**** 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 1.00000 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 = 0.0000000 0.0000000 0.0000000 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 0.00000 -0.70711 0.70711 1.00000 0.00000 0.00000 0.00000 0.70711 0.70711 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)= -0.07071 0.43000 0.39598 parallel to ly : (wjx,wjy,wjz)= -0.07071 0.11000 0.36770 parallel to lz : (wkx,wky,wkz)= 0.07071 -0.22000 0.52326 correlation shifts sx,sy,sz for libration 0.150000 0.240000 0.130000 Vibration rms along V-axes tx ,ty ,tz = 0.0000000 0.0000000 0.0000000 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 0.00432200031355 -0.00219400017522 -0.00021399976686 -0.00219400017522 0.00573949981481 -0.00320949964225 -0.00021399991238 -0.00320949987508 0.00781949982047 matrix L 0.03999999910593 0.00000000000000 0.00000000000000 0.00000000000000 0.05000000074506 0.03999999910593 0.00000000000000 0.03999999910593 0.05000000074506 matrix S 0.00960000045598 0.00840000063181 -0.01239999942482 -0.00730000063777 0.01865000091493 -0.00265000062063 -0.00170000083745 0.01284999959171 -0.00544999912381 ================ 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 0.004322 -0.002194 -0.000214 0.040000 0.000000 0.000000 0.009600 0.008400 -0.012400 -0.002194 0.005739 -0.003209 0.000000 0.050000 0.040000 -0.007300 0.018650 -0.002650 -0.000214 -0.003209 0.007819 0.000000 0.040000 0.050000 -0.001700 0.012850 -0.005450 ***** STEP B : libration amplitudes and axes three eigenvalues and corresponding eigenvectors: 0.010000 0.000000 -0.707107 0.707107 0.040000 1.000000 0.000000 0.000000 0.090000 0.000000 0.707107 0.707107 rotation matrix P->L and its transposal: 0.000000 1.000000 0.000000 0.000000 -0.707107 0.707107 -0.707107 0.000000 0.707107 1.000000 0.000000 0.000000 0.707107 0.000000 0.707107 0.000000 0.707107 0.707107 resulted matrices T[L] L[L] S[L] in the L-base 0.009989 0.001400 0.001040 0.010000 0.000000 0.000000 0.001500 0.003960 -0.004300 0.001400 0.004322 -0.001703 0.000000 0.040000 0.000000 -0.014708 0.009600 -0.002828 0.001040 -0.001703 0.003570 0.000000 0.000000 0.090000 -0.019800 -0.006364 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 0.395980 axis Ly crosses the point -0.070711 0.000000 0.367696 axis Lz crosses the point 0.070711 -0.220000 0.000000 ***** STEP D : optimal screw parameters D[L] matrix to be removed from the T matrix : -0.009764 -0.001400 -0.001040 -0.001400 -0.002018 0.001703 -0.001040 0.001703 -0.002049 resulted matrices TC[L] L[L] S[L] in the L-base 0.000225 0.000000 0.000000 0.010000 0.000000 0.000000 0.001500 0.003960 -0.004300 0.000000 0.002304 0.000000 0.000000 0.040000 0.000000 -0.014708 0.009600 -0.002828 0.000000 0.000000 0.001521 0.000000 0.000000 0.090000 -0.019800 -0.006364 0.011700 diagonal shift for the unconstrained min[tr(S)] 0.007600 checking Cauchy enequality general case : three librations ts limits : tminc,tmaxc 0.000000 0.003000 checking positive definition of the residual matrix eigenvalues of T[lambda] 0.00000 0.00009 0.00014 ts limits : tmint,tmaxt 0.000000 0.013200 ts limits : tmina,tmaxa 0.000000 0.013200 final limits : tmin,tmax 0.000000 0.003000 constrained ts to be removed from the S diagonal 0.003000 screw parameters sx,sy,sz -0.14997 0.16501 0.09667 C[L] matrix diagonal elements 0.00022 0.00109 0.00084 ***** STEP E : vibration parameters matrix V[L]: 0.000000 0.000000 0.000000 0.000000 0.001215 0.000000 0.000000 0.000000 0.000680 eigenvalues and eigenvectors in base [L]: 0.000000 -1.000000 0.000000 0.000001 0.000680 0.000001 0.000000 1.000000 0.001215 0.000000 1.000000 0.000000 rotation matrix [P] -> [L]: 0.000000 1.000000 0.000000 -0.707107 0.000000 0.707107 0.707107 0.000000 0.707107 vibration tx,ty,tz along V axes & axes in base [M]: 0.000300 0.000000 0.707107 -0.707106 0.026076 0.000000 0.707106 0.707107 0.034855 1.000000 0.000000 0.000000 W points recalculated in the P and M bases 0.430000 0.280000 0.280000 0.430000 0.280000 0.280000 0.000000 0.310000 0.210000 0.000000 0.310000 0.210000 -0.220000 -0.050000 0.050000 -0.220000 -0.050000 0.050000 ==================================================== *** 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 -0.70711 0.70711 1.00000 0.00000 0.00000 0.00000 0.70711 0.70711 rotation axes pass through the points in the M base parallel to lx : (wix,wiy,wiz)= 0.43000 0.28000 0.28000 parallel to ly : (wjx,wjy,wjz)= 0.00000 0.31000 0.21000 parallel to lz : (wkx,wky,wkz)= -0.22000 -0.05000 0.05000 rotation axes pass through the points in the L base parallel to lx : (wix,wiy,wiz)= 0.00000 0.43000 0.39598 parallel to ly : (wjx,wjy,wjz)= -0.07071 0.00000 0.36770 parallel to lz : (wkx,wky,wkz)= 0.07071 -0.22000 0.00000 correlation shifts sx,sy,sz for libration -0.149970 0.165008 0.096670 Vibration rms along V-axes tx ,ty ,tz = 0.0002999 0.0260757 0.0348554 vectors defining three Vibration axes 0.00000 0.70711 -0.70711 0.00000 0.70711 0.70711 1.00000 0.00000 0.00000 =================== TLS BUILT FROM THE BASE ELEMENTS ================== matrices T L S in the original M-base 0.004322 -0.002194 -0.000214 0.040000 0.000000 0.000000 0.006600 0.008400 -0.012400 -0.002194 0.005739 -0.003209 0.000000 0.050000 0.040000 -0.007300 0.015650 -0.002650 -0.000214 -0.003209 0.007819 0.000000 0.040000 0.050000 -0.001700 0.012850 -0.008450 =================== REMINDER OF THE INPUT MATRICES =================== matrices T L S in the original M-base 0.004322 -0.002194 -0.000214 0.040000 0.000000 0.000000 0.009600 0.008400 -0.012400 -0.002194 0.005739 -0.003209 0.000000 0.050000 0.040000 -0.007300 0.018650 -0.002650 -0.000214 -0.003209 0.007819 0.000000 0.040000 0.050000 -0.001700 0.012850 -0.005450 =============== MATRICES DIFFERENCE =============== matrices T L S : new - inital 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.003000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.003000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.003000