doc + pep8 fixes

Author: pancetta

docs/source/projects/doc_solar_system.rst

@@ -0,0 +1,8 @@
+Full code: `pySDC/projects/Hamiltonian/solar_system.py <https://github.com/Parallel-in-Time/pySDC/blob/master/pySDC/projects/Hamiltonian/solar_system.py>`_
+
+.. literalinclude:: ../../../pySDC/projects/Hamiltonian/solar_system.py
+
+Results:
+
+.. image:: ../../../data/outer_solar_system_hamiltonian.png
+   :scale: 50 %

pySDC/implementations/problem_classes/OuterSolarSystem.py

@@ -69,18 +69,18 @@ def u_exact(self, t):
         me = particles(self.init)
 
         me.pos.values[:, 0] = [0.0, 0.0, 0.0]
-        me.pos.values[:, 1] = [-3.5025653,-3.8169847,-1.5507963]
-        me.pos.values[:, 2] = [9.0755314,-3.0458353,-1.6483708]
-        me.pos.values[:, 3] = [8.3101420,-16.2901086,-7.2521278]
-        me.pos.values[:, 4] = [11.4707666,-25.7294829,-10.8169456]
-        me.pos.values[:, 5] = [-15.5387357,-25.2225594,-3.1902382]
+        me.pos.values[:, 1] = [-3.5025653, -3.8169847, -1.5507963]
+        me.pos.values[:, 2] = [9.0755314, -3.0458353, -1.6483708]
+        me.pos.values[:, 3] = [8.3101420, -16.2901086, -7.2521278]
+        me.pos.values[:, 4] = [11.4707666, -25.7294829, -10.8169456]
+        me.pos.values[:, 5] = [-15.5387357, -25.2225594, -3.1902382]
 
         me.vel.values[:, 0] = [0.0, 0.0, 0.0]
-        me.vel.values[:, 1] = [0.00565429,-0.00412490,-0.00190589]
+        me.vel.values[:, 1] = [0.00565429, -0.00412490, -0.00190589]
         me.vel.values[:, 2] = [0.00168318, 0.00483525, 0.00192462]
         me.vel.values[:, 3] = [0.00354178, 0.00137102, 0.00055029]
         me.vel.values[:, 4] = [0.00288930, 0.00114527, 0.00039677]
-        me.vel.values[:, 5] = [0.00276725, -0.0017072,-0.00136504]
+        me.vel.values[:, 5] = [0.00276725, -0.0017072, -0.00136504]
 
         me.m[0] = 1.00000597682
         me.m[1] = 0.000954786104043

pySDC/projects/Hamiltonian/README.rst

@@ -11,3 +11,13 @@ We first test the integrator for some rather simple problems, namely the harmoni
 For both problems we make use of the hook ``hamiltonian_output`` to monitor the deviation from the exact Hamiltonian.
 
 .. include:: doc_hamiltonian_simple.rst
+
+Solar system problem
+--------------------
+
+In this slightly more complex setup we simulate the movement of planets in the outer solar system.
+For this, only six planets are modeled, namely the Sun (which in its mass contains the inner planets), Jupiter, Saturn, Uranus, Neptune and Pluto.
+The gravitational forces are computed using a simple N^2 solver.
+All this is implemented within the ``OuterSolarSystem`` problem class.
+
+.. include:: doc_solar_system.rst