**** 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 0.000000 0.000000 0.000000 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 0.000000 0.000000 0.000000 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 0.03115526959300 -0.08998756110668 -0.15181362628937 -0.08998756110668 0.56595650315285 0.60028570890427 -0.15181365609169 0.60028564929962 1.83360230922699 matrix L 0.04177018627524 -0.01602484472096 0.00009316694923 -0.01602484472096 0.06664596498013 -0.03242236003280 0.00009316804790 -0.03242236003280 0.03158384934068 matrix S 0.00438508950174 0.00942235998809 -0.09667080640793 -0.03601242229342 0.15101863443851 0.27144098281860 0.02254657819867 -0.09381987154484 -0.15540373325348 ================ 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 0.031155 -0.089988 -0.151814 0.041770 -0.016025 0.000093 0.004385 0.009422 -0.096671 -0.089988 0.565957 0.600286 -0.016025 0.066646 -0.032422 -0.036012 0.151019 0.271441 -0.151814 0.600286 1.833602 0.000093 -0.032422 0.031584 0.022547 -0.093820 -0.155404 ***** 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 1.766428 -0.727554 -0.133334 0.010000 0.000000 0.000000 0.000000 0.002798 0.009221 -0.727554 0.331745 0.124939 0.000000 0.040000 0.000000 0.026110 0.000000 0.053452 -0.133334 0.124939 0.332540 0.000000 0.000000 0.090000 0.340936 -0.144321 0.000000 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 -0.922124 0.279752 axis Ly crosses the point 1.336306 0.000000 -0.652753 axis Lz crosses the point 1.603568 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 0.457857 -0.180839 -0.168225 0.010000 0.000000 0.000000 0.000000 0.002798 0.009221 -0.180839 0.099534 0.122359 0.000000 0.040000 0.000000 0.026110 0.000000 0.053452 -0.168225 0.122359 0.252609 0.000000 0.000000 0.090000 0.340936 -0.144321 0.000000 diagonal shift for the unconstrained min[tr(S)] 0.000000 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc -0.063098 0.063098 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00034 0.00410 0.02686 ts limits : tmint,tmaxt -0.096239 0.163904 ts limits : tmina,tmaxa -0.096239 0.163904 final limits : tmin,tmax -0.063098 0.063098 constrained ts to be removed from the S diagonal 0.000000 screw parameters sx,sy,sz 0.00000 0.00000 0.00000 C[L] matrix diagonal elements 0.00000 0.00000 0.00000 ***** STEP E : vibration parameters matrix V[L]: 0.457857 -0.180839 -0.168225 -0.180839 0.099534 0.122359 -0.168225 0.122359 0.252609 eigenvalues and eigenvectors in base [L]: 0.010000 0.267261 0.922123 -0.279752 0.160000 0.534522 0.099689 0.839254 0.640000 0.801784 -0.373834 -0.466252 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]: 0.100000 1.000000 0.000000 0.000000 0.400000 0.000000 1.000000 0.000000 0.800000 0.000000 0.000000 1.000000 W points recalculated in the P and M bases -0.928573 0.142857 0.214286 -0.928573 0.142857 0.214286 0.539752 0.166460 1.375776 0.539752 0.166460 1.375776 3.921739 1.234783 -0.130435 3.921739 1.234783 -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 -0.000001 0.000000 0.000000 Vibration rms along V-axes tx ,ty ,tz = 0.0999998 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 0.031155 -0.089988 -0.151814 0.041770 -0.016025 0.000093 0.004385 0.009422 -0.096671 -0.089988 0.565957 0.600286 -0.016025 0.066646 -0.032422 -0.036012 0.151019 0.271441 -0.151814 0.600286 1.833602 0.000093 -0.032422 0.031584 0.022547 -0.093820 -0.155404 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.031155 -0.089988 -0.151814 0.041770 -0.016025 0.000093 0.004385 0.009422 -0.096671 -0.089988 0.565957 0.600286 -0.016025 0.066646 -0.032422 -0.036012 0.151019 0.271441 -0.151814 0.600286 1.833602 0.000093 -0.032422 0.031584 0.022547 -0.093820 -0.155404 =============== 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