq2/2)*cos(qq3/2)+sin(qq1/2)*cos(qq2/2)*sin(qq3/2)
(514) input e3 = cos(qq1/2)*cos(qq2/2)*sin(qq3/2)-sin(qq1/2)*sin(qq2/2)*cos(qq3/2)
(515) input u = 1
(516) inputVecto = [dot(p_ahat_diskao>,n1>), dot(p_ahat_diskao>,n2>), &
dot(p_ahat_diskao>,n3>), &
dot(p_diskao_diskbo>,n1>) + dot(p_ahat_diskao>,n1>), &
dot(p_diskao_diskbo>,n2>) + dot(p_ahat_diskao>,n2>), &
dot(p_diskao_diskbo>,n3>) + dot(p_ahat_diskao>,n3>), &
0, 0, 0, dot(p_ahat_bhat>,n1>), dot(p_ahat_bhat>,n2>), 0, &
dot(v_diskao_n>,n1>),dot(v_diskao_n>,n2>), &
dot(v_diskao_n>,n3>),u1,u2,u3]
-> (517) inputVecto[1,1] = -Z4*Z24
-> (518) inputVecto[1,2] = -Z7*Z24
-> (519) inputVecto[1,3] = Z25 - Z10*Z24
-> (520) inputVecto[1,4] = -l*Z2 - Z4*Z24
-> (521) inputVecto[1,5] = -l*Z5 - Z7*Z24
-> (522) inputVecto[1,6] = Z25 - l*Z8 - Z10*Z24
-> (523) inputVecto[1,7] = 0
-> (524) inputVecto[1,8] = 0
-> (525) inputVecto[1,9] = 0
-> (526) inputVecto[1,10] = Z3*Z30 - l*Z2 - Z4*Z24
-> (527) inputVecto[1,11] = Z6*Z30 - l*Z5 - Z7*Z24
-> (528) inputVecto[1,12] = 0
-> (529) inputVecto[1,13] = -(Z2*Z59-Z61-Z3*Z60)*u
-> (530) inputVecto[1,14] = -(Z62+Z5*Z59-Z6*Z60)*u
-> (531) inputVecto[1,15] = -(Z8*Z59-Z9*Z60)*u
-> (532) inputVecto[1,16] = u1
-> (533) inputVecto[1,17] = u2
-> (534) inputVecto[1,18] = u3
(535) explicit(inputVecto)
-> (536) inputVecto[1,1] = -2*rad*(e1*e3+e2*e4)*(1-2*e1^2-2*e2^2)/(1-(1-2*e1^2-
2*e2^2)^2)^0.5
-> (537) inputVecto[1,2] = 2*rad*(e1*e4-e2*e3)*(1-2*e1^2-2*e2^2)/(1-(1-2*e1^2-2
*e2^2)^2)^0.5
-> (538) inputVecto[1,3] = rad*(1-(1-2*e1^2-2*e2^2)^2)^0.5
-> (539) inputVecto[1,4] = -1.414214*rad*(gamma*(1-2*e2^2-2*e3^2)+1.414214*(e1*
e3+e2*e4)*(1-2*e1^2-2*e2^2)/(1-(1-2*e1^2-2*e2^2)^2)^0.5)
-> (540) inputVecto[1,5] = -2*rad*(1.414214*gamma*(e1*e2+e3*e4)-(e1*e4-e2*e3)*(
1-2*e1^2-2*e2^2)/(1-(1-2*e1^2-2*e2^2)^2)^0.5)
-> (541) inputVecto[1,6] = -rad*(2.828427*gamma*(e1*e3-e2*e4)-(1-(1-2*e1^2-2*
e2^2)^2)^0.5)
-> (542) inputVecto[1,7] = 0
-> (543) inputVecto[1,8] = 0
-> (544) inputVecto[1,9] = 0
-> (545) inputVecto[1,10] = 1.414214*rad*(2.828427*(e1*e4+e2*e3)*(e1*e2-e3*e4)/
(1-4*(e1*e4+e2*e3)^2)^0.5-gamma*(1-2*e2^2-2*e3^2)-1.414214*(e1*e3+e2*
e4)*(1-2*e1^2-2*e2^2)/(1-(1-2*e1^2-2*e2^2)^2)^0.5)
-> (546) inputVecto[1,11] = -2*rad*(1.414214*gamma*(e1*e2+e3*e4)-(e1*e4+e2*e3)*
(1-2*e1^2-2*e3^2)/(1-4*(e1*e4+e2*e3)^2)^0.5-(e1*e4-e2*e3)*(1-2*e1^2-2*
e2^2)/(1-(1-2*e1^2-2*e2^2)^2)^0.5)
-> (547) inputVecto[1,12] = 0
-> (548) inputVecto[1,13] = -2*rad^2*(1.414214*(e1*e2-e3*e4)*(1-2*e1^2-2*e2^2)*
(gamma+1.414214*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*
e1^2-2*e2^2)^2)^0.5))/((1-(1-2*e1^2-2*e2^2)^2)^0.5*(-rad^2*(8*(e1*e4+
e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(
1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*
e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*
e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*
e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2
*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)
^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)-((e1*e4+e2*e3)*(1-2*e1^2-2*
e3^2)*(1/((1-4*(e1*e4+e2*e3)^2)^0.5*(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4
*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*
e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2
-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(
1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*
e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*
(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*
e1^2-2*e2^2)^2)^0.5))^0.5)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2
-2*e2^2)^2)^0.5)/(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^
0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2
-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*
e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)
^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1
-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)
^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^
0.5)+(e1*e4-e2*e3)*(1-2*e1^2-2*e2^2)*(1/((1-(1-2*e1^2-2*e2^2)^2)^0.5*(
-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-
2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/
(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(
1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*ga
mma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^
2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*
e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)+(1/(1-4*(e1*
e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(-rad^2*(8*(e1*e4+e2*
e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4
*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2
)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)
^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(
1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2
-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)
/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)-1.414214*(e1*e2+e3*e4)*(gamma+1.4
14214*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2
)^2)^0.5))/(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(
1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*
e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*
e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2
-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*
e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^
0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5-(
e1*e4+e2*e3)*(1-2*e1^2-2*e2^2)*(1-2*e2^2-2*e3^2)*(1/((1-4*(e1*e4+e2*
e3)^2)^0.5*(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(
1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*
e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*
e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2
-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*
e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^
0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)-
(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(-rad^2*(8
*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2
)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*
e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*
e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*
e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-
2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*
e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5))/(1-(1-2*e1^2-2*e2^2)
^2)^0.5)*u
-> (549) inputVecto[1,14] = -1.414214*rad^2*((1-2*e1^2-2*e2^2)*(1-2*e1^2-2*e3^2
)*(gamma+1.414214*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2
*e1^2-2*e2^2)^2)^0.5))/((1-(1-2*e1^2-2*e2^2)^2)^0.5*(-rad^2*(8*(e1*e4+
e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(
1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*
e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*
e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*
e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2
*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)
^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)-((1-2*e2^2-2*e3^2)*(gamma+1.
414214*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^
2)^2)^0.5))/(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-
1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(
e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-
2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)
^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2
*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^
0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5+
1.414214*(e1*e3+e2*e4)*(1-2*e1^2-2*e2^2)*(1/((1-(1-2*e1^2-2*e2^2)^2)^
0.5*(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*
e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*
e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2
)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656
854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*
e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-
(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)+(1/(1-4*(
e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(-rad^2*(8*(e1*e4+
e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(
1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*
e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*
e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*
e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2
*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)
^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)-2.828427*(e1*e4+e2*e3)*(e1*
e2-e3*e4)*(1/((1-4*(e1*e4+e2*e3)^2)^0.5*(-rad^2*(8*(e1*e4+e2*e3)^2*(
1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*
e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-
2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-
1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*
(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2
)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-
2*e1^2-2*e2^2)^2)^0.5))^0.5)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*
e1^2-2*e2^2)^2)^0.5)/(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^
2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gam
ma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1
-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)
^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-
1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+
e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^
0.5))^0.5)-2.828427*(e1*e2+e3*e4)*(e1*e4+e2*e3)*(1-2*e1^2-2*e2^2)*(1/(
(1-4*(e1*e4+e2*e3)^2)^0.5*(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+
e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5
-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2
/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2
*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)
^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*
e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2
)^0.5))^0.5)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^
0.5)/(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2
*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*
e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2
)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656
854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*
e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-
(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5))/(1-(1-2*
e1^2-2*e2^2)^2)^0.5)*u
-> (550) inputVecto[1,15] = -2.828427*rad^2*(e1*e4+e2*e3)*(1-2*e1^2-2*e2^2)*(
gamma+1.414214*(e1*e3-e2*e4)/(1-4*(e1*e4+e2*e3)^2)^0.5)*u/((1-(1-2*e1^
2-2*e2^2)^2)^0.5*(-rad^2*(4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)+(1-2
*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-2*gamma^2-(1/(1-4*(e1*e4+e2*
e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*
e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(4*(
e1*e4+e2*e3)^2+(1-2*e1^2-2*e2^2)^2)/((1-4*(e1*e4+e2*e3)^2)^0.5*(1-(1-2
*e1^2-2*e2^2)^2)^0.5)))^0.5)
-> (551) inputVecto[1,16] = -1.414214*rad*(gamma+1.414214*(e1*e3-e2*e4)*(1/(1-4
*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5))*u/(-rad^2*(4*(
e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)+(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-
2*e2^2)^2)-2*gamma^2-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^
2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5
-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(4*(e1*e4+e2*e3)^2+(1-2*e1^2-2*e2^2)
^2)/((1-4*(e1*e4+e2*e3)^2)^0.5*(1-(1-2*e1^2-2*e2^2)^2)^0.5)))^0.5
-> (552) inputVecto[1,17] = 2*rad*(e1*e4+e2*e3)*u/((1-(1-2*e1^2-2*e2^2)^2)^0.5*
(-rad^2*(4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)+(1-2*e1^2-2*e2^2)^2/(
1-(1-2*e1^2-2*e2^2)^2)-2*gamma^2-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-
2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+
e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(4*(e1*e4+e2*e3)^2+(1-2
*e1^2-2*e2^2)^2)/((1-4*(e1*e4+e2*e3)^2)^0.5*(1-(1-2*e1^2-2*e2^2)^2)^
0.5)))^0.5)
-> (553) inputVecto[1,18] = -rad*(1-2*e1^2-2*e2^2)*u/((1-4*(e1*e4+e2*e3)^2)^0.5
*(-rad^2*(4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)+(1-2*e1^2-2*e2^2)^2/
(1-(1-2*e1^2-2*e2^2)^2)-2*gamma^2-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1
-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+
e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(4*(e1*e4+e2*e3)^2+(1-2
*e1^2-2*e2^2)^2)/((1-4*(e1*e4+e2*e3)^2)^0.5*(1-(1-2*e1^2-2*e2^2)^2)^
0.5)))^0.5)
(554) inputVector = replace(inputVecto,e1=input(e1),e2=input(e2),e3=input(e3), &
e4=input(e4),u=input(u),a=input(a), &
gamma=input(gamma),rad=input(rad))
-> (555) inputVector = [0, 0.07071068, 0.07071068, -0.1414214, 0.07071068, 0.0
7071068, 0, 0, 0, -0.1414214, 0.1414214, 0, 0.05, 0.05000002, -0.05,
-0.707107, 0.5, -0.5]
(556) input posa1 = inputVector[1], posa2 = inputVector[2], posa3 = inputVector[3]
(557) input posb1 = inputVector[4], posb2 = inputVector[5], posb3 = inputVector[6]
(558) input cahat1 = 0, cahat2 = 0, cahat3 = 0
(559) input cbhat1 = inputVector[10], cbhat2 = inputVector[11], cbhat3 = 0
(560) output t,ke,pe,ke+pe,e1,e2,e3,e4,u, &
cahat1,cahat2,cahat3,cbhat1,cbhat2,cbhat3, &
u1,u2,u3,u4,u5,u6, q1,q2,q3, &
aforce1,aforce2,aforce3,bforce1,bforce2,bforce3
(561) %code dynamics() TwinDisksConstraintForcesExtra.m
(562) %exit
(563) explicit(u4)
-> (564) u4 = -2*rad^2*(1.414214*(e1*e2-e3*e4)*(1-2*e1^2-2*e2^2)*(gamma+1.4142
14*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2
)^0.5))/((1-(1-2*e1^2-2*e2^2)^2)^0.5*(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-
4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*
e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2
-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(
1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*
e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*
(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*
e1^2-2*e2^2)^2)^0.5))^0.5)-((e1*e4+e2*e3)*(1-2*e1^2-2*e3^2)*(1/((1-4*(
e1*e4+e2*e3)^2)^0.5*(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2
)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma
^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2
*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2
)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(
1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*
e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5)
)^0.5)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(-
rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2
*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(
1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1
-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gam
ma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2
)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*
e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)+(e1*e4-e2*e3)*
(1-2*e1^2-2*e2^2)*(1/((1-(1-2*e1^2-2*e2^2)^2)^0.5*(-rad^2*(8*(e1*e4+
e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(
1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*
e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*
e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*
e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2
*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)
^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)+(1/(1-4*(e1*e4+e2*e3)^2)^0.5-
1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(1-4*(e1*
e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+e2*e3)^2)^
0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*e1^2-2*e2^2
)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^
2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)
^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(
e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2
)^2)^0.5))^0.5)-1.414214*(e1*e2+e3*e4)*(gamma+1.414214*(e1*e3-e2*e4)*(
1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5))/(-rad^2*(8
*(e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2
)^0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*
e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*
e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*
e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-
2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*
e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5-(e1*e4+e2*e3)*(1-2*e1^
2-2*e2^2)*(1-2*e2^2-2*e3^2)*(1/((1-4*(e1*e4+e2*e3)^2)^0.5*(-rad^2*(8*(
e1*e4+e2*e3)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^
0.5)/(1-4*(e1*e4+e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*
e4+e2*e3)^2)-(1-2*e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*
e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*
e3-e2*e4)*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-
2*(1-2*e1^2-2*e2^2)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*
e2^2)^2)^0.5)/(1-(1-2*e1^2-2*e2^2)^2)^0.5))^0.5)-(1/(1-4*(e1*e4+e2*e3)
^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(-rad^2*(8*(e1*e4+e2*e3)^2*(1/(
1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-4*(e1*e4+
e2*e3)^2)^0.5-2*gamma^2-4*(e1*e4+e2*e3)^2/(1-4*(e1*e4+e2*e3)^2)-(1-2*
e1^2-2*e2^2)^2/(1-(1-2*e1^2-2*e2^2)^2)-(1/(1-4*(e1*e4+e2*e3)^2)^0.5-
1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)^2-5.656854*gamma*(e1*e3-e2*e4)*(1/(1-4*
(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)-2*(1-2*e1^2-2*e2^2
)^2*(1/(1-4*(e1*e4+e2*e3)^2)^0.5-1/(1-(1-2*e1^2-2*e2^2)^2)^0.5)/(1-(1-
2*e1^2-2*e2^2)^2)^0.5))^0.5))/(1-(1-2*e1^2-2*e2^2)^2)^0.5)*u
(565) z269
3
input(e3)))^2*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-2*(input(gamma))^2-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)-(1-2*(input(e1))^2-2*(input(e2))^2)^2/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)-(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)^2-5.656854*(input(gamma))*((input(e1))*(input(e3))-(input(e2))*(input(e4)))*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)-2*(1-2*(input(e1))^2-2*(input(e2))^2)^2*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5))^0.5)-2.828427*((input(e1))*(input(e2))+(input(e3))*(input(e4)))*((input(e1))*(input(e4))+(input(e2))*(input(e3)))*(1-2*(input(e1))^2-2*(input(e2))^2)*(1/((1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5*(-(input(rad))^2*(8*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-2*(input(gamma))^2-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)-(1-2*(input(e1))^2-2*(input(e2))^2)^2/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)-(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)^2-5.656854*(input(gamma))*((input(e1))*(input(e3))-(input(e2))*(input(e4)))*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)-2*(1-2*(input(e1))^2-2*(input(e2))^2)^2*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5))^0.5)-(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)/(-(input(rad))^2*(8*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-2*(input(gamma))^2-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)-(1-2*(input(e1))^2-2*(input(e2))^2)^2/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)-(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)^2-5.656854*(input(gamma))*((input(e1))*(input(e3))-(input(e2))*(input(e4)))*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)-2*(1-2*(input(e1))^2-2*(input(e2))^2)^2*(1/(1-4*((input(e1))*(input(e4))+(input(e2))*(input(e3)))^2)^0.5-1/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5))^0.5))/(1-(1-2*(input(e1))^2-2*(input(e2))^2)^2)^0.5)*(input(u))