91a3158b-b28e-41db-9651-c2358646fb61 26 3 5 auto

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

The Trifolium Eol project

x y Φ3 x 2^y 2^+ (2^1 x 3^3 x * y 2^* - (* - : x y Φ6 x 2^y 2^+ (4^1 x 3^3 x * y 2^* - (2^* - : x C 1 x 2^- sqrt : plot first the Sixfolium 41 line

x C Re x C Re - Φ3 3 1 sys

y F x y Φ3 0 ≡ x solve maple :

y F_Z_Z_Z 1 -_Z + (* 2 y 2^* + (* 3 y 2^* + (* y 4^+ RootOf

y F x y Φ3 0 ≡ x solve allvalues maple :

The Maple advanced expansion is in term of solutions "RootOf". The command "allvalues" restricts to explicit solutions wrt 't'. "simplify" is not needed either. "RootOf" has a workaround, but a monkey business ... never attempted yet, in Smath.

x F 3 el x F 2 el 2 1 sys x F 1 el Re x F 1 el Im 2 1 sys

<== slow plots

junction 0.5625 - 0.5625 - f 1 el + 15 black 15 mat :

x f x y Φ3 0 ≡ y solve maple :

plot x f 1 el x f 2 el x f 3 el x f 4 el 41 sys :

plot x C Re x C Re - junction 4 1 sys

Solving for the junction ... value in the Trifolium domain x f 1 el x f 3 el - abs 0 ≡ x 0.563 - 0.562 - solve 0.5625 - f 1 el 21 mat 0.562500000000000 - 0.726184377413890 21 mat

x f x 32 x * + 916 x * + sqrt - (* - sqrt 2 sqrt / x 32 x * + 916 x * + sqrt - (* - sqrt 2 sqrt / - x 32 x * + 916 x * + sqrt + (* - sqrt 2 sqrt / x 32 x * + 916 x * + sqrt + (* - sqrt 2 sqrt / - 41 mat :

junction 0.5625 - 0.5625 - f 1 el + 15 black 15 mat :

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx i * dx - (+ : for U 41 line :

N 100 :

x f 1 el x f 2 el x f 3 el x f 4 el junction 5 1 sys

u 0 0.5625 - N xd : v 10 N xd : 21 line

The 3 lobes complete through two branches each for a total of 6 circulations

b1 i 1 u rows range U i el u i el f 1 el eval : for u U Re augment 21 line :

b2 i 1 u rows range V i el u i el f 3 el eval : for u u reverse : V V Re reverse : 21 line u V augment 31 line :

b3 i 1 v rows range U i el v i el f 1 el eval : for v U augment 21 line :

b4 i 1 v rows range V i el v i el f 2 el eval : for v v reverse : V V reverse : 21 line v V augment 31 line :

b5 i 1 u rows range U i el u i el f 2 el eval : for u U Re augment 21 line :

b6 i 1 u rows range V i el u i el f 4 el eval : for u u reverse : V V Re reverse : 21 line u V augment 31 line :

b1 b2 b3 b4 b5 b6 6 1 sys

CWD C:\SmathFile CurrentDirectory :

b2 CWD b2 wfile 1

b2 CWD b2 rfile :

b4 CWD b4 wfile 1

b4 CWD b4 rfile :

b6 CWD b6 wfile 1

b6 CWD b6 rfile :

f1 b1 b2 stack : f2 b3 b4 stack : f3 b5 b6 stack : Trifolium f1 f2 f3 stack : 41 sys

f1 f2 f3 3 1 sys Trifolium

θ rot θ cos θ sin - θ sin θ cos 22 mat :

θ π 5 / - :

Smath 2D vectros rotation system t Eol Trifolium θ π 30 / t * + rot * eval :

x re x C Re 1 - x ≤ (x 1 ≤ (& cases :

x im x C Re - 1 - x ≤ (x 1 ≤ (& cases :

Hub 00.15 red 15 mat :

step1 060 range :

Smath "Wind Mill" project

t Eol x re x im Hub 4 1 sys

θ π 6 / - :

Trifolium Trifolium θ rot * θ x * 3 1 sys

Trifolium CWD TrifoliumBlue wfile 1

Trifolium θ rot * CWD TrifoliumRed wfile 1