Solution 1 to problem h

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

Expressions

The solution is given through the following expressions:


r10=0


r11=0


r12=0


r14=0


r15=0


m2=0


m1=0


n2=0


n1=0


a23=0


a22=a11


a13=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:

 r13, m3, n3, a33, a11, b12

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.

 
{r13,b12,{n3,m3}}

Relevance for the application:

The system of equations related to the Hamiltonian HAM:

      2                     2                     2
HAM=u1 *a11 + u1*v2*b12 + u2 *a11 - u2*v1*b12 + u3 *a33 + u3*n3 + v3*m3

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

FI=u3

which is not further factorizable.

{HAM,FI} = 0





And again in machine readable form:



HAM=u1**2*a11 + u1*v2*b12 + u2**2*a11 - u2*v1*b12 + u3**2*a33 + u3*n3 + v3*m3$

FI=u3$