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------------------------------------------------------------
revno: 2340
committer: bchareyre <bchareyre@dt-rv020>
branch nick: trunk
timestamp: Thu 2010-07-08 22:01:59 +0200
message:
  - More small fixes.
modified:
  doc/sphinx/formulation.rst


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=== modified file 'doc/sphinx/formulation.rst'
--- doc/sphinx/formulation.rst	2010-07-08 19:57:19 +0000
+++ doc/sphinx/formulation.rst	2010-07-08 20:01:59 +0000
@@ -724,9 +724,9 @@
 	
 	\vec{K}_{ij}=\sum_k (K_{Nk}-K_{Tk})\vec{n}_{i}\vec{n}_{j}+K_{Tk}=\sum_j K_{Nk}\left((1-\xi)\vec{n}_{i}\vec{n}_{j}+\xi\right)
 
-with $i$ and $j\in\{x,y,z\}$. Equations :eq:`eq-dtcr-global`, :eq:`eq-dtcr-axes` and :eq:`eq-dtcr-particle-stiffness` determine $\Dtcr$ in a simulation. A similar approach generalized to all 6 DOFs is implemented by the :yref:`GlobalStiffnessTimeStepper` engine in Yade. The derivation of generalized stiffness including rotational terms is very similar but not developped here, for simplicity. For full reference, see "PFC3D - Theoretical Background".
+with $i$ and $j\in\{x,y,z\}$. Equations :eq:`eq-dtcr-axes` and :eq:`eq-dtcr-particle-stiffness` determine $\Dtcr$ in a simulation. A similar approach generalized to all 6 DOFs is implemented by the :yref:`GlobalStiffnessTimeStepper` engine in Yade. The derivation of generalized stiffness including rotational terms is very similar but not developped here, for simplicity. For full reference, see "PFC3D - Theoretical Background".
 					
-For computation efficiency reasons, eigenvalues of the stiffness matrices are not computed. They are only approximated assuming than DOF's are uncoupled, and using diagonal terms of $K.M^{-1}$. They give good approximates in typical mechanical systems.
+Note that for computation efficiency reasons, eigenvalues of the stiffness matrices are not computed. They are only approximated assuming than DOF's are uncoupled, and using diagonal terms of $K.M^{-1}$. They give good approximates in typical mechanical systems.
 
 There is one important condition that $\omega_{\rm max}>0$: if there are no contacts between particles and $\omega_{\rm max}=0$, we would obtain value $\Dtcr=\infty$. While formally correct, this value is numerically erroneous: we were silently supposing that stiffness remains constant during each timestep, which is not true if contacts are created as particles collide. In case of no contact, therefore, stiffness must be pre-estimated based on future interactions, as shown in the next section.