Solution 5 to problem e3quant
Expressions |
Parameters |
Relevance |
Back to problem e3quant
Expressions
The solution is given through the following expressions:
a33=2*a22
b22=0
b31=0
b32=0
b33=0
c12=0
c13=0
c22=0
c23=0
c33=0
n1=0
n2=0
n3=0
m2=0
m3=0
r6=0
r5=0
3
- ---*k1*m1
2
r4=--------------
a22
r3=0
r2=0
r1=0
q20=0
2
k1*m1
q19=--------
2
a22
q18=0
q17=0
2
k1*m1
q16=--------
2
a22
2*k1*m1
q14=---------
a22
q13=0
4*k1*m1
q11=---------
a22
q10=0
q9=0
q8=0
7
q7= - ---*k1
2
q6=0
q5=0
q4=0
q3=0
q2=0
1
q1=---*k1
2
p56=0
p55=0
p54=0
p53=0
p52=0
p51=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
2*k1*m1
p24=---------
a22
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
- 4*k1*m1
p10=------------
a22
p9=0
p8= - 4*k1
p7=0
p6=0
p5=0
- 2*k1*m1
p4=------------
a22
p3=0
p2=0
p1=0
k125=0
k124=0
k123=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=0
k107=0
k106=0
k105=0
k104=0
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
k95=0
k94=0
k93=0
k91=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
k65=0
k64=0
k63=0
k62=0
k61=0
k59=0
k58=0
k57=k1
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
k29=0
k28=0
k27=0
k26=0
k25=0
k24=0
k23=0
k22=0
k21=0
k20=0
k19=0
k18=0
k17=0
k16=0
k15=0
k14=0
k13=0
k12=0
k11=0
k10=0
k9=0
k8=0
k7=2*k1
k6=0
k5=0
k4=0
k3=0
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,m1,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 + m1*v1
2 4 2 2 2 2 2 2
INT=(k1*(2*a22 *u1 + 4*a22 *u1 *u2*u3 + a22 *u1 + 2*a22 *u1*u2*v2
2 2 2
- 8*a22 *u1*u3 - 7*a22 *u1*v1 + 4*a22*m1*u1*u3*v2 + 8*a22*m1*u1*v2
3 3
- 4*a22*m1*u2 - 8*a22*m1*u3 + 4*a22*m1*v1*v2 - 3*a22*m1*v1
2 2 2
+ 2*m1 *u1*v3 + 2*m1 *v1*v3))/(2*a22 )
And again in machine readable form:
HAM=a22*u1**2 + a22*u2**2 + 2*a22*u3**2 + m1*v1$
INT=(k1*(2*a22**2*u1**4 + 4*a22**2*u1**2*u2*u3 + a22**2*u1**2 + 2*a22**2*u1*u2*
v2**2 - 8*a22**2*u1*u3**2 - 7*a22**2*u1*v1 + 4*a22*m1*u1*u3*v2 + 8*a22*m1*u1*v2
- 4*a22*m1*u2**3 - 8*a22*m1*u3**3 + 4*a22*m1*v1*v2 - 3*a22*m1*v1 + 2*m1**2*u1*v3
+ 2*m1**2*v1*v3))/(2*a22**2)$