**** 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 0.00000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= 0.00000 0.00000 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 0.00000 0.00000 axis 2 : (w2x,w2y,w2z)= 0.00000 0.00000 0.00000 axis 3 : (w3x,w3y,w3z)= 0.00000 0.00000 0.00000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 0.00000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= 0.00000 0.00000 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 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 0.01669099321589 -0.00966583844274 0.00504689430818 -0.00966583844274 0.19181180000305 -0.01631925441325 0.00504689430818 -0.01631925441325 0.65169719047844 matrix L 0.04177018627524 -0.01602484472096 0.00009316694923 -0.01602484472096 0.06664596498013 -0.03242236003280 0.00009316804790 -0.03242236003280 0.03158384934068 matrix S -0.00491614919156 -0.01518012396991 0.01342546567321 -0.01518012396991 0.04568323120475 -0.02206211164594 0.01342546567321 -0.02206211164594 0.01523291878402 ================ 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 0.016691 -0.009666 0.005047 0.041770 -0.016025 0.000093 -0.004916 -0.015180 0.013425 -0.009666 0.191812 -0.016319 -0.016025 0.066646 -0.032422 -0.015180 0.045683 -0.022062 0.005047 -0.016319 0.651697 0.000093 -0.032422 0.031584 0.013425 -0.022062 0.015233 ***** 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 0.460357 -0.180839 -0.168225 0.010000 0.000000 0.000000 0.005000 0.000000 0.000000 -0.180839 0.103134 0.122359 0.000000 0.040000 0.000000 0.000000 -0.012000 0.000000 -0.168225 0.122359 0.296709 0.000000 0.000000 0.090000 0.000000 0.000000 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 0.000000 0.000000 axis Ly crosses the point 0.000000 0.000000 0.000000 axis Lz crosses the point 0.000000 0.000000 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 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 0.000000 0.000000 -0.180839 0.103134 0.122359 0.000000 0.040000 0.000000 0.000000 -0.012000 0.000000 -0.168225 0.122359 0.296709 0.000000 0.000000 0.090000 0.000000 0.000000 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]: 0.001136 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 0.000000 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 ==================================================== *** 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)= 0.00000 0.00000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= 0.00000 0.00000 0.00000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 0.00000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.00000 0.00000 parallel to lz : (wkx,wky,wkz)= 0.00000 0.00000 0.00000 correlation shifts sx,sy,sz for libration -0.848204 -0.637051 0.550200 Vibration rms along V-axes tx ,ty ,tz = 0.0011356 0.4128609 0.7994198 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 0.016691 -0.009666 0.005047 0.041770 -0.016025 0.000093 -0.018398 -0.015180 0.013425 -0.009666 0.191812 -0.016319 -0.016025 0.066646 -0.032422 -0.015180 0.032201 -0.022062 0.005047 -0.016319 0.651697 0.000093 -0.032422 0.031584 0.013425 -0.022062 0.001751 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.016691 -0.009666 0.005047 0.041770 -0.016025 0.000093 -0.004916 -0.015180 0.013425 -0.009666 0.191812 -0.016319 -0.016025 0.066646 -0.032422 -0.015180 0.045683 -0.022062 0.005047 -0.016319 0.651697 0.000093 -0.032422 0.031584 0.013425 -0.022062 0.015233 =============== 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