Hello,
I want to sort the formulae to Psi and Beta, but I don't know how it works. I have tried it with sort, simplify, isolate, but that isn't what I'm searching.
It should looks like the simplier formula in the picture.
ab := (diff(Psii(t), t, t))*J-l[f]*(F[s, f, l]+F[s, f, r])+l[r]*(F[s, r, l]+F[s, r, r])-(1/2)*b[r]*(-F[s, r, l]*delta[l]+F[s, r, r]*delta[r]) = 0;
/ d / d \\
|--- |--- Psii(t)|| J - l[f] (F[s, f, l] + F[s, f, r])
\ dt \ dt //
+ l[r] (F[s, r, l] + F[s, r, r])
1
- - b[r] (-F[s, r, l] delta[l] + F[s, r, r] delta[r]) = 0
2
bc := (diff(betaa(t), t, t))*m*v*betaa(t)+F[s, r, l]*delta[l]+F[s, r, r]*delta[r]-(diff(Psii(t), t)) = 0;
/ d / d \\
|--- |--- betaa(t)|| m v betaa(t) + F[s, r, l] delta[l]
\ dt \ dt //
/ d \
+ F[s, r, r] delta[r] - |--- Psii(t)| = 0
\ dt /
cd := (diff(betaa(t), t))*m*v+F[s, r, l]+F[s, r, r]+F[s, f, l]+F[s, f, r]-(diff(Psii(t), t)) = 0;
/ d \
|--- betaa(t)| m v + F[s, r, l] + F[s, r, r] + F[s, f, l]
\ dt /
/ d \
+ F[s, f, r] - |--- Psii(t)| = 0
\ dt /
F[s, f, l] := c[fl]*alpha[fl];
c[fl] alpha[fl]
F[s, f, r] := c[fr]*alpha[fr];
c[fr] alpha[fr]
F[s, r, l] := c[rl]*alpha[rl];
c[rl] alpha[rl]
F[s, r, r] := c[rr]*alpha[rr];
c[rr] alpha[rr]
alpha[fl] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(-v+(1/2)*b[f]*(diff(Psii(t), t)));
/ d \
-v betaa - l[f] |--- Psii(t)|
\ dt /
-----------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /
alpha[fr] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(v-(1/2)*b[f]*(diff(Psii(t), t)));
/ d \
-v betaa - l[f] |--- Psii(t)|
\ dt /
-----------------------------
1 / d \
v - - b[f] |--- Psii(t)|
2 \ dt /
alpha[rl] := delta[l]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v+(1/2)*b[r]*(diff(Psii(t), t)));
/ d \
-v betaa + l[r] |--- Psii(t)|
\ dt /
delta[l] + -----------------------------
1 / d \
-v + - b[r] |--- Psii(t)|
2 \ dt /
alpha[rr] := delta[r]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v-(1/2)*b[r]*(diff(Psii(t), t)));
/ d \
-v betaa + l[r] |--- Psii(t)|
\ dt /
delta[r] + -----------------------------
1 / d \
-v - - b[r] |--- Psii(t)|
2 \ dt /
ab;
/
|
/ d / d \\ |
|--- |--- Psii(t)|| J - l[f] |
\ dt \ dt // |
|
\
/ / d \\
c[fl] |-v betaa - l[f] |--- Psii(t)||
\ \ dt //
-------------------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /
/ / d \\\ / /
c[fr] |-v betaa - l[f] |--- Psii(t)||| | |
\ \ dt //| | |
+ -------------------------------------| + l[r] |c[rl] |delta[
1 / d \ | | |
v - - b[f] |--- Psii(t)| | | |
2 \ dt / / \ \
/ d \\
-v betaa + l[r] |--- Psii(t)||
\ dt /|
l] + -----------------------------|
1 / d \ |
-v + - b[r] |--- Psii(t)| |
2 \ dt / /
/ / d \\\ /
| -v betaa + l[r] |--- Psii(t)||| |
| \ dt /|| 1 |
+ c[rr] |delta[r] + -----------------------------|| - - b[r] |
| 1 / d \ || 2 |
| -v - - b[r] |--- Psii(t)| || |
\ 2 \ dt / // \
/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
-c[rl] |delta[l] + -----------------------------| delta[l]
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /
/ / d \\ \
| -v betaa + l[r] |--- Psii(t)|| |
| \ dt /| |
+ c[rr] |delta[r] + -----------------------------| delta[r]| =
| 1 / d \ | |
| -v - - b[r] |--- Psii(t)| | |
\ 2 \ dt / / /
0
bc;
/ d / d \\
|--- |--- betaa(t)|| m v betaa(t)
\ dt \ dt //
/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rl] |delta[l] + -----------------------------| delta[l]
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /
/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rr] |delta[r] + -----------------------------| delta[r]
| 1 / d \ |
| -v - - b[r] |--- Psii(t)| |
\ 2 \ dt / /
/ d \
- |--- Psii(t)| = 0
\ dt /
cd;
/ d \
|--- betaa(t)| m v
\ dt /
/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rl] |delta[l] + -----------------------------|
| 1 / d \ |
| -v + - b[r] |--- Psii(t)| |
\ 2 \ dt / /
/ / d \\
| -v betaa + l[r] |--- Psii(t)||
| \ dt /|
+ c[rr] |delta[r] + -----------------------------|
| 1 / d \ |
| -v - - b[r] |--- Psii(t)| |
\ 2 \ dt / /
/ / d \\
c[fl] |-v betaa - l[f] |--- Psii(t)||
\ \ dt //
+ -------------------------------------
1 / d \
-v + - b[f] |--- Psii(t)|
2 \ dt /
/ / d \\
c[fr] |-v betaa - l[f] |--- Psii(t)||
\ \ dt // / d \
+ ------------------------------------- - |--- Psii(t)| = 0
1 / d \ \ dt /
v - - b[f] |--- Psii(t)|
2 \ dt /
