Solution 1 to problem over

Expressions | Parameters | Inequalities | Relevance | Back to problem over

Expressions

The solution is given through the following expressions:


r10=0


         1
      - ---*b33*n2*r29
         2
r11=-------------------
              2
           a11


         1
      - ---*b33*n1*r29
         2
r12=-------------------
              2
           a11


      - n3*r29
r13=-----------
        a11


      - n2*r29
r14=-----------
        a11


      - n1*r29
r15=-----------
        a11


r20=0


r21=0


r22=0


r23=0


r24=0


r26=0


r27=0


r28=0


r210=0


r212=0


r213=0


r214=0


r215=0


r216=0


r217=0


r218=0


r219=0


     - b33*n3
m3=-----------
       a11


        1
     - ---*b33*n2
        2
m2=---------------
         a11


        1
     - ---*b33*n1
        2
m1=---------------
         a11


         1     2
      - ---*b33
         4
c33=-------------
         a11


c23=0


c22=0


c13=0


c12=0


b32=0


b31=0


b11=0

Parameters

Apart from the condition that they must not vanish to give a non-trivial solution and a non-singular solution with non-vanishing denominators, the following parameters are free:

 r29, n3, n1, b33, n2, a11

Inequalities

In the following not identically vanishing expressions are shown. Any auxiliary variables g00?? are used to express that at least one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3 means that either p4 or p3 or both are non-vanishing.

 
{a11,r29}

Relevance for the application:

The system of equations related to the Hamiltonian HAM:

       2    2                 2    2
HAM=(u1 *a11  + u1*a11*n1 + u2 *a11  + u2*a11*n2 + u3*v3*a11*b33 + u3*a11*n3

         1               1               1    2    2
      - ---*v1*b33*n1 - ---*v2*b33*n2 - ---*v3 *b33  - v3*b33*n3)/a11
         2               2               4

has apart from the Hamiltonian and Casimirs only the following first integral: 

                                2    2                1
FI= - u1*a11*n1 - u2*a11*n2 + u3 *a11  - u3*a11*n3 - ---*v1*b33*n1
                                                      2

       1
    - ---*v2*b33*n2
       2

{HAM,FI} = 0





And again in machine readable form:



HAM=(u1**2*a11**2 + u1*a11*n1 + u2**2*a11**2 + u2*a11*n2 + u3*v3*a11*b33 + u3*
a11*n3 - 1/2*v1*b33*n1 - 1/2*v2*b33*n2 - 1/4*v3**2*b33**2 - v3*b33*n3)/a11$

FI= - u1*a11*n1 - u2*a11*n2 + u3**2*a11**2 - u3*a11*n3 - 1/2*v1*b33*n1 - 1/2*v2*
b33*n2$