Solution 53 to problem e3null
Expressions |
Parameters |
Relevance |
Back to problem e3null
Expressions
The solution is given through the following expressions:
a33=2*a22
b22=0
b31=0
b33=0
c12=0
c13=0
c22=0
c23=0
1 2
- ---*b32
4
c33=-------------
a22
n1=0
n2=0
n3=0
m1=0
m2=0
m3=0
r6=0
r5=0
r4=0
r3=0
r2=0
r1=0
q19=0
q18=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
q3=0
q2=0
q1=0
p50=0
p49=0
p48=0
p47=0
p46=0
p45=0
p44=0
p43=0
p42=0
p41=0
p40=0
p39=0
p38=0
p37=0
p36=0
p35=0
p34=0
p33=0
p32=0
p31=0
p30=0
p29=0
p28=0
p27=0
p26=0
p25=0
p24=0
p23=0
p22=0
p21=0
p20=0
p19=0
p18=0
p17=0
p16=0
p15=0
p14=0
p13=0
p12=0
p11=0
p10=0
p9=0
p8=0
p7=0
p6=0
p5=0
p4=0
p3=0
p2=0
p1=0
k104=0
k103=0
k102=0
k101=0
k100=0
1 4
- ---*b32 *k1
8
k99=----------------
4
a22
k98=0
1 3
- ---*b32 *k1
2
k97=----------------
3
a22
k96=0
k95=0
1 4
- ---*b32 *k1
8
k94=----------------
4
a22
k93=0
k92=0
2
- 2*b32 *k1
k91=--------------
2
a22
k90=0
k89=0
1 2
- ---*b32 *k1
2
k88=----------------
2
a22
k87=0
1 2
- ---*b32 *k1
2
k86=----------------
2
a22
k85=0
k84=0
k83=0
k82=0
k81=0
k80=0
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
4*b32*k1
k64=----------
a22
k63=0
k62=0
k61=0
k60=0
k59=0
k58=0
k57=0
k56=0
1 4
- ----*b32 *k1
16
k55=-----------------
4
a22
k54=0
k53=0
k52=0
k51=0
1 4
- ---*b32 *k1
8
k50=----------------
4
a22
k49=0
k48=0
k47=0
k46=0
k45=0
k44=0
k43=0
k42=0
k41=0
k40=0
k39=0
k38=0
k37=0
k36=0
k35=0
k34=0
k33=0
2*b32*k1
k32=----------
a22
k31=0
2*b32*k1
k30=----------
a22
k29=0
k28=0
k27=0
k26=0
1 4
- ----*b32 *k1
16
k25=-----------------
4
a22
k24=0
k23=0
k21=0
k20=0
k19=0
k18=0
k17=0
k16=0
k14=0
k13=0
k12=0
k11=0
k10=0
k9=0
k8=0
k7=0
k6=0
k5=k1
k4=0
k3=2*k1
k2=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:
k1,b32,a22
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
2 2 2 2 2 2 2 2
4*a22 *u1 + 4*a22 *u2 + 8*a22 *u3 + 4*a22*b32*u3*v2 - b32 *v3
HAM=-------------------------------------------------------------------
4*a22
4 4 4 2 2 4 4 3 2
INT=(k1*(16*a22 *u1 + 32*a22 *u1 *u2 + 16*a22 *u2 + 32*a22 *b32*u1 *u3*v2
3 2 3 2 2 2 2 2
+ 32*a22 *b32*u2 *u3*v2 + 64*a22 *b32*u2*u3 *v3 - 8*a22 *b32 *u1 *v3
2 2 2 2 2 2 2 2 3 2
- 8*a22 *b32 *u2 *v3 - 32*a22 *b32 *u3 *v3 - 8*a22*b32 *u3*v2*v3
4 4 4 2 2 4 2 2 4 4
- b32 *v1 - 2*b32 *v1 *v2 - 2*b32 *v1 *v3 - b32 *v2
4 2 2 4
- 2*b32 *v2 *v3 ))/(16*a22 )
And again in machine readable form:
HAM=(4*a22**2*u1**2 + 4*a22**2*u2**2 + 8*a22**2*u3**2 + 4*a22*b32*u3*v2 - b32**2
*v3**2)/(4*a22)$
INT=(k1*(16*a22**4*u1**4 + 32*a22**4*u1**2*u2**2 + 16*a22**4*u2**4 + 32*a22**3*
b32*u1**2*u3*v2 + 32*a22**3*b32*u2**2*u3*v2 + 64*a22**3*b32*u2*u3**2*v3 - 8*a22
**2*b32**2*u1**2*v3**2 - 8*a22**2*b32**2*u2**2*v3**2 - 32*a22**2*b32**2*u3**2*v3
**2 - 8*a22*b32**3*u3*v2*v3**2 - b32**4*v1**4 - 2*b32**4*v1**2*v2**2 - 2*b32**4*
v1**2*v3**2 - b32**4*v2**4 - 2*b32**4*v2**2*v3**2))/(16*a22**4)$