**** 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 -2.00000 0.00000 0.00000 1.00000 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 0.26726 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 -0.44721 0.89443 0.00000 0.59628 0.29814 0.74536 0.66667 0.33333 -0.66667 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base matrix T 0.52841559052467 0.19061572849751 -0.20995725831017 0.19061572290957 0.49939361214638 -0.08893624320626 -0.20995725970715 -0.08893622085452 0.38932246156037 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 0.528416 0.190616 -0.209957 0.041770 -0.016025 0.000093 0.022233 0.107379 0.023742 0.190616 0.499394 -0.088936 -0.016025 0.066646 -0.032422 -0.123056 0.025149 -0.022298 -0.209957 -0.088936 0.389322 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 0.318955 0.015586 0.088806 0.010000 0.000000 0.000000 0.005000 -0.000932 0.006480 0.015586 0.695116 0.215877 0.000000 0.040000 0.000000 0.070870 -0.012000 0.096214 0.088806 0.215877 0.403061 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 0.158452 -0.059347 -0.081662 0.010000 0.000000 0.000000 0.005000 -0.000932 0.006480 -0.059347 0.534314 0.216482 0.000000 0.040000 0.000000 0.070870 -0.012000 0.096214 -0.081662 0.216482 0.167433 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 -0.034806 0.044806 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00102 0.00522 0.03179 ts limits : tmint,tmaxt -0.115284 0.166284 ts limits : tmina,tmaxa -0.115284 0.166284 final limits : tmin,tmax -0.034806 0.044806 constrained ts to be removed from the S diagonal 0.018661 screw parameters sx,sy,sz -1.36614 -0.76654 0.49265 C[L] matrix diagonal elements 0.01866 0.02350 0.02184 ***** STEP E : vibration parameters matrix V[L]: 0.139789 -0.059347 -0.081662 -0.059347 0.510811 0.216482 -0.081662 0.216482 0.145590 eigenvalues and eigenvectors in base [L]: 0.021988 0.423696 -0.323287 0.846148 0.146687 0.887846 0.333308 -0.317229 0.627515 -0.179472 0.885658 0.428251 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]: 0.148284 -0.421584 0.904381 0.066050 0.382997 0.633383 0.241565 0.735168 0.792158 0.648916 0.351770 -0.674660 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 -1.366145 -0.766536 0.492651 Vibration rms along V-axes tx ,ty ,tz = 0.1482835 0.3829975 0.7921584 vectors defining three Vibration axes -0.42158 0.90438 0.06605 0.63338 0.24157 0.73517 0.64892 0.35177 -0.67466 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.528416 0.190616 -0.209957 0.041770 -0.016025 0.000093 0.003571 0.107379 0.023742 0.190616 0.499394 -0.088936 -0.016025 0.066646 -0.032422 -0.123056 0.006488 -0.022298 -0.209957 -0.088936 0.389322 0.000093 -0.032422 0.031584 0.072960 -0.042559 -0.010043 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.528416 0.190616 -0.209957 0.041770 -0.016025 0.000093 0.022233 0.107379 0.023742 0.190616 0.499394 -0.088936 -0.016025 0.066646 -0.032422 -0.123056 0.025149 -0.022298 -0.209957 -0.088936 0.389322 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 -0.018661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.018661 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.018661