Solution 56 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
b32=0
b33=0
c13=0
c22=0
c23=0
c33=0
n1=0
n2=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
2
- k1*n3
q3=-----------
2
a22
q2=0
2
- k1*n3
q1=-----------
2
a22
p50=0
p49=0
p48=0
p47=0
p46=0
p45=0
p44=0
p43=0
p42=0
p41=0
2*c12*k1*n3
p40=-------------
2
a22
p39=0
p38=0
2*c12*k1*n3
p37=-------------
2
a22
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
- 2*k1*n3
p7=------------
a22
p6=0
- 2*k1*n3
p5=------------
a22
p4=0
p3=0
p2=0
p1=0
k104=0
k103=0
k102=0
k101=0
k100=0
2
- 2*c12 *k1
k99=--------------
2
a22
k98=0
k97=0
k96=0
k95=0
2
- 2*c12 *k1
k94=--------------
2
a22
k93=0
k92=0
k91=0
k90=0
k89=0
k88=0
4*c12*k1
k87=----------
a22
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
k65=0
k64=0
k63=0
k62=0
k61=0
k60=0
k59=0
k58=0
k57=0
k56=0
2
- c12 *k1
k55=------------
2
a22
k54=0
k53=0
k52=0
k51=0
2
- 2*c12 *k1
k50=--------------
2
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
k32=0
k31=0
k30=0
k29=0
k28=0
k27=0
k26=0
2
- c12 *k1
k25=------------
2
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,c12,n3,a22
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
2 2 2
HAM=a22*u1 + a22*u2 + 2*a22*u3 + 2*c12*v1*v2 + n3*u3
2 4 2 2 2 2 4 2
INT=(k1*(a22 *u1 + 2*a22 *u1 *u2 + a22 *u2 + 4*a22*c12*u1*u2*v3
2 2 2 4 2 2 2
- 2*a22*n3*u1 *u3 - 2*a22*n3*u2 *u3 - c12 *v1 - 2*c12 *v1 *v2
2 2 2 2 4 2 2 2
- 2*c12 *v1 *v3 - c12 *v2 - 2*c12 *v2 *v3 + 2*c12*n3*u1*v2*v3
2 2 2 2 2
+ 2*c12*n3*u2*v1*v3 - n3 *u1 - n3 *u2 ))/a22
And again in machine readable form:
HAM=a22*u1**2 + a22*u2**2 + 2*a22*u3**2 + 2*c12*v1*v2 + n3*u3$
INT=(k1*(a22**2*u1**4 + 2*a22**2*u1**2*u2**2 + a22**2*u2**4 + 4*a22*c12*u1*u2*v3
**2 - 2*a22*n3*u1**2*u3 - 2*a22*n3*u2**2*u3 - c12**2*v1**4 - 2*c12**2*v1**2*v2**
2 - 2*c12**2*v1**2*v3**2 - c12**2*v2**4 - 2*c12**2*v2**2*v3**2 + 2*c12*n3*u1*v2*
v3 + 2*c12*n3*u2*v1*v3 - n3**2*u1**2 - n3**2*u2**2))/a22**2$