### Related

##### psi-rhs-solve-subst

eq1: 0 = uD+omega*Lq*iq;

eq2: 0 = uq-omega*(Ld...

eq3: solve([eq1, eq2]...

Calculate

##### psi

eq1:uD = iD*R -w*LQ*iQ;

eq2:uQ = iQ*R + w*LD*...

eq3: u^2 = uD^2+uQ^2;

Calculate

##### psi-rhs-subst

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

##### psi-rhs-subst

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

##### psi-rhs-subst

eq1:uD = iD*R -w*LQ*iQ;

eq2:uQ = iQ*R + w*LD*...

eq3: u^2 = uD^2+uQ^2;

Calculate

##### psi

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

? psi;

Calculate

##### psi

eq1: 0 = uD+omega*Lq*iq;

eq2: 0 = uq-omega*(Ld...

Calculate

##### psi-rhs-subst

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

##### psi-rhs-subst

eq1: uD = iD*R -w*LQ*iQ;

eq2: uQ = iQ*R + w*LD...

eq3: u^2 = uD^2+uQ^2;

Calculate

### psi

Run Example
```(%i1)hex(psi) := 1.02 * exp(5.66 *psi);
(%o1)                   hex(psi) := 1.02 exp(5.66 psi)
(%i2) hex(-1.0);
(%o2)                         0.0035521672361759
(%i3) dhex(psi) := ''(diff(hex(psi),psi));
5.66 psi
(%o3)                   dhex(psi) := 5.7732 %e
(%i4) dhex(-1.0);
(%o4)                          0.020105266556756
(%i5) f_vanL(ftsw)  := 1- exp(-5* ftsw);
(%o5)                 f_vanL(ftsw) := 1 - exp((- 5) ftsw)
(%i6) f_lebon(ftsw) := ftsw/0.4;
ftsw
(%o6)                        f_lebon(ftsw) := ----
0.4
(%i7) fh_vanL(psi)  := f_vanL(hex(psi));
(%o7)                  fh_vanL(psi) := f_vanL(hex(psi))
(%i8) fh_lebon(psi) := f_lebon(hex(psi));
(%o8)                 fh_lebon(psi) := f_lebon(hex(psi))
(%i9) g_vanL(psi)  := fh_vanL(psi)  / dhex(psi);
fh_vanL(psi)
(%o9)                     g_vanL(psi) := ------------
dhex(psi)
(%i10) g_lebon(psi) := fh_lebon(psi) / dhex(psi);
fh_lebon(psi)
(%o10)                   g_lebon(psi) := -------------
dhex(psi)
(%i11) g_vanL(-1.0);
(%o11)                         0.87559357230093
(%i12) g_lebon(-1.0);
(%o12)                          0.4416961130742
(%i13) plot2d([f_lebon,f_vanL],[ftsw,0,0.4]);
plotplot2d([g_lebon,g_vanL],[psi,-1.5,-0.33]);
plot```
Run Example
```f(x) := (32*x^5-240*x^4+560*x^3-360*x^2-150*x+117)*exp(-1/2*x^2+3/2*x-9/8);
5        4        3            2
(%o1) f(x) := (32 x  - 240 x  + 560 x  + (- 360) x  + (- 150) x + 117)
- 1  2   3     - 9
exp(--- x  + - x + ---)
2       2      8
(%i2) a:integrate((f(x))^2, x, minf, inf);
(%o2)                           3840 sqrt(%pi)
(%i3) N : 1/sqrt(a);
1
(%o3)                         ------------------
1/4
16 sqrt(15) %pi
(%i4) psi(x) := N*f(x);
(%o4)                          psi(x) := N f(x)
(%i5) plot2d(psi(x), [x,-5, 5]);
plot```
Run Example
```rx:matrix([1,         0,        0],[0,  cos(phi), sin(phi)],[0, -sin(phi), cos(phi)]);
[ 1      0          0     ]
[                         ]
(%o1)                     [ 0   cos(phi)   sin(phi) ]
[                         ]
[ 0  - sin(phi)  cos(phi) ]
(%i2) ry:matrix([cos(theta),  0,  -sin(theta)],[         0,  1,            0],[sin(theta),  0,   cos(theta)]);
[ cos(theta)  0  - sin(theta) ]
[                             ]
(%o2)                   [     0       1       0       ]
[                             ]
[ sin(theta)  0   cos(theta)  ]
(%i3) rz:matrix([ cos(psi),  sin(psi),  0],[-sin(psi),  cos(psi),  0],[        0,         0,  1]);
[  cos(psi)   sin(psi)  0 ]
[                         ]
(%o3)                     [ - sin(psi)  cos(psi)  0 ]
[                         ]
[     0          0      1 ]
(%i4) r:rx.ry.rz;
[               cos(psi) cos(theta)                ]
[                                                  ]
(%o4)  Col 1 = [ sin(phi) cos(psi) sin(theta) - cos(phi) sin(psi) ]
[                                                  ]
[ cos(phi) cos(psi) sin(theta) + sin(phi) sin(psi) ]
[               sin(psi) cos(theta)                ]
[                                                  ]
Col 2 = [ sin(phi) sin(psi) sin(theta) + cos(phi) cos(psi) ]
[                                                  ]
[ cos(phi) sin(psi) sin(theta) - sin(phi) cos(psi) ]
[    - sin(theta)     ]
[                     ]
Col 3 = [ sin(phi) cos(theta) ]
[                     ]
[ cos(phi) cos(theta) ]
(%i5) recef:matrix([x],[y],[z]);
[ x ]
[   ]
(%o5)                                [ y ]
[   ]
[ z ]
(%i6) r.recef;
(%o6) matrix([- sin(theta) z + sin(psi) cos(theta) y + cos(psi) cos(theta) x],
[sin(phi) cos(theta) z + (sin(phi) sin(psi) sin(theta) + cos(phi) cos(psi)) y
+ (sin(phi) cos(psi) sin(theta) - cos(phi) sin(psi)) x],
[cos(phi) cos(theta) z + (cos(phi) sin(psi) sin(theta) - sin(phi) cos(psi)) y
+ (cos(phi) cos(psi) sin(theta) + sin(phi) sin(psi)) x])
(%i7) ```

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