Note that Lucas (4-35) is actually for EIods(POIo,t=0), not ETods(POIo,t).
I did both in (4-35), so just refer to it for the derivations.
/*++++++++++++++++++++++++++++++++++++++
/*add_eqn same issues as 04_35
04_36
Er in terms of E0(rs) and L(vs)
/$L ET(rs,vs) = E0(rs) + Ei(rs,vs) all measures at t=0
= E0(rs) *(1 + 3/2*β^2*sin(θ)^2 + 15/8*β^4*sin(θ)^4 )
- E0(rs)*L(vs)*(1 + 3/2*β^2*sin(θ)^2 )
/$H ET(rs,vs) = E0(rs) + Ei(rs,vs) all measures at t=0
= + E0(rs) *(1 + 3/2*β^2*sin(θ)^2 + 15/8*β^4*sin(θ)^4 )
- E0(rs)*L(vs)*(1 + 3/2*β^2*sin(θ)^2)
/* OK - very simple. /%
ETods(POIo,t=0,2nd stage)
= + E0ods(POIo,t) *{ 1 + 3/2*β^2*sin(Aθpc(POIo(t),t=0))^2 + 21/8*β^4*sin(Aθpc(POIo(t),t=0))^4 }
- E0ods(POIo,t)*λ(Vons(PART)) *{ 1 + β^2*sin(Aθpc(POIo(t),t=0))^2 }
/* 03Sep2019 the numerical factors differ from Lucas - hopefully that will self-fix with further iterations?
/*_file_insert_path "$d_Lucas""relativistic factor, restrictive conditions.txt"