Solution 32 to problem e3null
Expressions |
Parameters |
Relevance |
Back to problem e3null
Expressions
The solution is given through the following expressions:
3
a22=---*a33
4
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
c33=0
n1=0
n2=0
m1=0
m2=0
4 2
- ---*m3 *p5
3
r6=---------------
a33*b33
r5=0
r4=0
r2=0
r1=0
q19=0
q18=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
- m3*p5
q3=----------
b33
q2=0
- m3*p5
q1=----------
b33
p50=0
p49=0
p48=0
p47=p15
p46=0
p45=0
p44=0
p43=0
p42=0
p41=0
p40=0
p39=0
p38=0
p37=0
4 4
---*b33*p5 + ---*k10*m3
3 3
p36=-------------------------
a33
p35=0
p34=0
p33=0
p32=0
p31=0
p30=0
p29=0
p28=p15
p27=0
p26=0
p25=0
p24=0
p23=0
p22=0
p21=0
p20=0
p19=0
p18=0
p17=0
p16=0
p14=0
p13=0
p12=0
p11=0
p9=0
p8=0
p7=p5
p6=0
p4=0
p3=0
p2=0
p1=0
k104=0
k103=0
k101=0
k100=0
k99=0
k98=0
k97=0
k96=0
k95=0
k94=0
k93=0
k92=0
k90=0
k89=0
k88=0
k87=0
k86=0
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
4
---*b33*k10
3
k65=-------------
a33
k64=0
k63=0
k62=0
k61=0
k60=0
k59=0
k58=0
k57=0
k56=0
k55=0
k54=0
k53=0
k52=0
k51=0
k50=0
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
k32=0
k31=0
k30=0
k28=0
k27=0
k26=0
k25=0
k24=0
k23=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:
n3,m3,r3,p15,p10,p5,b33,k10,a33
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
2 2 2
3*a33*u1 + 3*a33*u2 + 4*a33*u3 + 4*b33*u3*v3 + 4*m3*v3 + 4*n3*u3
HAM=---------------------------------------------------------------------
4
2 2 2 2 3
INT=(3*a33*b33*k10*u1 *u3 + 3*a33*b33*k10*u2 *u3 + 3*a33*b33*p10*u3
2 2 2
+ 3*a33*b33*p15*u3*v1 + 3*a33*b33*p15*u3*v2 + 3*a33*b33*p15*u3*v3
2 2
+ 3*a33*b33*p5*u1 *u3 + 3*a33*b33*p5*u2 *u3 + 3*a33*b33*r3*u3
2 2 2 3 2 2
- 3*a33*m3*p5*u1 - 3*a33*m3*p5*u2 + 4*b33 *k10*u3 *v3 + 4*b33 *p5*u3 *v3
2 2
+ 4*b33*k10*m3*u3 *v3 - 4*m3 *p5*v3)/(3*a33*b33)
And again in machine readable form:
HAM=(3*a33*u1**2 + 3*a33*u2**2 + 4*a33*u3**2 + 4*b33*u3*v3 + 4*m3*v3 + 4*n3*u3)/
4$
INT=(3*a33*b33*k10*u1**2*u3**2 + 3*a33*b33*k10*u2**2*u3**2 + 3*a33*b33*p10*u3**3
+ 3*a33*b33*p15*u3*v1**2 + 3*a33*b33*p15*u3*v2**2 + 3*a33*b33*p15*u3*v3**2 + 3*
a33*b33*p5*u1**2*u3 + 3*a33*b33*p5*u2**2*u3 + 3*a33*b33*r3*u3 - 3*a33*m3*p5*u1**
2 - 3*a33*m3*p5*u2**2 + 4*b33**2*k10*u3**3*v3 + 4*b33**2*p5*u3**2*v3 + 4*b33*k10
*m3*u3**2*v3 - 4*m3**2*p5*v3)/(3*a33*b33)$