02f6270b-3947-41a8-9cae-08be7c587abf 29 4 5 fraction

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

6

Euler rotation : Roll, Pitch, Yaw

b 0.4 :

r 1 b 2^- :

angle Ω1 Roll [Roulis, rotation around X] ≡

angle Ω2 Pitch [Azimuth, up/down aroud Y] ≡

w r sqrt :

angle Ω3 Yaw [Horizon, rotation around Z] ≡

t0 1 time :

u v d b w b u * cosh (2^* b w v * sin * (2^+ (* :

<= optimiz = Numeric

u v f u - 2 r * b u * cosh * b u * sinh * u v d / + 2 w * b u * cosh * w v cos * w v * cos * - v sin w v * sin * - (* u v d / 2 w * b u * cosh * w v sin * w v * cos * - v cos w v * sin * - (* u v d / 31 mat :

<= optimiz = Numeric

M u v f 13.2 - 13.2 37.4 - 37.4 2020 CreateMesh :

<= optimiz = None

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 6 / - :

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

β 0 π * :

φ 0.2 π * :

θ π 16 / :

γ α Ω1 β Ω2 * φ Ω3 * eval :

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

γ 0.809 0.5878 - 0 0.509 0.7006 0.5 0.2939 - 0.4045 - 0.866 33 mat

For plotting, 'step1' from plot menu [brush over click left, Animate] check step1 option.

step1 00 range :

c 00 + 200 red 15 mat :

Figure 55 Breather 14 magenta 15 mat :

M t f c Figure 3 1 sys

From fresh Smath, WS computes in 80 sec. Click left and hold, you can move Breather anywhwere in the canvas, gorgeous !

1 time t0 - 30 sec *

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 6 / - :

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

β 0 π * :

φ 0.2 π * :

θ π 18 / :

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 :

plot M f :

plot

Animation parameter 't' removed

M f

α β φ θ 41 mat ° 30 - 0361041 mat