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compare-cos-diff-phi-ratsimp-sin

v_r:(1-(3/2)*(R/r)+(1...

v_th:(-1+(3/4)*(R/r)+...

P:pr-(h*g*z)-(3/2)*m*...

Calculate

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compare(1,1);

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compare-kill

kill(x);

compare(%e^%pi, %pi^%e);

compare(x^2+1,2*x);

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compare-cos-diff-phi-sin

v_r:(1-(3/2)*(R/r)+(1...

v_th:(-1+(3/4)*(R/r)+...

P:pr-(h*g*z)-(3/2)*m*...

Calculate

compare

compare( [1, 2, 3], [...

Calculate

compare-cos-diff-phi-sin

v_r:(1-(3/2)*(R/r)+(1...

v_th:(-1+(3/4)*(R/r)+...

P:pr-(h*g*z)-(3/2)*m*...

Calculate

compare-cos-diff-phi-sin

v_r:(1-(3/2)*(R/r)+(1...

v_th:(-1+(3/4)*(R/r)+...

P:pr-(h*g*z)-(3/2)*m*...

Calculate

compare-cos-diff-sin

v_r:(1-(3/2)*(R/r)+(1...

v_th:(-1+(3/4)*(R/r)+...

P:pr-(h*g*z)-(3/2)*m*...

Calculate

compare-cos-diff-phi-sin

v_r:(1-(3/2)*(R/r)+(1...

v_th:(-1+(3/4)*(R/r)+...

P:pr-(h*g*z)-(3/2)*m*...

Calculate

compare

Run Example
(%i1)v_r:(1-(3/2)*(R/r)+(1/2)*(R/r)^3)*cos(th);
                                      3
                                     R     3 R
(%o1)                      cos(th) (---- - --- + 1)
                                       3   2 r
                                    2 r
(%i2) v_th:(-1+(3/4)*(R/r)+(1/4)*(R/r)^3)*sin(th);
                                      3
                                     R     3 R
(%o2)                      sin(th) (---- + --- - 1)
                                       3   4 r
                                    4 r
(%i3) P:pr-(h*g*z)-(3/2)*m*(R/r^2)*cos(th);
                           3 m cos(th) R
(%o3)                    - ------------- - g h z + pr
                                  2
                               2 r
(%i4) v_phi:0;
(%o4)                                  0
(%i5) f_1:h*(v_r*diff(v_r)+v_th/r)*diff(v_th,r)-(v_th^2/r);
                      3                     3
                   3 R    3 R              R     3 R
(%o5) h sin(th) (- ---- - ----) (cos(th) (---- - --- + 1)
                      4      2               3   2 r
                   4 r    4 r             2 r
              2                            3
           3 R     3                      R     3 R
 (cos(th) (---- - ---) del(R) - sin(th) (---- - --- + 1) del(th)
              3   2 r                       3   2 r
           2 r                           2 r
                                              3
                                             R     3 R
                                   sin(th) (---- + --- - 1)
                      3                        3   4 r
            3 R    3 R                      4 r
 + cos(th) (---- - ----) del(r)) + ------------------------)
               2      4                       r
            2 r    2 r
               3
      2       R     3 R     2
   sin (th) (---- + --- - 1)
                3   4 r
             4 r
 - --------------------------
               r
(%i6) f_2:-diff(P,r)+m*((1/r^2)*diff(diff(r^2/v_r,r),r)+(1/(r^2*sin(th))*(diff(sin(th)*diff(v_r,th),th))));
                                                        3
                                              3 R    3 R
                                         4 r (---- - ----)
                                                 2      4
                     2                        2 r    2 r
(%o6) m ((------------------------ - -------------------------
                     3                          3
                    R     3 R                  R     3 R     2
          cos(th) (---- - --- + 1)   cos(th) (---- - --- + 1)
                      3   2 r                    3   2 r
                   2 r                        2 r
               3                                  3
         2  6 R    3 R               2  3 R    3 R  2
        r  (---- - ---)           2 r  (---- - ----)
              5     3                      2      4
             r     r                    2 r    2 r         2
 - ------------------------- + -------------------------)/r
              3                           3
             R     3 R     2             R     3 R     3
   cos(th) (---- - --- + 1)    cos(th) (---- - --- + 1)
               3   2 r                     3   2 r
            2 r                         2 r
                3
               R     3 R
   2 cos(th) (---- - --- + 1)
                 3   2 r
              2 r                3 m cos(th) R
 - --------------------------) - -------------
                2                      3
               r                      r
(%i7) compare(f_1,f_2);
(%o7)                               unknown
(%i8) 1/(r*sin(th))*diff(v_phi,phi);
(%o8)                                  0
(%i9) 
Run Example
v_r:(1-(3/2)*(R/r)+(1/2)*(R/r)^3)*cos(th);
                                      3
                                     R     3 R
(%o1)                      cos(th) (---- - --- + 1)
                                       3   2 r
                                    2 r
(%i2) v_th:(-1+(3/4)*(R/r)+(1/4)*(R/r)^3)*sin(th);
                                      3
                                     R     3 R
(%o2)                      sin(th) (---- + --- - 1)
                                       3   4 r
                                    4 r
(%i3) P:pr-(h*g*z)-(3/2)*m*(R/r^2)*cos(th);
                           3 m cos(th) R
(%o3)                    - ------------- - g h z + pr
                                  2
                               2 r
(%i4) f_1:h*(v_r*diff(v_r)+v_th/r)*diff(v_th,r)-(v_th^2/r);
                      3                     3
                   3 R    3 R              R     3 R
(%o4) h sin(th) (- ---- - ----) (cos(th) (---- - --- + 1)
                      4      2               3   2 r
                   4 r    4 r             2 r
              2                            3
           3 R     3                      R     3 R
 (cos(th) (---- - ---) del(R) - sin(th) (---- - --- + 1) del(th)
              3   2 r                       3   2 r
           2 r                           2 r
                                              3
                                             R     3 R
                                   sin(th) (---- + --- - 1)
                      3                        3   4 r
            3 R    3 R                      4 r
 + cos(th) (---- - ----) del(r)) + ------------------------)
               2      4                       r
            2 r    2 r
               3
      2       R     3 R     2
   sin (th) (---- + --- - 1)
                3   4 r
             4 r
 - --------------------------
               r
(%i5) f_2:-diff(P,r)+h*g+m*((1/r^2)*diff(diff(r^2/v_r,r),r)+(1/(r^2*sin(th))*(diff(sin(th)*diff(v_r,th),th))));
                                                        3
                                              3 R    3 R
                                         4 r (---- - ----)
                                                 2      4
                     2                        2 r    2 r
(%o5) m ((------------------------ - -------------------------
                     3                          3
                    R     3 R                  R     3 R     2
          cos(th) (---- - --- + 1)   cos(th) (---- - --- + 1)
                      3   2 r                    3   2 r
                   2 r                        2 r
               3                                  3
         2  6 R    3 R               2  3 R    3 R  2
        r  (---- - ---)           2 r  (---- - ----)
              5     3                      2      4
             r     r                    2 r    2 r         2
 - ------------------------- + -------------------------)/r
              3                           3
             R     3 R     2             R     3 R     3
   cos(th) (---- - --- + 1)    cos(th) (---- - --- + 1)
               3   2 r                     3   2 r
            2 r                         2 r
                3
               R     3 R
   2 cos(th) (---- - --- + 1)
                 3   2 r
              2 r                3 m cos(th) R
 - --------------------------) - ------------- + g h
                2                      3
               r                      r
(%i6) compare(f_1,f_2);
(%o6)                               unknown
(%i7) 
Run Example
compare (-abs(1+x)/(sqrt(x)*(1+x)^2), -1/(sqrt(x)*abs(x)));
(%o1)                                  >
(%i2) 

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