<p> Euler system [radian] </p>

bb2fe550-8e70-4c7b-bea6-f7f7c96453cf 18 4 5 decimal

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

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 :

Bivariate explorer

=>X

user 200 0.75 12 mat :

x user 11 el : y user 12 el : 12 mat

W1 x/y 504005000 0.1 0.02 0.16 1.65 0.2 0.08 0.71 6.83 0.3 0.16 1.55 15.2 0.4 0.26 2.57 25.4 0.5 0.37 3.75 37.7 0.6 0.48 5.05 52 0.7 0.62 6.49 66.1 0.8 0.76 8.09 83.1 0.9 0.82 9.84 1031 1.09 11.8 156114 mat :

W2 x/y 504005000 0.1 0.02 0.18 2.18 0.2 0.08 0.73 10.6 0.3 0.16 1.5 19.1 0.4 0.26 2.54 31.7 0.5 0.37 3.86 45.9 0.6 0.47 5.22 61.5 0.7 0.61 6.77 81.1 0.8 0.75 8.47 104 0.9 0.9 10.4 1611 1.07 12.3 198114 mat :

W3 x/y 504005000 0.1 0.02 0.17 2.79 0.2 0.07 0.72 10.6 0.3 0.14 1.49 24.4 0.4 0.23 2.5 40.4 0.5 0.32 3.8 58.4 0.6 0.42 5.17 78.4 0.7 0.54 6.7 103 0.8 0.66 8.36 133 0.9 0.8 10.3 2051 0.95 12.2 253114 mat :

sanity W1 50 0.6 Spline W2 400 0.3 Spline W3 50001 Spline 31 mat 0.48 1.5 25331 mat

user x y W1 W2 W3 31 mat x y Spline vectorize 13 mat 200 0.75 3.52 3.65 3.57 31 mat 13 mat

data 0.02 0.17 2.79 0.07 0.72 10.6 0.14 1.49 24.4 0.23 2.5 40.4 0.32 3.8 58.4 0.42 5.17 78.4 0.54 6.7 103 0.66 8.36 133 0.8 10.3 205 0.95 12.2 253103 mat :

New x/y 0.3333 0.6667 1 0.1 0.02 0.17 2.79 0.2 0.07 0.72 10.6 0.3 0.14 1.49 24.4 0.4 0.23 2.5 40.4 0.5 0.32 3.8 58.4 0.6 0.42 5.17 78.4 0.7 0.54 6.7 103 0.8 0.66 8.36 133 0.9 0.8 10.3 2051 0.95 12.2 253114 mat :

sanity
sanity
user New 0.6667 0.5 Spline New 11 Spline New 0.75 0.75 Spline 31 mat 3.8 253 35.14 31 mat

1. Construct the 3D plot

<= 3D vector function u v q u v New u v Spline 31 mat :

CreateMesh paramaters L 1 - : H 1 : N 21 : 31 sys

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

<p> Euler system [radian] </p>

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

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

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

α π 4 / :

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

β 0.0 - (π * :

φ 0.0 - (π * :

<= Rotate around Y θ π 8 / :

2. Construct the 2D interpolated surface plot

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

X 0 :

m 5 :

2D surface axes system XY X m - X X X X X X m + 00 m 0 m - 0027 mat transpose :

M f B M θ Ω3 * γ * eval : B 1 col B 2 col augment 21 line :

plot the 2D surface plot plot M f :

click left in plot, move [X,Y] by mouse ... resize the plot frame.

plot XY 2 1 sys