<p> Euler system </p>

1db1fd6e-8571-4b9f-bfe1-0af2ef160421 10 4 5 decimal

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

Spline/interpolate rectangular matrix

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 CC j el B C 1 C rows j j submatrix y linterp : for A transpose CC x linterp 51 line :

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

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

CreateMesh paramaters L 1 - : H 1 : N 31 : 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 </p>

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

Pitch angle Ω2 angle cos 0 angle sin 010 angle sin - 0 angle cos 33 mat :

Yaw angle Ω3 angle cos angle sin - 0 angle sin angle 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 0.5 :

2. Construct the 2D interpolated surface plot

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

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

x y axes x y / - :

plot the 2D surface plot plot M f :

plot axes 2 1 sys