**** GENERATION OF THE TLS MATRICES **** ** input control information ** Libration rms around L-axes dx ,dy ,dz = 0.2000000 0.3000000 0.1000000 vectors defining two first Libration axes 0.40000 -0.70000 0.00000 0.70000 0.10000 0.50000 rotation axes pass through the points in the M(main) base parallel to lx : (wix,wiy,wiz)= 0.11000 0.31000 0.21000 parallel to ly : (wjx,wjy,wjz)= -0.22000 0.32000 0.42000 parallel to lz : (wkx,wky,wkz)= 0.43000 0.33000 0.23000 correlation shifts sx,sy,sz for libration 0.240000 0.130000 0.150000 Vibration rms along V-axes tx ,ty ,tz = 0.1600000 0.2800000 0.1400000 vectors defining two first Vibration axes 1.00000 1.00000 1.00000 -1.00000 2.00000 0.50000 center of reaction will not be used for decomposition ==================================================== *** ORIGINAL ELEMENTS OF THE TLS MATRICES *** ** after correction of the axes order ** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 unit vectors defining three Libration axes 0.52562 0.30035 -0.79594 -0.49614 0.86824 0.00000 0.69107 0.39489 0.60538 rotation axes pass through the points in the M base axis 1 : (w1x,w1y,w1z)= 0.35327 0.11758 0.45615 axis 2 : (w2x,w2y,w2z)= 0.33997 -0.05287 0.18418 axis 3 : (w3x,w3y,w3z)= 0.53594 -0.13946 -0.14323 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= -0.14207 -0.07318 0.56671 parallel to ly : (wjx,wjy,wjz)= 0.01622 -0.21458 0.32556 parallel to lz : (wkx,wky,wkz)= 0.35382 -0.38699 0.22859 correlation shifts sx,sy,sz for libration 0.150000 0.240000 0.130000 Vibration rms along V-axes tx ,ty ,tz = 0.1400000 0.1600000 0.2800000 vectors defining three Vibration axes 0.40825 0.40825 -0.81650 0.57735 0.57735 0.57735 0.70711 -0.70711 0.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base matrix T 0.05398021521978 -0.02749669639161 -0.00005280086771 -0.02749669535842 0.07217863202095 -0.01018063887022 -0.00005280040205 -0.01018063793890 0.03375164885074 matrix L 0.05559036880732 0.00890878029168 0.03346865251660 0.00890878029168 0.04509073123336 0.01912494376302 0.03346865251660 0.01912494376302 0.03931890055537 matrix S 0.00859345495701 -0.02248973399401 0.01832015812397 -0.00794242043048 -0.00746113620698 0.02285907231271 0.00458437297493 -0.02477829530835 0.02166767790914 ================ TLS DECOMPOSITION ================ ***** STEP A : from M-base to P-base P-shift : 0.000000 0.000000 0.000000 transition P-matrix and its transposal 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 resulted matrices T[P] L[P] S[P] in the P-base 0.053980 -0.027497 -0.000053 0.055590 0.008909 0.033469 0.008593 -0.022490 0.018320 -0.027497 0.072179 -0.010181 0.008909 0.045091 0.019125 -0.007942 -0.007461 0.022859 -0.000053 -0.010181 0.033752 0.033469 0.019125 0.039319 0.004584 -0.024778 0.021668 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.010000 0.525618 0.300353 -0.795936 0.040000 -0.496139 0.868243 0.000000 0.090000 0.691066 0.394895 0.605381 rotation matrix P->L and its transposal: 0.525618 -0.496139 0.691066 0.525618 0.300353 -0.795936 0.300353 0.868243 0.394895 -0.496139 0.868243 0.000000 -0.795936 0.000000 0.605381 0.691066 0.394895 0.605381 resulted matrices T[L] L[L] S[L] in the L-base 0.039037 0.003309 0.001852 0.010000 0.000000 0.000000 0.001500 0.005667 0.000732 0.003309 0.091388 -0.010207 0.000000 0.040000 0.000000 -0.013023 0.009600 0.000649 0.001852 -0.010207 0.029485 0.000000 0.000000 0.090000 -0.034829 -0.031843 0.011700 libration amplitudes around the L axes: 0.100000 0.200000 0.300000 ***** STEP C : W points in the L-base axis Lx crosses the point 0.000000 -0.073181 0.566711 axis Ly crosses the point 0.016219 0.000000 0.325565 axis Lz crosses the point 0.353816 -0.386988 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -0.017718 -0.012323 0.000211 -0.012323 -0.014478 -0.000415 0.000211 -0.000415 -0.000064 resulted matrices TC[L] L[L] S[L] in the L-base 0.021319 -0.009014 0.002063 0.010000 0.000000 0.000000 0.001500 0.005667 0.000732 -0.009014 0.076910 -0.010622 0.000000 0.040000 0.000000 -0.013023 0.009600 0.000649 0.002063 -0.010622 0.029421 0.000000 0.000000 0.090000 -0.034829 -0.031843 0.011700 diagonal shift for the unconstrained min[tr(S)] 0.007600 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc -0.013101 0.016101 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00020 0.00219 0.00354 ts limits : tmint,tmaxt -0.043435 0.061036 ts limits : tmina,tmaxa -0.043435 0.061036 final limits : tmin,tmax -0.013101 0.016101 constrained ts to be removed from the S diagonal 0.007597 screw parameters sx,sy,sz -0.60973 0.05007 0.04559 C[L] matrix diagonal elements 0.00372 0.00010 0.00019 ***** STEP E : vibration parameters matrix V[L]: 0.017601 -0.009014 0.002063 -0.009014 0.076810 -0.010622 0.002063 -0.010622 0.029234 eigenvalues and eigenvectors in base [L]: 0.016239 -0.989266 -0.139696 0.042873 0.026972 0.012622 0.210608 0.977489 0.080434 -0.145580 0.967538 -0.206585 rotation matrix [P] -> [L]: 0.525618 -0.496139 0.691066 0.300353 0.868243 0.394895 -0.795936 0.000000 0.605381 vibration tx,ty,tz along V axes & axes in base [M]: 0.127431 -0.421040 -0.401489 0.813346 0.164232 0.577653 0.572656 0.581707 0.283609 -0.699316 0.714753 -0.009190 W points recalculated in the P and M bases 0.427943 0.160253 0.343076 0.427943 0.160253 0.343076 0.233512 0.133435 0.184181 0.233512 0.133435 0.184181 0.377972 -0.229730 -0.281615 0.377972 -0.229730 -0.281615 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 unit vectors defining three Libration axes 0.52562 0.30035 -0.79594 -0.49614 0.86824 0.00000 0.69107 0.39489 0.60538 rotation axes pass through the points in the M base parallel to lx : (wix,wiy,wiz)= 0.42794 0.16025 0.34308 parallel to ly : (wjx,wjy,wjz)= 0.23351 0.13344 0.18418 parallel to lz : (wkx,wky,wkz)= 0.37797 -0.22973 -0.28161 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 -0.07318 0.56671 parallel to ly : (wjx,wjy,wjz)= 0.01622 0.00000 0.32556 parallel to lz : (wkx,wky,wkz)= 0.35382 -0.38699 0.00000 correlation shifts sx,sy,sz for libration -0.609735 0.050066 0.045585 Vibration rms along V-axes tx ,ty ,tz = 0.1274311 0.1642324 0.2836089 vectors defining three Vibration axes -0.42104 -0.40149 0.81335 0.57765 0.57266 0.58171 -0.69932 0.71475 -0.00919 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.053980 -0.027497 -0.000053 0.055590 0.008909 0.033469 0.000996 -0.022490 0.018320 -0.027497 0.072179 -0.010181 0.008909 0.045091 0.019125 -0.007942 -0.015058 0.022859 -0.000053 -0.010181 0.033752 0.033469 0.019125 0.039319 0.004584 -0.024778 0.014070 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.053980 -0.027497 -0.000053 0.055590 0.008909 0.033469 0.008593 -0.022490 0.018320 -0.027497 0.072179 -0.010181 0.008909 0.045091 0.019125 -0.007942 -0.007461 0.022859 -0.000053 -0.010181 0.033752 0.033469 0.019125 0.039319 0.004584 -0.024778 0.021668 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.007597 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.007597 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.007597