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

Method of variation of constants
First construct soln to the ‘unperturbed’ system, defined by
˙x = v ,
˙v = A0(x, v).
The solution to the exact system
˙x = v ,
˙v = A(x, v) ,
obtained by varying the constants in the generic solutions of
the unperturbed system. The method assumes ( true for
A conservative
2P N
or Aconservative 3P N ) that the unperturbed system
admits sufficiently many integrals of motion to be integrable.
E.g. if A0 = A2P N, we have four first integrals: the 2PN
accurate energy and 2PN accurate angular momentum of
the binary written in the 2PN accurate center of mass frame
as c1 and ci BRI-IHP06-I – p.102/??
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