**** 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 2.00000 3.00000 parallel to ly : (wjx,wjy,wjz)= -1.00000 0.00000 2.00000 parallel to lz : (wkx,wky,wkz)= 4.00000 1.00000 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 2.00000 3.00000 axis 2 : (w2x,w2y,w2z)= -1.00000 0.00000 2.00000 axis 3 : (w3x,w3y,w3z)= 4.00000 1.00000 0.00000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 3.47440 -0.92212 0.27975 parallel to ly : (wjx,wjy,wjz)= 1.33631 -1.66979 -0.65275 parallel to lz : (wkx,wky,wkz)= 1.60357 3.78818 -0.27975 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 0.03784626163542 -0.09965340048075 -0.14676673710346 -0.09965340793133 0.59776830673218 0.58396643400192 -0.14676675200462 0.58396643400192 1.84529972076416 matrix L 0.04177018627524 -0.01602484472096 0.00009316694923 -0.01602484472096 0.06664596498013 -0.03242236003280 0.00009316804790 -0.03242236003280 0.03158384934068 matrix S -0.00053105974803 -0.00575776770711 -0.08324535191059 -0.05119254440069 0.19670186936855 0.24937887489796 0.03597204759717 -0.11588197946548 -0.14017079770565 ================ 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 0.037846 -0.099653 -0.146767 0.041770 -0.016025 0.000093 -0.000531 -0.005758 -0.083245 -0.099653 0.597768 0.583966 -0.016025 0.066646 -0.032422 -0.051193 0.196702 0.249379 -0.146767 0.583966 1.845300 0.000093 -0.032422 0.031584 0.035972 -0.115882 -0.140171 ***** 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 1.768929 -0.727554 -0.133334 0.010000 0.000000 0.000000 0.005000 0.002798 0.009221 -0.727554 0.335345 0.124939 0.000000 0.040000 0.000000 0.026110 -0.012000 0.053452 -0.133334 0.124939 0.376640 0.000000 0.000000 0.090000 0.340936 -0.144321 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 -0.922123 0.279752 axis Ly crosses the point 1.336306 0.000000 -0.652753 axis Lz crosses the point 1.603567 3.788180 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -1.308571 0.546714 -0.034891 0.546714 -0.232211 -0.002580 -0.034891 -0.002580 -0.079932 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 0.002798 0.009221 -0.180839 0.103134 0.122359 0.000000 0.040000 0.000000 0.026110 -0.012000 0.053452 -0.168225 0.122359 0.296709 0.000000 0.000000 0.090000 0.340936 -0.144321 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 0.062174 0.839722 0.639072 0.794656 -0.367351 -0.483295 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]: 0.001132 0.999403 0.033560 -0.008251 0.412861 -0.033409 0.999284 0.017753 0.799420 0.008840 -0.017467 0.999808 W points recalculated in the P and M bases -0.928572 0.142857 0.214286 -0.928572 0.142857 0.214286 0.539751 0.166460 1.375776 0.539751 0.166460 1.375776 3.921739 1.234782 -0.130435 3.921739 1.234782 -0.130435 ==================================================== *** 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)= -0.92857 0.14286 0.21429 parallel to ly : (wjx,wjy,wjz)= 0.53975 0.16646 1.37578 parallel to lz : (wkx,wky,wkz)= 3.92174 1.23478 -0.13043 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 -0.92212 0.27975 parallel to ly : (wjx,wjy,wjz)= 1.33631 0.00000 -0.65275 parallel to lz : (wkx,wky,wkz)= 1.60357 3.78818 0.00000 correlation shifts sx,sy,sz for libration -0.848204 -0.637051 0.550200 Vibration rms along V-axes tx ,ty ,tz = 0.0011325 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 0.037846 -0.099653 -0.146767 0.041770 -0.016025 0.000093 -0.014013 -0.005758 -0.083245 -0.099653 0.597768 0.583966 -0.016025 0.066646 -0.032422 -0.051193 0.183220 0.249379 -0.146767 0.583966 1.845300 0.000093 -0.032422 0.031584 0.035972 -0.115882 -0.153653 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.037846 -0.099653 -0.146767 0.041770 -0.016025 0.000093 -0.000531 -0.005758 -0.083245 -0.099653 0.597768 0.583966 -0.016025 0.066646 -0.032422 -0.051193 0.196702 0.249379 -0.146767 0.583966 1.845300 0.000093 -0.032422 0.031584 0.035972 -0.115882 -0.140171 =============== 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