I have the following equation:
eq=E0[x,y,z]+E1[x,y,z]*Cos[phi]+E2[x,y,z]*Cos[phi]^2+E3[x,y,z]*Sin[phi]
Now E0,E1,E2
and E3
are already series expansions of expressions in x,y,z
. Therefore I would like to series expand the result of
Solve[D[eq,phi]==0,phi]
However, this is some giant arctan expression and Mathematica seems to take forever.
Question: Is there a more clever approach to this (not calling Series at the end only), or is there some way I can tune the Series
command?
Here are the real expressions I am dealing with, if someone wants to try something out:
Ecp = (s1*s3*Abs[J]/DE^2/2 - 1/DE*s2*s3*KroneckerDelta[1, s1])*(t1^2 -
t2^2) /. KroneckerDelta[1, s1] -> (1 + s1)/2 /.
t1 -> tt1*DE /. t2 -> tt2*DE /. xi -> xii*DE /. J -> Jj*DE
Ec2p = s2/DE^2*KroneckerDelta[1, s1] (t1^2 - t2^2)^2/Abs[J] /.
KroneckerDelta[1, s1] -> (1 + s1)/2 /. t1 -> tt1*DE /.
t2 -> tt2*DE /. xi -> xii*DE /. J -> Jj*DE
Esp = s2*s3/DE^2*t1*t2*xi*
Abs[J]/(Abs[xi] KroneckerDelta[-1, s1] +
Abs[J] KroneckerDelta[1, s1]) /.
KroneckerDelta[1, s1] -> (1 + s1)/2 /.
KroneckerDelta[-1, s1] -> (1 - s1)/2 /. t1 -> tt1*DE /.
t2 -> tt2*DE /. xi -> xii*DE /. J -> Jj*DE
Solve[D[E00 + Cos[phi]*Ecp + Cos[phi]^2*Ec2p + Sin[phi]*Esp, phi] == 0, phi]
The small parameters are tt1,tt2,Jj,xii
. Usually I then introduce a "smallness-paramter" as suggested here on SE to perform the multi series.