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atvalue-diff-laplace-solve

v(t):=0;

i(t):=IL;

atvalue(vc(t), t=0, VG);

Calculate

atvalue-diff-log-ode2-plot3d
plot3d(

log(k1)=7.176-(3.85/T...

log(k2)=9.942-(4.05/T...

OH=10^(pH-14);

Calculate

atvalue-desolve-diff-exp-integrate-plot2d
plot2d(sol,[t,0,5]);

e:100=0.1*'diff(i1(t)...

atvalue(i1(t),t=0,10);

desolve(e,[i1(t)]);

Calculate

atvalue-depends-diff-log-ode2-plot3d
plot3d(

log(k1)=7.176-(3.85/T...

log(k2)=9.942-(4.05/T...

OH=10^(pH-14);

Calculate

atvalue-diff-ode2-plot3d
plot3d(

k1:10^(7.176-(3.85/Te...

k2:10^(9.942-(4.05/Te...

OH=10^(pH-14);

Calculate

atvalue-depends-diff-log-ode2-plot3d
plot3d(

log(k1)=7.176-(3.85/T...

log(k2)=9.942-(4.05/T...

OH=10^(pH-14);

Calculate

atvalue-diff-laplace-solve

v(t):=0;

i(t):=IL;

atvalue(vc(t), t=0, VG);

Calculate

atvalue-desolve-diff

eqn:diff(y(x),x,2)=1;

atvalue(y(x),x=0,1);

atvalue(diff(y(x),x),...

Calculate

atvalue-desolve-diff-exp

eqn1:diff(y(x),x) = z...

eqn2:diff(z(x),x) = 3...

atvalue(y(x),x=0,0);

Calculate

atvalue-desolve-diff

eq : diff(y(t),t,4) =...

eq1 : diff(y0(t),t) =...

eq2 : diff(y1(t),t) =...

Calculate

atvalue

Run Example
(%i1)gpot: 2;
(%o1)                                  2
(%i2) r: sqrt(x(t)^2 +y(t)^2);
                                    2       2
(%o2)                         sqrt(y (t) + x (t))
(%i3) r_potf: r^-(gpot+1);
                                      1
(%o3)                         ------------------
                                2       2    3/2
                              (y (t) + x (t))
(%i4) dgl_xt: 'diff(x(t),t,2)=-x(t)*r_potf;
                        2
                       d                     x(t)
(%o4)                  --- (x(t)) = - ------------------
                         2              2       2    3/2
                       dt             (y (t) + x (t))
(%i5) dgl_yt: 'diff(y(t),t,2)=-y(t)*r_potf;
                        2
                       d                     y(t)
(%o5)                  --- (y(t)) = - ------------------
                         2              2       2    3/2
                       dt             (y (t) + x (t))
(%i6) atvalue(x(t),t=0,1);
(%o6)                                  1
(%i7) atvalue(y(t),t=0,0);
(%o7)                                  0
(%i8) atvalue('diff(x(t),t),t=0,0);
(%o8)                                  0
(%i9) atvalue('diff(y(t),t),t=0,1);
(%o9)                                  1
(%i10) desolve([dgl_xt,dgl_yt],[x(t),y(t)]);
                                           x(t)
                   g33270 - laplace(------------------, t, g33270)
                                      2       2    3/2
                                    (y (t) + x (t))
(%o10) [x(t) = ilt(-----------------------------------------------, g33270, 
                                             2
                                       g33270
                                       y(t)
                        laplace(------------------, t, g33270) - 1
                                  2       2    3/2
                                (y (t) + x (t))
       t), y(t) = ilt(- ------------------------------------------, g33270, t)]
                                               2
                                         g33270
(%i11) 
Run Example
Gc:0;
(%o1)                                  0
(%i2)  Rg:0;
(%o2)                                  0
(%i3)  Ro1:0;
(%o3)                                  0
(%i4)  Ro2:0;
(%o4)                                  0
(%i5) v(t):=0;
(%o5)                              v(t) := 0
(%i6) i(t):=IL;
(%o6)                             i(t) := IL
(%i7) atvalue(vc(t), t=0, VG);
(%o7)                                 VG
(%i8) atvalue(ig(t), t=0, IL);
(%o8)                                 IL
(%i9) atvalue(i1(t), t=0, IL);
(%o9)                                 IL
(%i10) atvalue(i2(t), t=0, 0);
(%o10)                                 0
(%i11) atvalue(vut1(t), t=0, 0);
(%o11)                                 0
(%i12) atvalue(iut1(t), t=0, 0);
(%o12)                                 0
(%i13) vFW1(t):=-VG;
(%o13)                          vFW1(t) := - VG
(%i14) iFW1(t):=0;
(%o14)                           iFW1(t) := 0
(%i15) vFW2(t):=0;
(%o15)                           vFW2(t) := 0
(%i16) atvalue(vut2(t), t=0, 0);
(%o16)                                 0
(%i17) eqi1:laplace(ig(t) = Gc*vc(t) + C*'diff(vc(t),t,1) + i(t),t,s);
                                                                   IL
(%o17)    laplace(ig(t), t, s) = C (s laplace(vc(t), t, s) - VG) + --
                                                                   s
(%i18) eqi2:laplace(i(t) + iFW1(t) = i1(t),t,s);
                           IL
(%o18)                     -- = laplace(i1(t), t, s)
                           s
(%i19) eqi3:laplace(Gc*vc(t) + C*'diff(vc(t),t,1) + iut1(t) = iFW1(t),t,s);
(%o19)   C (s laplace(vc(t), t, s) - VG) + laplace(iut1(t), t, s) = 0
(%i20) eqv1:laplace(VG = Rg*ig(t) + v(t) + Ro1*i1(t) + Lo1*'diff(i1(t),t,1) + Lu*'diff(i2(t),t,1),t,s);
       VG
(%o20) -- = Lo1 (s laplace(i1(t), t, s) - IL) + Lu s laplace(i2(t), t, s)
       s
(%i21) eqv2:laplace(vut1(t) = vFW1(t) + Ro1*i1(t) + Lo1*'diff(i1(t),t,1) + Lu*'diff(i2(t),t,1),t,s);
                                  VG
(%o21) laplace(vut1(t), t, s) = - -- + Lo1 (s laplace(i1(t), t, s) - IL)
                                  s
                                                    + Lu s laplace(i2(t), t, s)
(%i22) eqv3:laplace(v(t) = vc(t) + vFW1(t),t,s);
                                                    VG
(%o22)                   0 = laplace(vc(t), t, s) - --
                                                    s
(%i23) eqv4:laplace(vut2(t) = vFW2(t) + Ro2*i2(t) + Lo2*'diff(i2(t),t,1) + Lu*'diff(i1(t),t,1),t,s);
(%o23) laplace(vut2(t), t, s) = Lu (s laplace(i1(t), t, s) - IL)
                                                   + Lo2 s laplace(i2(t), t, s)
(%i24) sol:solve([	eqi1,	eqi2,	eqi3,	eqv1,	eqv2,	eqv3,	eqv4],[	'laplace(vc(t),t,s),	'laplace(ig(t),t,s),	'laplace(i1(t),t,s),	'laplace(iFW1(t),t,s),	'laplace(i2(t),t,s),	'laplace(vut2(t),t,s),	'laplace(vFW1(t),t,s)]);
(%o24)                                []
(%i25) 
Run Example
assume(R0>
=0,R1>
=0,R2>
=0,E0>
0,E1>
0,E2>
0,L>
0,C>
0,ESR>
=0,RL>
=0,Vc0>
0,Il0>
0);
(%o1) [R0 >= 0, R1 >= 0, R2 >= 0, E0 > 0, E1 > 0, E2 > 0, L > 0, C > 0, 
                                           ESR >= 0, RL >= 0, Vc0 > 0, Il0 > 0]
(%i2) ESR:0;
(%o2)                                  0
(%i3) RL:0;
(%o3)                                  0
(%i4) R0:0;
(%o4)                                  0
(%i5) R1:0;
(%o5)                                  0
(%i6) R2:0;
(%o6)                                  0
(%i7) atvalue(vc(t),t=0,Vc0);
(%o7)                                 Vc0
(%i8) atvalue(il(t),t=0,Il0);
(%o8)                                 Il0
(%i9) eq1:laplace(ic(t)=C*'diff(vc(t),t,1),t,s);
(%o9)       laplace(ic(t), t, s) = (s laplace(vc(t), t, s) - Vc0) C
(%i10) eq2:laplace(vc(t)+ESR*ic(t)=E1-R1*ic(t)+E2+R2*i2(t),t,s);
                                               E2 + E1
(%o10)                  laplace(vc(t), t, s) = -------
                                                  s
(%i11) eq3:laplace(il(t)=ic(t)+i2(t),t,s);
(%o11) laplace(il(t), t, s) = laplace(ic(t), t, s) + laplace(i2(t), t, s)
(%i12) eq4:laplace(vl(t)=L*'diff(il(t),t,1),t,s);
(%o12)      laplace(vl(t), t, s) = (s laplace(il(t), t, s) - Il0) L
(%i13) eq5:laplace(vl(t)+RL*il(t)+E0+R0*il(t)+E2+R2*i2(t)=0,t,s);
                      E2   E0
(%o13)                -- + -- + laplace(vl(t), t, s) = 0
                      s    s
(%i14) sol:solve([eq1,eq2,eq3,eq4,eq5],[laplace(vc(t),t,s),laplace(il(t),t,s),laplace(i2(t),t,s),laplace(ic(t),t,s),laplace(vl(t),t,s)]);
                                E2 + E1
(%o14) [[laplace(vc(t), t, s) = -------, 
                                   s
                       Il0 s L - E2 - E0
laplace(il(t), t, s) = -----------------, 
                              2
                             s  L
                           2                    2
                       C (s  (- E2 L - E1 L) + s  Vc0 L) + Il0 s L - E2 - E0
laplace(i2(t), t, s) = -----------------------------------------------------, 
                                                2
                                               s  L
                                                                   E2 + E0
laplace(ic(t), t, s) = C (E2 + E1 - Vc0), laplace(vl(t), t, s) = - -------]]
                                                                      s
(%i15) ilt(sol[1][1],s,t);
(%o15)                          vc(t) = E2 + E1
(%i16) ilt(sol[1][2],s,t);
                                    t E2   t E0
(%o16)                    il(t) = - ---- - ---- + Il0
                                     L      L
(%i17) ilt(sol[1][3],s,t);
                       2                    2
                   C (s  (- E2 L - E1 L) + s  Vc0 L) + Il0 s L - E2 - E0
(%o17) i2(t) = ilt(-----------------------------------------------------, s, t)
                                            2
                                           s  L
(%i18) ilt(sol[1][4],s,t);
(%o18)               ic(t) = ilt(C (E2 + E1 - Vc0), s, t)
(%i19) ilt(sol[1][5],s,t);
(%o19)                         vl(t) = - E2 - E0
(%i20) limit(s*sol[1][1],s,0);
(%o20)              limit  s laplace(vc(t), t, s) = E2 + E1
                    s -> 0
(%i21) limit(s*sol[1][2],s,0);
(%o21)             limit  s laplace(il(t), t, s) = infinity
                   s -> 0
(%i22) limit(s*sol[1][3],s,0);
(%o22)             limit  s laplace(i2(t), t, s) = infinity
                   s -> 0
(%i23) limit(s*sol[1][4],s,0);
(%o23)                 limit  s laplace(ic(t), t, s) = 0
                       s -> 0
(%i24) limit(s*sol[1][5],s,0);
(%o24)             limit  s laplace(vl(t), t, s) = - E2 - E0
                   s -> 0
(%i25) 
[assume,atvalue,desolve,diff] [assume,atvalue,diff,exp,laplace] [assume,atvalue,diff,exp] [assume,atvalue,diff,ilt,laplace,limit,solve] [assume,atvalue,diff,ilt,laplace,solve] [assume,atvalue,diff,laplace,limit,solve] [assume,atvalue,diff,laplace,solve] [assume,atvalue,diff,ode2,solve] [assume,atvalue,diff,ode2] [atvalue,bc2,desolve,diff,ode2,ratsimp] [atvalue,bc2,diff,ode2,plot2d,rhs] [atvalue,bc2,diff,ode2] [atvalue,cos,desolve,diff,integrate,pi,ratsimp] [atvalue,cos,desolve,diff,sin] [atvalue,cos,desolve,diff] [atvalue,delta,diff,ilt,lambda,laplace,map,solve] [atvalue,delta,diff,ilt,solve] [atvalue,depends,diff,integrate,log,plot3d,solve] [atvalue,depends,diff,integrate,log,plot3d] [atvalue,depends,diff,log,ode2,plot3d] [atvalue,desolve,diff,ev,rhs] [atvalue,desolve,diff,exp,ilt,plot2d] [atvalue,desolve,diff,exp,integrate,plot2d] [atvalue,desolve,diff,exp,plot2d] [atvalue,desolve,diff,exp] [atvalue,desolve,diff,expand] [atvalue,desolve,diff,ilt] [atvalue,desolve,diff,log] [atvalue,desolve,diff,ratsimp] [atvalue,desolve,diff,rhs] [atvalue,desolve,diff,sin] [atvalue,desolve,diff] [atvalue,diff,ev,ilt,laplace,solve] [atvalue,diff,exp,integrate,plot3d,solve] [atvalue,diff,exp,ode2,plot3d] [atvalue,diff,exp] [atvalue,diff,ilt,lambda,laplace,map,solve] [atvalue,diff,ilt,laplace,solve] [atvalue,diff,ilt,laplace] [atvalue,diff,laplace,solve] [atvalue,diff,laplace] [atvalue,diff,log,ode2,plot3d,solve] [atvalue,diff,log,ode2,plot3d] [atvalue,diff,ode2,plot3d,solve] [atvalue,diff,ode2,plot3d] [atvalue,diff,ode2] [atvalue,diff,plot3d] [atvalue,diff,solve] [atvalue,diff] [atvalue]

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