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allbut-cos-derivabbrev-diff-sin-subst-true

derivabbrev:true ;

x(t):= r(t)*sin(theta...

y(t):=r(t)*cos(theta(...

Calculate

allbut-cos-derivabbrev-diff-sin-subst-true

derivabbrev:true ;

x(t):= r(t)*sin(theta...

y(t):=r(t)*cos(theta(...

Calculate

allbut-constant-cos-declare-derivabbrev-diff-mainvar-sin-solve-subst-true

derivabbrev:true ;

declare (t, mainvar);

declare (m, constant);

Calculate

allbut-constant-cos-declare-derivabbrev-diff-mainvar-sin-solve-true

derivabbrev:true ;

declare (t, mainvar);

declare (m, constant);

Calculate

allbut-cos-derivabbrev-diff-sin-subst-true

derivabbrev:true ;

x(t):= r(t)*sin(theta...

y(t):=r(t)*cos(theta(...

Calculate

allbut-append-constant-cos-declare-derivabbrev-diff-mainvar-sin-solve-subst-true

derivabbrev:true ;

declare (t, mainvar);

declare (m, constant);

Calculate

allbut-constant-cos-declare-derivabbrev-diff-mainvar-sin-solve-true

derivabbrev:true ;

declare (t, mainvar);

declare (m, constant);

Calculate

allbut-constant-cos-declare-derivabbrev-diff-mainvar-sin-solve-subst-true

derivabbrev:true ;

declare (t, mainvar);

declare (m, constant);

Calculate

allbut-constant-cos-declare-derivabbrev-diff-mainvar-sin-solve-true

derivabbrev:true ;

declare (t, mainvar);

declare (m, constant);

Calculate

allbut-kill-part

expr : e + d + c + b ...

part (expr, [2, 5]);

expr : e + d + c + b...

Calculate

allbut

Run Example
(%i1)derivabbrev:true ;
(%o1)                                true
(%i2) x(t):= r(t)*sin(theta(t));
(%o2)                     x(t) := r(t) sin(theta(t))
(%i3) y(t):=r(t)*cos(theta(t));
(%o3)                     y(t) := r(t) cos(theta(t))
(%i4) xdot(t):= diff(x(t), t, 1);
(%o4)                     xdot(t) := diff(x(t), t, 1)
(%i5) ydot(t):= diff(y(t), t, 1);
(%o5)                     ydot(t) := diff(y(t), t, 1)
(%i6) xdotdot(t):= diff(xdot(t), t, 1);
(%o6)                  xdotdot(t) := diff(xdot(t), t, 1)
(%i7) ydotdot(t):= diff(ydot(t), t, 1);
(%o7)                  ydotdot(t) := diff(ydot(t), t, 1)
(%i8) thetadot(t):= diff(theta(t), t, 1);
(%o8)                 thetadot(t) := diff(theta(t), t, 1)
(%i9) thetadotdot(t) := diff(thetadot(t), t, 1);
(%o9)              thetadotdot(t) := diff(thetadot(t), t, 1)
(%i10) Assumption1: xdotdot(t)=0;
                                                                      2
(%o10) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
                  + 2 r(t)  cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
                          t                       t       t t
(%i11) Assumption2: ydotdot(t)=0;
                                                                        2
(%o11) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
                                    t t                               t
                  - 2 r(t)  sin(theta(t)) theta(t)  + r(t)    cos(theta(t)) = 0
                          t                       t       t t
(%i12) E1_1: subst(rdot, diff(r(t), t, 1), Assumption1);
                                                                      2
(%o12) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
                   + 2 rdot cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
                                                  t       t t
(%i13) E1_2: subst(rdotdot, diff(diff(r(t), t, 1),t,1), E1_1);
                                                                      2
(%o13) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                  t t                               t
                   + 2 rdot cos(theta(t)) theta(t)  + rdotdot sin(theta(t)) = 0
                                                  t
(%i14) E1_3: subst(rr, r(t), E1_2);
                                                                  2
(%o14) rr cos(theta(t)) theta(t)    - rr sin(theta(t)) (theta(t) )
                                t t                             t
                   + 2 rdot cos(theta(t)) theta(t)  + rdotdot sin(theta(t)) = 0
                                                  t
(%i15) E2_1: subst(rdot, diff(r(t), t, 1), Assumption2);
                                                                        2
(%o15) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
                                    t t                               t
                   - 2 rdot sin(theta(t)) theta(t)  + r(t)    cos(theta(t)) = 0
                                                  t       t t
(%i16) E2_2: subst(rdotdot, diff(diff(r(t), t, 1),t,1), E2_2);
(%o16)                               E2_2
(%i17) E2_3: subst(rr, r(t), E1_2);
                                                                  2
(%o17) rr cos(theta(t)) theta(t)    - rr sin(theta(t)) (theta(t) )
                                t t                             t
                   + 2 rdot cos(theta(t)) theta(t)  + rdotdot sin(theta(t)) = 0
                                                  t
(%i18) elim_allbut([E1_3, E2_3], [rdotdot, theta]);
(%o18) elim_allbut([rr cos(theta(t)) theta(t)
                                             t t
                               2
 - rr sin(theta(t)) (theta(t) )  + 2 rdot cos(theta(t)) theta(t)
                             t                                  t
 + rdotdot sin(theta(t)) = 0, rr cos(theta(t)) theta(t)
                                                       t t
                               2
 - rr sin(theta(t)) (theta(t) )  + 2 rdot cos(theta(t)) theta(t)
                             t                                  t
 + rdotdot sin(theta(t)) = 0], [rdotdot, theta])
(%i19) 
Run Example
derivabbrev:true ;
(%o1)                                true
(%i2) declare (t, mainvar);
(%o2)                                done
(%i3) declare (m, constant);
(%o3)                                done
(%i4) x(t):= r(t)*sin(theta(t));
(%o4)                     x(t) := r(t) sin(theta(t))
(%i5) y(t):=r(t)*cos(theta(t));
(%o5)                     y(t) := r(t) cos(theta(t))
(%i6) Assumption1: diff(x(t), t, 2)=0;
                                                                     2
(%o6) r(t) cos(theta(t)) theta(t)    - r(t) sin(theta(t)) (theta(t) )
                                 t t                               t
                  + 2 r(t)  cos(theta(t)) theta(t)  + r(t)    sin(theta(t)) = 0
                          t                       t       t t
(%i7) R1: subst(fdot(t), diff(r(t),t,2), solve(Assumption1, r(t)));
                2 r(t)  cos(theta(t)) theta(t)  + fdot(t) sin(theta(t))
                      t                       t
(%o7) [r(t) = - -------------------------------------------------------]
                                                                     2
                cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
                                      t t                          t
(%i8) Assumption2: diff(y(t), t, 2)=0;
                                                                       2
(%o8) - r(t) sin(theta(t)) theta(t)    - r(t) cos(theta(t)) (theta(t) )
                                   t t                               t
                  - 2 r(t)  sin(theta(t)) theta(t)  + r(t)    cos(theta(t)) = 0
                          t                       t       t t
(%i9) R2: subst(fdot(t), diff(r(t),t,2), solve(Assumption2, r(t)));
               fdot(t) cos(theta(t)) - 2 r(t)  sin(theta(t)) theta(t)
                                             t                       t
(%o9)  [r(t) = -------------------------------------------------------]
                                                                    2
               sin(theta(t)) theta(t)    + cos(theta(t)) (theta(t) )
                                     t t                          t
(%i10) Linear: diff(y(t), t, 1)=m*diff(x(t), t, 1);
(%o10) r(t)  cos(theta(t)) - r(t) sin(theta(t)) theta(t)  = 
           t                                            t
                         m (r(t) cos(theta(t)) theta(t)  + r(t)  sin(theta(t)))
                                                       t       t
(%i11) solve(Linear, r(t));
                        r(t)  (m sin(theta(t)) - cos(theta(t)))
                            t
(%o11)  [r(t) = - ---------------------------------------------------]
                  sin(theta(t)) theta(t)  + m cos(theta(t)) theta(t)
                                        t                           t
(%i12) Doppler: diff(r(t),t,2)=fdot(t);
(%o12)                         r(t)    = fdot(t)
                                   t t
(%i13) elim_allbut(append(R1,R2), [theta(t)]);
(%o13) elim_allbut([r(t) = 
  2 r(t)  cos(theta(t)) theta(t)  + fdot(t) sin(theta(t))
        t                       t
- -------------------------------------------------------, 
                                                       2
  cos(theta(t)) theta(t)    - sin(theta(t)) (theta(t) )
                        t t                          t
       fdot(t) cos(theta(t)) - 2 r(t)  sin(theta(t)) theta(t)
                                     t                       t
r(t) = -------------------------------------------------------], [theta(t)])
                                                            2
       sin(theta(t)) theta(t)    + cos(theta(t)) (theta(t) )
                             t t                          t
(%i14) 
Run Example
expr : e + d + c + b + a;
(%o1)                          e + d + c + b + a
(%i2)  part (expr, [2, 5]);
(%o2)                                d + a
(%i3)  expr : e + d + c + b + a;
(%o3)                          e + d + c + b + a
(%i4)  part (expr, allbut (2, 5));
(%o4)                              e + c + b
(%i5)  [aa : 11, bb : 22, cc : 33, dd : 44, ee : 55];
(%o5)                        [11, 22, 33, 44, 55]
(%i6)  kill (allbut (cc, dd));
(%o0)                                done
(%i1)  [aa, bb, cc, dd];
(%o1)                          [aa, bb, 33, 44]
(%i2) 

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