Add documentation of past evolution

docs/References.bib

@@ -444,6 +444,20 @@ @article{Buchman:2012dw
     year = "2012"
 }
 
+@article{Buonanno2005xu,
+    author = "Buonanno, Alessandra and Chen, Yanbei and Damour, Thibault",
+    title = "{Transition from inspiral to plunge in precessing binaries of
+              spinning black holes}",
+    eprint = "gr-qc/0508067",
+    archivePrefix = "arXiv",
+    doi = "10.1103/PhysRevD.74.104005",
+    journal = "Phys. Rev. D",
+    volume = "74",
+    pages = "104005",
+    year = "2006",
+    url = "https://doi.org/10.1103/PhysRevD.74.104005"
+}
+
 @article{Casoni2012,
   author  = {Casoni, E. and Peraire, J. and Huerta, A.},
   title   = {One-dimensional shock-capturing for high-order discontinuous

src/PointwiseFunctions/AnalyticData/Xcts/BinaryWithGravitationalWaves.hpp

@@ -556,6 +556,29 @@ struct BinaryWithGravitationalWavesVariables
  *
  * \warning The class is still being worked on. The Solver was not tested yet,
  * for now we still see a very slow convergence.
+ *
+ * To be able to calculate equations \f$\eqref{eq:retarded_term}\f$ and
+ * \f$\eqref{eq:integral_term}\f$ we need to look into the past history
+ * of the binary at least up to the time were the generated wave can reach the
+ * furthest point on the grid. To do so we must evolve the binary backward in
+ * time. Because we are only looking into the inspiral phase we can follow a
+ * simple Hamiltonian evolution computed in Post-Newtonian orders. The
+ * equations to be solved are
+ *
+ * \f{equation}{
+ * \frac{d X^i}{d t}=\frac{\partial H}{\partial P_i}
+ * \f}
+ *
+ * and
+ *
+ * \f{equation}{
+ * \frac{d P_i}{d t}=-\frac{\partial H}{\partial X^i}+F_i,
+ * \f}
+ *
+ * where $H$ is the Post-Newtonian Hamiltonian, $X^i$ is the separation
+ * vector between the two particles, $P_i$ is the momentum of one particle
+ * in the center of mass frame and $F_i$ is the radiation-reaction flux term.
+ * The Post-Newtonian Hamiltonian is given in \cite Buonanno2005xu.
  */
 class BinaryWithGravitationalWaves
     : public elliptic::analytic_data::Background,