**** 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 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 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 0.00000 -1.00000 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 0.00000 0.00000 1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 rotation axes pass through the points in the M base axis 1 : (w1x,w1y,w1z)= 0.43000 0.33000 0.23000 axis 2 : (w2x,w2y,w2z)= 0.11000 0.31000 0.21000 axis 3 : (w3x,w3y,w3z)= -0.22000 0.32000 0.42000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.23000 0.43000 0.33000 parallel to ly : (wjx,wjy,wjz)= 0.21000 0.11000 0.31000 parallel to lz : (wkx,wky,wkz)= 0.42000 -0.22000 0.32000 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 0.00000 0.00000 -1.00000 0.70711 0.70711 0.00000 0.70711 -0.70711 0.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base matrix T 0.07126899994910 -0.02781899808906 0.00831599999219 -0.02781899808906 0.05713400105014 -0.00260400003754 0.00831599999219 -0.00260400003754 0.02802500035614 matrix L 0.03999999910593 0.00000000000000 0.00000000000000 0.00000000000000 0.09000000357628 0.00000000000000 0.00000000000000 0.00000000000000 0.00999999977648 matrix S 0.00960000045598 0.00839999970049 -0.01240000035614 -0.03779999911785 0.01169999968261 -0.01979999989271 0.00330000021495 -0.00430000014603 0.00150000001304 ================ 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 0.071269 -0.027819 0.008316 0.040000 0.000000 0.000000 0.009600 0.008400 -0.012400 -0.027819 0.057134 -0.002604 0.000000 0.090000 0.000000 -0.037800 0.011700 -0.019800 0.008316 -0.002604 0.028025 0.000000 0.000000 0.010000 0.003300 -0.004300 0.001500 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.010000 0.000000 0.000000 1.000000 0.040000 1.000000 0.000000 0.000000 0.090000 0.000000 1.000000 0.000000 rotation matrix P->L and its transposal: 0.000000 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 1.000000 1.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 resulted matrices T[L] L[L] S[L] in the L-base 0.028025 0.008316 -0.002604 0.010000 0.000000 0.000000 0.001500 0.003300 -0.004300 0.008316 0.071269 -0.027819 0.000000 0.040000 0.000000 -0.012400 0.009600 0.008400 -0.002604 -0.027819 0.057134 0.000000 0.000000 0.090000 -0.019800 -0.037800 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 0.430000 0.330000 axis Ly crosses the point 0.210000 0.000000 0.310000 axis Lz crosses the point 0.420000 -0.220000 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -0.008200 -0.008316 0.002604 -0.008316 -0.016965 0.001419 0.002604 0.001419 -0.003613 resulted matrices TC[L] L[L] S[L] in the L-base 0.019825 0.000000 0.000000 0.010000 0.000000 0.000000 0.001500 0.003300 -0.004300 0.000000 0.054304 -0.026400 0.000000 0.040000 0.000000 -0.012400 0.009600 0.008400 0.000000 -0.026400 0.053521 0.000000 0.000000 0.090000 -0.019800 -0.037800 0.011700 diagonal shift for the unconstrained min[tr(S)] 0.007600 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc -0.012580 0.015580 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00020 0.00143 0.00556 ts limits : tmint,tmaxt -0.058972 0.076052 ts limits : tmina,tmaxa -0.058972 0.076052 final limits : tmin,tmax -0.012580 0.015580 constrained ts to be removed from the S diagonal 0.007600 screw parameters sx,sy,sz -0.60995 0.05001 0.04556 C[L] matrix diagonal elements 0.00372 0.00010 0.00019 ***** STEP E : vibration parameters matrix V[L]: 0.016105 0.000000 0.000000 0.000000 0.054204 -0.026400 0.000000 -0.026400 0.053334 eigenvalues and eigenvectors in base [L]: 0.016105 -1.000000 0.000000 0.000000 0.027365 0.000000 0.701259 0.712906 0.080173 0.000000 0.712906 -0.701259 rotation matrix [P] -> [L]: 0.000000 1.000000 0.000000 0.000000 0.000000 1.000000 1.000000 0.000000 0.000000 vibration tx,ty,tz along V axes & axes in base [M]: 0.126904 0.000000 0.000000 -1.000000 0.165425 0.701259 0.712906 0.000000 0.283148 0.712906 -0.701259 0.000000 W points recalculated in the P and M bases 0.430000 0.330000 0.000000 0.430000 0.330000 0.000000 0.000000 0.310000 0.210000 0.000000 0.310000 0.210000 -0.220000 0.000000 0.420000 -0.220000 0.000000 0.420000 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.2000000 0.3000000 unit vectors defining three Libration axes 0.00000 0.00000 1.00000 1.00000 0.00000 0.00000 0.00000 1.00000 0.00000 rotation axes pass through the points in the M base parallel to lx : (wix,wiy,wiz)= 0.43000 0.33000 0.00000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.31000 0.21000 parallel to lz : (wkx,wky,wkz)= -0.22000 0.00000 0.42000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 0.43000 0.33000 parallel to ly : (wjx,wjy,wjz)= 0.21000 0.00000 0.31000 parallel to lz : (wkx,wky,wkz)= 0.42000 -0.22000 0.00000 correlation shifts sx,sy,sz for libration -0.609951 0.050012 0.045561 Vibration rms along V-axes tx ,ty ,tz = 0.1269039 0.1654252 0.2831477 vectors defining three Vibration axes 0.00000 0.00000 -1.00000 0.70126 0.71291 0.00000 0.71291 -0.70126 0.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.071269 -0.027819 0.008316 0.040000 0.000000 0.000000 0.002000 0.008400 -0.012400 -0.027819 0.057134 -0.002604 0.000000 0.090000 0.000000 -0.037800 0.004100 -0.019800 0.008316 -0.002604 0.028025 0.000000 0.000000 0.010000 0.003300 -0.004300 -0.006100 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.071269 -0.027819 0.008316 0.040000 0.000000 0.000000 0.009600 0.008400 -0.012400 -0.027819 0.057134 -0.002604 0.000000 0.090000 0.000000 -0.037800 0.011700 -0.019800 0.008316 -0.002604 0.028025 0.000000 0.000000 0.010000 0.003300 -0.004300 0.001500 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.007600 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.007600 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.007600