Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

Method of variation of constants
dcα
dt = Fα(l; cβ) ; α, β = 1, 2, l, λ ,
where RHS is linear in the perturbing acceleration, A ′ . Note the
presence of the sole angle l (apart from the implicit time dependence
of cβ) on the RHS.
dc1
dt = ∂c1(x, v)
∂vi dc2
dt = ∂c2(x, v)
∂vj dcl
dt
dcλ
dt
= −
A′i ,
A′j ,
−1 ∂S ∂S
∂l
= − ∂W
∂l
dcl
dt
∂c1
− ∂W
∂c1
dc1
dt
dc1
dt
+ ∂S
∂c2
− ∂W
∂c2
dc2
dt
dc2
dt .
Evolution eqns for c1 and c2 clearly arise from the fact that c1 and c2
were defined as some first integrals in phase-space.
,
BRI-IHP06-I – p.108/??