<p> Euler system </p>

5942db67-788a-4d4f-a85b-9cfe1169f717 4 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

n 3 :

R 373 :

x y P n R * y x / * :

T 15 1.5 range : V 15 1.5 range : i 1 T rows range j 1 V rows range data i j el n R * T i el V j el / * eval : for for 31 line

Lo 0 : Hi 5 : 12 mat

M x y Spline A M 112 M cols submatrix : B M 2 M rows 11 submatrix : C M 2 M rows 2 M cols submatrix : j 1 A length 2 range s j el B C 1 C rows j j submatrix y linterp : for A transpose s x linterp 51 line :

data 1119746 559.5 447.6 373 319.7 279.8 248.7 223.8 1678.5 1119 839.2 671.4 559.5 479.6 419.6 373 335.7 223814921119 895.2 746 639.4 559.5 497.3 447.6 2797.5 1865 1398.8 1119 932.5 799.3 699.4 621.7 559.5 33572238 1678.5 1342.8 1119 959.1 839.2 746 671.4 3916.5 2611 1958.2 1566.6 1305.5 1119 979.1 870.3 783.3 447629842238 1790.4 1492 1278.9 1119 994.7 895.2 5035.5 3357 2517.8 2014.2 1678.5 1438.7 1258.9 1119 1007.1 55953730 2797.5 22381865 1598.6 1398.8 1243.3 111999 mat

rangeX i 1 data cols range vx i el i Hi Lo - data cols 1 + / * : for vx 21 line :

rangeY i 1 data rows range vy i 1 + el i Hi Lo - data rows 1 + / * : for vy 21 line :

New rangeY rangeX transpose data stack augment : 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1119746 559.5 447.6 373 319.71 279.75 248.67 223.8 1 1678.5 1119 839.25 671.4 559.5 479.57 419.62 373 335.7 1.5 223814921119 895.2 746 639.43 559.5 497.33 447.6 2 2797.5 1865 1398.75 1119 932.5 799.29 699.38 621.67 559.5 2.5 33572238 1678.5 1342.8 1119 959.14 839.25 746 671.4 3 3916.5 2611 1958.25 1566.6 1305.5 1119 979.12 870.33 783.3 3.5 447629842238 1790.4 1492 1278.86 1119 994.67 895.2 4 5035.5 3357 2517.75 2014.2 1678.5 1438.71 1258.88 1119 1007.1 4.5 55953730 2797.5 22381865 1598.57 1398.75 1243.33 11191010 mat

New 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1119746 559.5 447.6 373 319.71 279.75 248.67 223.8 1 1678.5 1119 839.25 671.4 559.5 479.57 419.62 373 335.7 1.5 223814921119 895.2 746 639.43 559.5 497.33 447.6 2 2797.5 1865 1398.75 1119 932.5 799.29 699.38 621.67 559.5 2.5 33572238 1678.5 1342.8 1119 959.14 839.25 746 671.4 3 3916.5 2611 1958.25 1566.6 1305.5 1119 979.12 870.33 783.3 3.5 447629842238 1790.4 1492 1278.86 1119 994.67 895.2 4 5035.5 3357 2517.75 2014.2 1678.5 1438.71 1258.88 1119 1007.1 4.5 55953730 2797.5 22381865 1598.57 1398.75 1243.33 11191010 mat :

<= Introduce the 3D surface plot u v q u v New u v Spline 31 mat :

CreateMesh paramaters Lo 0 : Hi 5 : 12 mat N 21 : 21 sys

N mesh within the bounds [L, H] in each directions M u v q Lo Hi Lo Hi N N CreateMesh :

<p> Euler system </p>

angle Ω1 1000 angle cos angle sin - 0 angle sin angle cos 33 mat :

Матрица преобразования для поворота вокруг оси y angle Ω2 angle cos 0 angle sin 010 angle sin - 0 angle cos 33 mat :

Матрица преобразования для поворота вокруг оси z angle Ω3 angle cos angle sin - 0 angle sin angle cos 000133 mat :

α π 4 / :

φ 0.0 - (π * :

α β φ 13 mat π 6 / - 0 π * 0.2 π * 13 mat ≡

β 0.0 - (π * :

<= Rotate around Y θ 0.375 π * :

Euler combined γ α Ω1 β Ω2 * φ Ω3 * eval :

M f B M θ Ω3 * γ * eval : B 1 col B 3 col augment 21 line :

x y axes x y / - :

plot the 2D surface plot plot M f :

plot plot axes 2 1 sys