Solution 16 to problem e3quant
Expressions |
Parameters |
Relevance |
Back to problem e3quant
Expressions
The solution is given through the following expressions:
a22=4*a33
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
1 2
- ----*b33
16
c33=--------------
a33
n2=0
n3=0
5
- ----*b33*n1
24
m1=----------------
a33
m2=0
m3=0
r6=0
r5=0
1
- ----*b33*n1*q1
24
r4=-------------------
2
a33
r3=0
r2=0
1
---*n1*q1
3
r1=-----------
a33
q20=0
1 2
----*b33 *q1
64
q19=--------------
2
a33
q18=0
q17=0
1 2
----*b33 *q1
64
q16=--------------
2
a33
q14=0
q13=0
q11=0
1
- a33*k38 - ---*b33*q1
4
q10=-------------------------
a33
q9=0
q8=0
q7=q1
q6=0
q5=0
1
- a33*k38 - ---*b33*q1
4
q4=-------------------------
a33
q3=0
q2=0
p56=0
p55=0
p54=0
p53=0
1
- ----*b33*k16*n1
24
p52=--------------------
2
a33
p51=0
1
- ----*b33*k16*n1
24
p50=--------------------
2
a33
p49=0
p48=0
1
- ----*b33*k16*n1
24
p47=--------------------
2
a33
p46=0
p45=0
p44=0
1
- ----*b33*k38*n1
24
p43=--------------------
2
a33
p42=0
p41=0
p40=0
p39=0
p38=0
p37=0
p36=0
p35=0
p34=0
p33=0
1
- ----*b33*k38*n1
24
p32=--------------------
2
a33
p31=0
p30=0
p29=0
p28=2*k38
p27=0
p26=0
p25=0
p24=0
p23=0
p22=0
1
---*k16*n1
3
p21=------------
a33
p20=0
1
---*k16*n1
3
p19=------------
a33
p18=0
p17=0
1 1
---*a33*k16*n1 - ----*b33*k38*n1
3 24
p16=----------------------------------
2
a33
1
- ---*k38*n1
3
p15=---------------
a33
p14= - 2*k38
p13=0
p12=0
p11=0
1
- ---*k38*n1
3
p10=---------------
a33
p9=0
p8=0
p7=0
p6=0
p5=0
1
- ---*k38*n1
3
p4=---------------
a33
p3=0
p2=0
p1=0
k125=0
1 2
----*b33 *k16
64
k124=---------------
2
a33
k123=0
1 2
----*b33 *k16
64
k122=---------------
2
a33
k121=0
k120=0
k119=0
k118=0
1 2
----*b33 *k16
64
k117=---------------
2
a33
k116=0
1 2
----*b33 *k16
32
k115=---------------
2
a33
k114=0
k113=0
1 2
----*b33 *k16
64
k112=---------------
2
a33
k110=0
k109=0
k108=0
k107=0
k106=0
k105=0
k104=0
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
k95=k38
k94=0
k93=0
k91=0
1
- ---*b33*k16
4
k90=----------------
a33
k89=0
1
- ---*b33*k16
4
k88=----------------
a33
k87=0
k86=0
k85=0
k84=0
1
- ---*b33*k16
4
k83=----------------
a33
k82=0
k81=0
k80=0
k79=0
k78=0
k77=0
k76=0
k75=0
k74=k38
k73=0
k72=0
k71=k16
k70=0
k69=k16
k68=0
k67=0
k66=k16
k65=0
k64=0
k63=0
k62=0
k61=0
k59=0
k58=0
k57=0
k56=0
k55=0
k54=0
k53=0
1
- ---*b33*k16
4
k52=----------------
a33
k51=0
1
- ---*b33*k16
4
k50=----------------
a33
k49=0
k48=0
1
- ---*b33*k16
4
k47=----------------
a33
k46=0
k45=0
k44=0
k43=0
k42=0
k41=0
k40=0
k39=0
k37=0
k36=0
k35=0
k34=0
k33=0
k32=0
k31=0
k30=0
k29=0
k28=0
k27=0
k26=0
k25=0
k24=0
k23=0
k22=0
k21=k16
k20=0
k19=k16
k18=0
k17=0
k15=0
k14=0
k13=0
k12=0
k11=0
k10=0
k9=0
k8=0
k7=0
k6=0
k5=0
k4=0
k3=0
k2=0
k1=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:
b33,q1,k16,k38,n1,a33
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
2 2 2 2 2 2
HAM=(192*a33 *u1 + 192*a33 *u2 + 48*a33 *u3 + 48*a33*b33*u3*v3 + 48*a33*n1*u1
2 2
- 3*b33 *v3 - 10*b33*n1*v1)/(48*a33)
2 3 2 3 2
INT=(192*a33 *k16*u1 *v1 + 192*a33 *k16*u1 *v3 + 192*a33 *k16*u1*u2*u3*v1
2 3 2 3 2 3
+ 192*a33 *k16*u1*v2 + 192*a33 *k16*u2 *v1 + 192*a33 *k16*v1*v2
2 2 2 2
+ 192*a33 *k38*u1*u2 *v2 - 384*a33 *k38*u1*u3*v1 - 192*a33 *k38*u1*u3
2 3 2 2
+ 192*a33 *k38*u2 *v3 + 192*a33 *k38*u2*u3*v2*v3 + 384*a33 *k38*u2*v1*v2
2 2 2 2 2
- 192*a33 *k38*v1 + 192*a33 *q1*u1 + 192*a33 *q1*u1*v1
2
- 48*a33*b33*k16*u1*u2*v1*v2 - 48*a33*b33*k16*u1*v1 *v2
2
- 48*a33*b33*k16*u2 *v1*v3 - 48*a33*b33*k16*u2*u3*v1*v2
2 3
- 48*a33*b33*k16*u2*v1 *v3 - 48*a33*b33*k16*v1 *v3 - 48*a33*b33*q1*u1*u3
2 2 2
- 48*a33*b33*q1*v1 + 64*a33*k16*n1*u1 *v2 + 64*a33*k16*n1*u3 *v1
2 3
+ 64*a33*k16*n1*u3*v1 - 64*a33*k38*n1*u2 - 64*a33*k38*n1*u2*u3*v1
3 2 2
- 64*a33*k38*n1*u3 + 64*a33*n1*q1*u1 + 3*b33 *k16*u1*v1*v3
2 2 2 3 2 2 2
+ 3*b33 *k16*u2*v2*v3 + 3*b33 *k16*u2*v3 + 6*b33 *k16*v1 *v3
2 3 2 2
+ 3*b33 *k16*v1*v3 + 3*b33 *q1*u1*v3 + 3*b33 *q1*v1*v3
2 2
- 8*b33*k16*n1*u2*v2*v3 - 8*b33*k16*n1*u2*v3 - 8*b33*k16*n1*v2 *v3
2 2
- 8*b33*k38*n1*u2*v1*v3 - 8*b33*k38*n1*u2*v2 - 8*b33*k38*n1*u3 *v1
2
- 8*b33*n1*q1*v1)/(192*a33 )
And again in machine readable form:
HAM=(192*a33**2*u1**2 + 192*a33**2*u2**2 + 48*a33**2*u3**2 + 48*a33*b33*u3*v3 +
48*a33*n1*u1 - 3*b33**2*v3**2 - 10*b33*n1*v1)/(48*a33)$
INT=(192*a33**2*k16*u1**3*v1 + 192*a33**2*k16*u1**3*v3 + 192*a33**2*k16*u1*u2*u3
*v1 + 192*a33**2*k16*u1*v2**3 + 192*a33**2*k16*u2**3*v1 + 192*a33**2*k16*v1*v2**
3 + 192*a33**2*k38*u1*u2**2*v2 - 384*a33**2*k38*u1*u3*v1 - 192*a33**2*k38*u1*u3
+ 192*a33**2*k38*u2**3*v3 + 192*a33**2*k38*u2*u3*v2*v3 + 384*a33**2*k38*u2*v1*v2
- 192*a33**2*k38*v1**2 + 192*a33**2*q1*u1**2 + 192*a33**2*q1*u1*v1 - 48*a33*b33
*k16*u1*u2*v1*v2 - 48*a33*b33*k16*u1*v1**2*v2 - 48*a33*b33*k16*u2**2*v1*v3 - 48*
a33*b33*k16*u2*u3*v1*v2 - 48*a33*b33*k16*u2*v1**2*v3 - 48*a33*b33*k16*v1**3*v3 -
48*a33*b33*q1*u1*u3 - 48*a33*b33*q1*v1**2 + 64*a33*k16*n1*u1**2*v2 + 64*a33*k16
*n1*u3**2*v1 + 64*a33*k16*n1*u3*v1**2 - 64*a33*k38*n1*u2**3 - 64*a33*k38*n1*u2*
u3*v1 - 64*a33*k38*n1*u3**3 + 64*a33*n1*q1*u1 + 3*b33**2*k16*u1*v1*v3**2 + 3*b33
**2*k16*u2*v2*v3**2 + 3*b33**2*k16*u2*v3**3 + 6*b33**2*k16*v1**2*v3**2 + 3*b33**
2*k16*v1*v3**3 + 3*b33**2*q1*u1*v3 + 3*b33**2*q1*v1*v3 - 8*b33*k16*n1*u2*v2*v3 -
8*b33*k16*n1*u2*v3**2 - 8*b33*k16*n1*v2**2*v3 - 8*b33*k38*n1*u2*v1*v3 - 8*b33*
k38*n1*u2*v2**2 - 8*b33*k38*n1*u3**2*v1 - 8*b33*n1*q1*v1)/(192*a33**2)$