**** GENERATION OF THE TLS MATRICES **** ** input control information ** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 vectors defining two first Libration axes 1.00000 2.00000 3.00000 3.00000 1.00000 0.00000 rotation axes pass through the points in the M(main) base parallel to lx : (wix,wiy,wiz)= 0.00000 1.00000 2.00000 parallel to ly : (wjx,wjy,wjz)= 3.00000 0.00000 2.00000 parallel to lz : (wkx,wky,wkz)= -1.00000 3.00000 0.00000 correlation shifts sx,sy,sz for libration 0.500000 -0.300000 0.700000 Vibration rms along V-axes tx ,ty ,tz = 0.1000000 0.4000000 0.8000000 vectors defining two first Vibration axes 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 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 0.26726 0.53452 0.80178 0.92212 0.09969 -0.37383 -0.27975 0.83925 -0.46625 rotation axes pass through the points in the M base axis 1 : (w1x,w1y,w1z)= 0.00000 1.00000 2.00000 axis 2 : (w2x,w2y,w2z)= 3.00000 0.00000 2.00000 axis 3 : (w3x,w3y,w3z)= -1.00000 3.00000 0.00000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 2.13809 -0.64798 -0.09325 parallel to ly : (wjx,wjy,wjz)= 2.40535 2.01870 -1.77176 parallel to lz : (wkx,wky,wkz)= 1.33631 -0.62306 2.79751 correlation shifts sx,sy,sz for libration 0.500000 -0.300000 0.700000 Vibration rms along V-axes tx ,ty ,tz = 0.1000000 0.4000000 0.8000000 vectors defining three Vibration axes 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 1.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base matrix T 0.19508225657046 0.02394905686378 0.00337608018890 0.02394905127585 0.56606027483940 0.01773042604327 0.00337607879192 0.01773044839501 0.65598911233246 matrix L 0.04177018627524 -0.01602484472096 0.00009316694923 -0.01602484472096 0.06664596498013 -0.03242236003280 0.00009316804790 -0.03242236003280 0.03158384934068 matrix S 0.02223291620612 0.10737888514996 0.02374224178493 -0.12305589020252 0.02514906972647 -0.02229813300073 0.07295962423086 -0.04255900904536 0.00861800741404 ================ 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 0.195082 0.023949 0.003376 0.041770 -0.016025 0.000093 0.022233 0.107379 0.023742 0.023949 0.566060 0.017730 -0.016025 0.066646 -0.032422 -0.123056 0.025149 -0.022298 0.003376 0.017730 0.655989 0.000093 -0.032422 0.031584 0.072960 -0.042559 0.008618 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.010000 0.267261 0.534522 0.801784 0.040000 0.922123 0.099689 -0.373834 0.090000 -0.279751 0.839254 -0.466252 rotation matrix P->L and its transposal: 0.267261 0.922123 -0.279751 0.267261 0.534522 0.801784 0.534522 0.099689 0.839254 0.922123 0.099689 -0.373834 0.801784 -0.373834 -0.466252 -0.279751 0.839254 -0.466252 resulted matrices T[L] L[L] S[L] in the L-base 0.620860 -0.105906 0.002243 0.010000 0.000000 0.000000 0.005000 -0.000932 0.006480 -0.105906 0.263935 0.121755 0.000000 0.040000 0.000000 0.070870 -0.012000 0.096214 0.002243 0.121755 0.532336 0.000000 0.000000 0.090000 -0.056075 -0.120268 0.063000 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 -0.647979 -0.093250 axis Ly crosses the point 2.405351 0.000000 -1.771759 axis Lz crosses the point 1.336306 -0.623056 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -0.160503 -0.074933 -0.170468 -0.074933 -0.160801 0.000604 -0.170468 0.000604 -0.235627 resulted matrices TC[L] L[L] S[L] in the L-base 0.460357 -0.180839 -0.168225 0.010000 0.000000 0.000000 0.005000 -0.000932 0.006480 -0.180839 0.103134 0.122359 0.000000 0.040000 0.000000 0.070870 -0.012000 0.096214 -0.168225 0.122359 0.296709 0.000000 0.000000 0.090000 -0.056075 -0.120268 0.063000 diagonal shift for the unconstrained min[tr(S)] 0.018667 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc -0.062850 0.052229 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00051 0.00469 0.03023 ts limits : tmint,tmaxt -0.101023 0.161873 ts limits : tmina,tmaxa -0.101023 0.161873 final limits : tmin,tmax -0.062850 0.052229 constrained ts to be removed from the S diagonal 0.013482 screw parameters sx,sy,sz -0.84820 -0.63705 0.55020 C[L] matrix diagonal elements 0.00719 0.01623 0.02724 ***** STEP E : vibration parameters matrix V[L]: 0.453163 -0.180839 -0.168225 -0.180839 0.086901 0.122359 -0.168225 0.122359 0.269464 eigenvalues and eigenvectors in base [L]: 0.000001 0.278425 0.928002 -0.247572 0.170454 0.539445 0.062173 0.839722 0.639072 0.794656 -0.367351 -0.483296 rotation matrix [P] -> [L]: 0.267261 0.922123 -0.279751 0.534522 0.099689 0.839254 0.801784 -0.373834 -0.466252 vibration tx,ty,tz along V axes & axes in base [M]: 0.001130 0.999403 0.033560 -0.008251 0.412861 -0.033409 0.999284 0.017753 0.799420 0.008841 -0.017467 0.999808 W points recalculated in the P and M bases -0.571429 -0.142857 0.285714 -0.571429 -0.142857 0.285714 1.138509 -0.201242 2.754658 1.138509 -0.201242 2.754658 -0.217391 0.652174 1.304348 -0.217391 0.652174 1.304348 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 unit vectors defining three Libration axes 0.26726 0.53452 0.80178 0.92212 0.09969 -0.37383 -0.27975 0.83925 -0.46625 rotation axes pass through the points in the M base parallel to lx : (wix,wiy,wiz)= -0.57143 -0.14286 0.28571 parallel to ly : (wjx,wjy,wjz)= 1.13851 -0.20124 2.75466 parallel to lz : (wkx,wky,wkz)= -0.21739 0.65217 1.30435 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 -0.64798 -0.09325 parallel to ly : (wjx,wjy,wjz)= 2.40535 0.00000 -1.77176 parallel to lz : (wkx,wky,wkz)= 1.33631 -0.62306 0.00000 correlation shifts sx,sy,sz for libration -0.848203 -0.637051 0.550200 Vibration rms along V-axes tx ,ty ,tz = 0.0011298 0.4128609 0.7994197 vectors defining three Vibration axes 0.99940 0.03356 -0.00825 -0.03341 0.99928 0.01775 0.00884 -0.01747 0.99981 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.195082 0.023949 0.003376 0.041770 -0.016025 0.000093 0.008751 0.107379 0.023742 0.023949 0.566060 0.017730 -0.016025 0.066646 -0.032422 -0.123056 0.011667 -0.022298 0.003376 0.017730 0.655989 0.000093 -0.032422 0.031584 0.072960 -0.042559 -0.004864 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.195082 0.023949 0.003376 0.041770 -0.016025 0.000093 0.022233 0.107379 0.023742 0.023949 0.566060 0.017730 -0.016025 0.066646 -0.032422 -0.123056 0.025149 -0.022298 0.003376 0.017730 0.655989 0.000093 -0.032422 0.031584 0.072960 -0.042559 0.008618 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.013482 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.013482 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.013482