Solution 2 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
r10=0
r11=0
r12=0
r13=0
r14=0
r15=0
a11*c33*r29 - a22*c33*r29
r20=---------------------------
a11*a22
r21=0
a11*c33*r29 - a22*c33*r29
r22=---------------------------
a11*a22
r23=0
r24=0
r26=0
r27=0
r28=0
r210=0
r212=0
r213=0
a11*r29 - a22*r29
r214=-------------------
a11
r215=0
r216=0
r217=0
r218=0
r219=0
m3=0
m2=0
m1=0
n3=0
n2=0
n1=0
c23=0
c22=0
c13=0
c12=0
c11=0
b33=0
b32=0
b31=0
b23=0
b22=0
b21=0
b13=0
b12=0
b11=0
a33=0
a23=0
a13=0
a12=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, c33, a22, 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,a22,a11 - a22,r29,c33}
Relevance for the application:
This solution is contained in the CLEBSCH1 case.
This solution is contained in the STEKLOV_LYAPUNOV1 case.
This solution is contained in the CLEBSCH2 case.
This solution is contained in the STEKLOV_LYAPUNOV2 case.
This solution is contained in the CLEBSCH3 case.
This solution is contained in the STEKLOV_LYAPUNOV3 case.
The system of equations related to the Hamiltonian HAM:
2 2 2
HAM=u1 *a11 + u2 *a22 + v3 *c33
has apart from the Hamiltonian and Casimirs only the following first integral:
2 2 2 2
FI=u2 *(a11*a22 - a22 ) + u3 *a11*a22 + v2 *(a11*c33 - a22*c33)
2
+ v3 *(a11*c33 - a22*c33)
which the program can not factorize further.
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u2**2*a22 + v3**2*c33$
FI=u2**2*(a11*a22 - a22**2) + u3**2*a11*a22 + v2**2*(a11*c33 - a22*c33) + v3**2*
(a11*c33 - a22*c33)$