[Boost-commit] svn:boost r63653 - in sandbox/odeint/libs/numeric/odeint/doc: . html html/boost_numeric_odeint

Subject: [Boost-commit] svn:boost r63653 - in sandbox/odeint/libs/numeric/odeint/doc: . html html/boost_numeric_odeint
From: karsten.ahnert_at_[hidden]
Date: 2010-07-05 10:58:49

Author: karsten
Date: 2010-07-05 10:58:49 EDT (Mon, 05 Jul 2010)
New Revision: 63653
URL: http://svn.boost.org/trac/boost/changeset/63653

Log:
changing the formulas in the solar system documentation
Text files modified: 
   sandbox/odeint/libs/numeric/odeint/doc/html/boost_numeric_odeint/tutorial.html |    25 ++++++++++++++++++-------               
   sandbox/odeint/libs/numeric/odeint/doc/html/index.html                         |     2 +-                                      
   sandbox/odeint/libs/numeric/odeint/doc/tutorial.qbk                            |    23 ++++++++++++++---------                 
   3 files changed, 33 insertions(+), 17 deletions(-)

Modified: sandbox/odeint/libs/numeric/odeint/doc/html/boost_numeric_odeint/tutorial.html
==============================================================================
--- sandbox/odeint/libs/numeric/odeint/doc/html/boost_numeric_odeint/tutorial.html	(original)
+++ sandbox/odeint/libs/numeric/odeint/doc/html/boost_numeric_odeint/tutorial.html	2010-07-05 10:58:49 EDT (Mon, 05 Jul 2010)
@@ -420,30 +420,41 @@
           The next example in this tutorial is a simulation of the solar system.
           In the solar system each planet, and of course also the sun will be represented
           by mass points. The interaction force between each object is the gravitational
-          force which can be written as Fij = - gamma m M / (qi-qj)3 * (qi-qj)
+          force which can be written as
         </p>
 <p>
-          where gamma is the gravitational constant, mi and mj are the masses and
-          qi and qj are the locations of the two objects.
+          F_ij = -gamma m_i m_j (q_i-q_j)/|q_i-q_j|^3
         </p>
 <p>
-          dqi = pi dpi = 1/m sum ji Fij
+          where gamma is the gravitational constant, m_i and m_j are the masses and
+          q_i and q_j are the locations of the two objects. The equations of motion
+          are then
+        </p>
+<p>
+          dq_i/dt = p_i dp_i/dt = 1/m_i sum_ji F_ij
         </p>
 <p>
           where pi is the momenta of object i. The equations of motion can also be
           derived from the Hamiltonian
         </p>
 <p>
-          H = sum over i pi^2 / 2 m_i + sum j V( qi , qj )
+          H = sum_i p_i^2/(2m_i) + sum_j V( qi , qj )
+        </p>
+<p>
+          with the interaction potential V(q_i,q_j). The Hamiltonian equations give
+          the equations of motion
+        </p>
+<p>
+          dq_i/dt = dH/dp_i
         </p>
 <p>
-          via dqi = dH / dpi, dpi = - dH / dq1. V(qi,qj) is the interaction potential.
+          dp_i = -dH/dq_i.
         </p>
 <p>
           In time independent Hamiltonian system the energy is conserved and special
           integration methods have to be applied in order to ensure energy conservation.
           The odeint library provides classes for Hamiltonian systems, which are
-          separable and can be written in the form H = sum pi^2/2 mi + Hq(q), where
+          separable and can be written in the form H = sum p_i^2/2m_i + Hq(q), where
           Hq(q) only depends on the coordinates.
         </p>
 <p>

Modified: sandbox/odeint/libs/numeric/odeint/doc/html/index.html
==============================================================================
--- sandbox/odeint/libs/numeric/odeint/doc/html/index.html	(original)
+++ sandbox/odeint/libs/numeric/odeint/doc/html/index.html	2010-07-05 10:58:49 EDT (Mon, 05 Jul 2010)
@@ -246,7 +246,7 @@
 </div>
 </div>
 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left"><p><small>Last revised: July 05, 2010 at 14:50:52 GMT</small></p></td>
+<td align="left"><p><small>Last revised: July 05, 2010 at 14:58:03 GMT</small></p></td>
 <td align="right"><div class="copyright-footer"></div></td>
 </tr></table>
 <hr>

Modified: sandbox/odeint/libs/numeric/odeint/doc/tutorial.qbk
==============================================================================
--- sandbox/odeint/libs/numeric/odeint/doc/tutorial.qbk	(original)
+++ sandbox/odeint/libs/numeric/odeint/doc/tutorial.qbk	2010-07-05 10:58:49 EDT (Mon, 05 Jul 2010)
@@ -146,26 +146,31 @@
 solar system each planet, and of course also the sun will be represented by
 mass points. The interaction force between each object is the gravitational
 force which can be written as
-Fij = - gamma m M / (qi-qj)3 * (qi-qj)
 
-where gamma is the gravitational constant, mi and mj are the masses and qi and
-qj are the locations of the two objects.
+F_ij = -gamma m_i m_j (q_i-q_j)/|q_i-q_j|^3
 
-dqi = pi
-dpi = 1/m sum ji Fij
+where gamma is the gravitational constant, m_i and m_j are the masses and q_i
+and q_j are the locations of the two objects. The equations of motion are then
+
+dq_i/dt = p_i
+dp_i/dt = 1/m_i sum_ji F_ij
 
 where pi is the momenta of object i. The equations of motion can also be
 derived from the Hamiltonian
 
-H = sum over i pi^2 / 2 m_i + sum j V( qi , qj ) 
+H = sum_i p_i^2/(2m_i) + sum_j V( qi , qj ) 
+
+with the interaction potential V(q_i,q_j). The Hamiltonian equations give the
+equations of motion
+
+dq_i/dt = dH/dp_i
 
-via dqi = dH / dpi, dpi = - dH / dq1. V(qi,qj) is the interaction
-potential.
+dp_i = -dH/dq_i.
 
 In time independent Hamiltonian system the energy is conserved and special
 integration methods have to be applied in order to ensure energy
 conservation. The odeint library provides classes for Hamiltonian
-systems, which are separable and can be written in the form H = sum pi^2/2 mi +
+systems, which are separable and can be written in the form H = sum p_i^2/2m_i +
 Hq(q), where Hq(q) only depends on the coordinates.
 
 hamiltonian_stepper_euler