**** GENERATION OF THE TLS MATRICES **** ** input control information ** Libration rms around L-axes dx ,dy ,dz = 0.1000000 0.0000000 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 = 0.0000000 0.1000000 0.3000000 unit vectors defining three Libration axes -0.92212 -0.09969 0.37383 0.26726 0.53452 0.80178 -0.27975 0.83925 -0.46625 rotation axes pass through the points in the M base axis 1 : (w1x,w1y,w1z)= -0.72298 -0.40248 3.50932 axis 2 : (w2x,w2y,w2z)= 1.19503 1.12919 1.51553 axis 3 : (w3x,w3y,w3z)= 0.14907 3.12422 -0.46584 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 2.01870 2.40535 -1.77176 parallel to ly : (wjx,wjy,wjz)= -0.64798 2.13809 -0.09325 parallel to lz : (wkx,wky,wkz)= -0.62306 1.33631 2.79751 correlation shifts sx,sy,sz for libration -0.300000 0.500000 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 0.44927228242159 0.13697694242001 -0.30255399644375 0.13697694242001 0.13176232576370 -0.10674760008260 -0.30255399644375 -0.10674759771064 0.47550328820944 matrix L 0.00775776384398 -0.01970186270773 0.01388198696077 -0.01970186457038 0.06624844670296 -0.03093167766929 0.01388198789209 -0.03093167766929 0.02599378861487 matrix S 0.03237453103065 -0.02058633603156 -0.01496583875269 -0.09406460076571 0.05793913081288 0.05475777015090 0.05477329343557 -0.03532919287682 -0.02231366559863 ================ 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 0.449272 0.136977 -0.302554 0.007758 -0.019702 0.013882 0.032375 -0.020586 -0.014966 0.136977 0.131762 -0.106748 -0.019702 0.066248 -0.030932 -0.094065 0.057939 0.054758 -0.302554 -0.106748 0.475503 0.013882 -0.030932 0.025994 0.054773 -0.035329 -0.022314 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.000000 -0.922123 -0.099689 0.373834 0.010000 0.267261 0.534522 0.801784 0.090000 -0.279751 0.839254 -0.466252 rotation matrix P->L and its transposal: -0.922123 0.267261 -0.279751 -0.922123 -0.099689 0.373834 -0.099689 0.534522 0.839254 0.267261 0.534522 0.801784 0.373834 0.801784 -0.466252 -0.279751 0.839254 -0.466252 resulted matrices T[L] L[L] S[L] in the L-base 0.691516 0.134281 -0.217086 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.134281 0.193390 -0.081662 0.000000 0.010000 0.000000 0.000933 0.005000 -0.006480 -0.217086 -0.081662 0.171632 0.000000 0.000000 0.090000 0.120268 0.056075 0.063000 libration amplitudes around the L axes: 0.000000 0.100000 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 -0.647978 0.000000 -0.093251 axis Lz crosses the point -0.623056 1.336306 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -0.160801 -0.074933 0.000604 -0.074933 -0.034938 0.000000 0.000604 0.000000 -0.004199 resulted matrices TC[L] L[L] S[L] in the L-base 0.530714 0.059347 -0.216482 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.059347 0.158452 -0.081662 0.000000 0.010000 0.000000 0.000933 0.005000 -0.006480 -0.216482 -0.081662 0.167433 0.000000 0.000000 0.090000 0.120268 0.056075 0.063000 diagonal shift for the unconstrained min[tr(S)] - non applicable checking Cauchy enequality special case : one of librations is degenerated ts limits : tminc,tmaxc - non applicable checking positive definition of the residual matrix eigenvalues of T[lambda] - non applicable ts limits : tmint,tmaxt - non applicable ts limits : tmina,tmaxa - non applicable final limits : tmin,tmax - non applicable constrained ts to be removed from the S diagonal 0.000000 screw parameters sx,sy,sz 0.00000 0.50000 0.70000 C[L] matrix diagonal elements 0.00000 0.00250 0.04410 ***** STEP E : vibration parameters matrix V[L]: 0.530714 0.059347 -0.216482 0.059347 0.155952 -0.081662 -0.216482 -0.081662 0.123333 eigenvalues and eigenvectors in base [L]: 0.010000 -0.323221 -0.358569 -0.875760 0.160000 -0.300930 0.916342 -0.264118 0.640000 0.897201 0.178174 -0.404085 rotation matrix [P] -> [L]: -0.922123 0.267261 -0.279751 -0.099689 0.534522 0.839254 0.373834 0.801784 -0.466252 vibration tx,ty,tz along V axes & axes in base [M]: 0.100000 0.447213 -0.894427 0.000000 0.400000 0.596285 0.298142 0.745356 0.800000 -0.666667 -0.333333 0.666667 W points recalculated in the P and M bases 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.623603 -0.013665 -0.198758 0.623603 -0.013665 -0.198758 0.931677 0.776398 0.838509 0.931677 0.776398 0.838509 ==================================================== *** TLS DECOMPOSED : BASIC ELEMENTS *** Libration rms around L-axes dx ,dy ,dz = 0.0000000 0.1000000 0.3000000 unit vectors defining three Libration axes -0.92212 -0.09969 0.37383 0.26726 0.53452 0.80178 -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)= 0.62360 -0.01366 -0.19876 parallel to lz : (wkx,wky,wkz)= 0.93168 0.77640 0.83851 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)= -0.64798 0.00000 -0.09325 parallel to lz : (wkx,wky,wkz)= -0.62306 1.33631 0.00000 correlation shifts sx,sy,sz for libration 0.000000 0.500001 0.700000 Vibration rms along V-axes tx ,ty ,tz = 0.0999998 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 0.449272 0.136977 -0.302554 0.007758 -0.019702 0.013882 0.032375 -0.020586 -0.014966 0.136977 0.131762 -0.106748 -0.019702 0.066248 -0.030932 -0.094065 0.057939 0.054758 -0.302554 -0.106748 0.475503 0.013882 -0.030932 0.025994 0.054773 -0.035329 -0.022314 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.449272 0.136977 -0.302554 0.007758 -0.019702 0.013882 0.032375 -0.020586 -0.014966 0.136977 0.131762 -0.106748 -0.019702 0.066248 -0.030932 -0.094065 0.057939 0.054758 -0.302554 -0.106748 0.475503 0.013882 -0.030932 0.025994 0.054773 -0.035329 -0.022314 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 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 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000