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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

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([f_lebon,f_vanL],[ftsw,0,0.4]);plot2d([g_lebon,g_vanL],[psi,-1.5,-0.33]);
plotplot2d([g_lebon,g_vanL],[psi,-1.5,-0.33]);
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]);
plotplot2d(psi(x), [x,-5, 5]);
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) 
[abs,append,col,exp,invert,matrix,psi,radcan,submatrix,transpose] [abs,cos,psi,sin] [addcol,define,diff,eigenvectors,exp,function,ident,integrate,invert,load,matrix,nullity,nullspace,psi,ratsimp] [append,col,exp,invert,matrix,psi,radcan,sqrt,transpose] [append,col,exp,invert,matrix,psi,radcan,submatrix,transpose] [asin,cos,lambda,psi,ratsimp,sin,subst] [coeff,expand,psi,rhs,solve,subst] [coeff,expand,psi,rhs,subst] [coeff,psi,ratsimp,rhs,solve,subst] [col,exp,invert,matrix,psi,radcan,sqrt,transpose] [collectterms,denom,expand,psi,ratsimp,rhs,solve,subst] [collectterms,expand,psi,ratsimp,rhs,solve,subst] [collectterms,expand,psi,rhs,solve,subst] [collectterms,expand,psi,rhs,subst] [cos,determinant,matrix,print,psi,sin,subst,trigreduce] [cos,determinant,matrix,print,psi,sin,subst] [cos,diff,phi,psi,rhs,sin,solve,subst,trigreduce] [cos,display2d,false,psi,sin,solve] [cos,display2d,false,psi,sin] [cos,jacobian,psi,sin,sqrt] [cos,matrix,phi,psi,sin] [cos,matrix,psi,sin] [cos,psi,ratsimp,sin,trigexpand] [cos,psi,sin,sqrt,trigexpand] [cos,psi,sin,trigexpand] [cos,psi,sin,trigsimp] [cos,psi,sin] [diff,ev,integrate,plot2d,psi,solve] [diff,exp,fortran,psi] [diff,exp,integrate,plot2d,psi,rhs,solve,sqrt] [diff,exp,integrate,plot2d,psi,sin,sqrt] [diff,exp,integrate,plot2d,psi,solve,sqrt] [diff,exp,integrate,plot2d,psi,sqrt] [diff,exp,integrate,psi,sin,sqrt] [diff,exp,integrate,psi,sqrt] [diff,exp,plot2d,psi] [diff,exp,psi] [diff,psi,solve,sublis,sum,tex] [diff,psi] [exp,integrate,plot2d,psi,sqrt] [exp,integrate,psi,sqrt] [exp,psi,riemann,sin] [exp,psi] [integrate,log,psi,ratsimp,sin] [psi,rhs,solve,subst] [psi,rhs,subst] [psi]

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