Solution 47 to problem e3c2new
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Parameters |
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Expressions
The solution is given through the following expressions:
a22= - a33
b22=0
b31=0
b32=0
b33=0
c12=0
c13=0
c22=0
c23=0
c33=0
n2=0
n3=0
m1=0
m2=0
m3=0
r6=0
r5=0
r4=0
r3=0
r2=0
1 2 1 3
- ---*a33 *n1*q1 - ---*k10*n1
2 8
r1=---------------------------------
3
a33
q20=0
q19=0
q17=0
q16=0
q15=0
q14=0
q13=0
q12=0
q11=0
q10=0
q9=0
q8=0
q7=0
q5=0
q4=0
2 1 2
a33 *q1 + ---*k10*n1
4
q3=-----------------------
2
a33
q2=0
p56=0
p55=0
p54=0
p53=0
p52=0
1
- ---*k26*n1
2
p51=---------------
a33
p50=0
p49=0
p48=0
p47=0
p46=0
p45=0
p44=0
p43=0
p42=0
p41=0
p40=0
1
---*k23*n1
2
p39=------------
a33
p38=0
p37=0
p36=0
p35=0
p34=0
p33=0
p32=0
1
- ---*k26*n1
2
p31=---------------
a33
p30=0
p29=0
p28=0
p27=0
p26=0
p25=0
p24=0
p23=0
1
---*k23*n1
2
p22=------------
a33
p21=0
p20=0
p19=0
p18=0
1
- ---*k26*n1
2
p17=---------------
a33
p16=0
p15=0
p14=0
p13=0
p12=0
1
---*k23*n1
2
p11=------------
a33
p10=0
p9=0
1
- ---*k10*n1
2
p8=---------------
a33
p7=0
p6=0
p5=0
p4=0
1
---*k10*n1
2
p3=------------
a33
p2=0
1
---*k10*n1
2
p1=------------
a33
k125=0
k124=0
k122=0
k121=0
k120=0
k119=0
k118=0
k117=0
k116=0
k115=0
k114=0
k113=0
k112=0
k110=0
k109=0
k108=k26
k107=0
k106=k26
k105=0
k104=0
k103=0
k102=0
k101=0
k100=0
k99=0
k98=0
k97=0
k96=0
k95=0
k94=0
k93=0
k92=0
k91=0
k90=0
k89=0
k88=0
k87=0
k86=0
k85=0
k84=0
k83=0
k82=0
k81=0
k80=k23
k79=0
k78=0
k77=0
k76=0
k75=0
k74=0
k73=0
k72=0
k71=0
k70=0
k69=0
k68=0
k67=0
k66=0
k65=0
k64=0
k63=0
k62=0
k61=0
k60=0
k59=0
k58=k26
k57=0
k56=k26
k55=0
k54=0
k53=0
k52=0
k51=0
k50=0
k49=0
k48=0
k47=0
k46=0
k45=0
k44=k23
k43=0
k42=0
k41=0
k40=0
k38=0
k37=0
k36=0
k35=0
k34=0
k33=0
k32=0
k30=0
k29=0
k28=k26
k27=0
k25=0
k24=0
k22=0
k21=0
k20=0
k19=0
k18=0
k17=0
k16=0
k14=0
k13=0
k12=k10
k11=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:
q1,k26,k23,k10,n1,a33
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
2 2 2
HAM= - a33*u1 - a33*u2 + a33*u3 + n1*u1
3 2 2 3 2 2 3 2
INT=(8*a33 *k10*u1 *u3 + 8*a33 *k10*u2 *u3 + 8*a33 *k23*u1*u3 *v1
3 2 3 3 3 2 2
+ 8*a33 *k23*u2*u3 *v2 + 8*a33 *k23*u3 *v3 + 8*a33 *k26*u1 *v1
3 2 2 3 2 2 3 2 2
+ 8*a33 *k26*u1 *v2 + 8*a33 *k26*u1 *v3 + 8*a33 *k26*u2 *v1
3 2 2 3 2 2 3 2 3 2
+ 8*a33 *k26*u2 *v2 + 8*a33 *k26*u2 *v3 + 8*a33 *q1*u1 + 8*a33 *q1*u2
2 3 2 2 2 2
+ 4*a33 *k10*n1*u1 + 4*a33 *k10*n1*u1*u2 - 4*a33 *k10*n1*u1*u3
2 2 2 2
+ 4*a33 *k23*n1*u1 *v1 + 4*a33 *k23*n1*u1*u2*v2 + 4*a33 *k23*n1*u1*u3*v3
2 2 2 2 2 2
- 4*a33 *k26*n1*u1*v1 - 4*a33 *k26*n1*u1*v2 - 4*a33 *k26*n1*u1*v3
2 2 2 3 3
- 4*a33 *n1*q1*u1 + 2*a33*k10*n1 *u2 - k10*n1 *u1)/(8*a33 )
And again in machine readable form:
HAM= - a33*u1**2 - a33*u2**2 + a33*u3**2 + n1*u1$
INT=(8*a33**3*k10*u1**2*u3**2 + 8*a33**3*k10*u2**2*u3**2 + 8*a33**3*k23*u1*u3**2
*v1 + 8*a33**3*k23*u2*u3**2*v2 + 8*a33**3*k23*u3**3*v3 + 8*a33**3*k26*u1**2*v1**
2 + 8*a33**3*k26*u1**2*v2**2 + 8*a33**3*k26*u1**2*v3**2 + 8*a33**3*k26*u2**2*v1
**2 + 8*a33**3*k26*u2**2*v2**2 + 8*a33**3*k26*u2**2*v3**2 + 8*a33**3*q1*u1**2 +
8*a33**3*q1*u2**2 + 4*a33**2*k10*n1*u1**3 + 4*a33**2*k10*n1*u1*u2**2 - 4*a33**2*
k10*n1*u1*u3**2 + 4*a33**2*k23*n1*u1**2*v1 + 4*a33**2*k23*n1*u1*u2*v2 + 4*a33**2
*k23*n1*u1*u3*v3 - 4*a33**2*k26*n1*u1*v1**2 - 4*a33**2*k26*n1*u1*v2**2 - 4*a33**
2*k26*n1*u1*v3**2 - 4*a33**2*n1*q1*u1 + 2*a33*k10*n1**2*u2**2 - k10*n1**3*u1)/(8
*a33**3)$