From 0cd23706229d55781f028fef05368ec25adac811 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Wed, 8 Feb 2012 18:00:23 +0000
Subject: [PATCH] Add a method to get the second derivatives of the directors
with respect to the quaternion coordinates. Or, in other words, the second
derivative of the map from quaternions to orthogonal matrices.
[[Imported from SVN: r8407]]
---
dune/gfe/rotation.hh | 25 +++++++++++++++++++++++++
1 file changed, 25 insertions(+)
diff --git a/dune/gfe/rotation.hh b/dune/gfe/rotation.hh
index 394ee544..758ae5dd 100644
--- a/dune/gfe/rotation.hh
+++ b/dune/gfe/rotation.hh
@@ -610,6 +610,31 @@ public:
}
+ /** \brief Compute the second derivatives of the director vectors with respect to the quaternion coordinates
+ *
+ * Let \f$ d_k(q) = (d_{k,1}, d_{k,2}, d_{k,3})\f$ be the k-th director vector at \f$ q \f$.
+ * Then the return value of this method is
+ * \f[ A_{ijkl} = \frac{\partial^2 d_{i,j}}{\partial q_k \partial q_l} \f]
+ */
+ static void getSecondDerivativesOfDirectors(Dune::array<Tensor3<T,3, 4, 4>, 3>& dd_dq_dq)
+ {
+ for (int i=0; i<3; i++)
+ dd_dq_dq[i] = 0;
+
+ dd_dq_dq[0][0][0][0] = 2; dd_dq_dq[0][0][1][1] = -2; dd_dq_dq[0][0][2][2] = -2; dd_dq_dq[0][0][3][3] = 2;
+ dd_dq_dq[0][1][0][1] = 2; dd_dq_dq[0][1][1][0] = 2; dd_dq_dq[0][1][2][3] = 2; dd_dq_dq[0][1][3][2] = 2;
+ dd_dq_dq[0][2][0][2] = 2; dd_dq_dq[0][2][1][3] = -2; dd_dq_dq[0][2][2][0] = 2; dd_dq_dq[0][2][3][1] = -2;
+
+ dd_dq_dq[1][0][0][1] = 2; dd_dq_dq[1][0][1][0] = 2; dd_dq_dq[1][0][2][3] = -2; dd_dq_dq[1][0][3][2] = -2;
+ dd_dq_dq[1][1][0][0] = -2; dd_dq_dq[1][1][1][1] = 2; dd_dq_dq[1][1][2][2] = -2; dd_dq_dq[1][1][3][3] = 2;
+ dd_dq_dq[1][2][0][3] = 2; dd_dq_dq[1][2][1][2] = 2; dd_dq_dq[1][2][2][1] = 2; dd_dq_dq[1][2][3][0] = 2;
+
+ dd_dq_dq[2][0][0][2] = 2; dd_dq_dq[2][0][1][3] = 2; dd_dq_dq[2][0][2][0] = 2; dd_dq_dq[2][0][3][1] = 2;
+ dd_dq_dq[2][1][0][3] = -2; dd_dq_dq[2][1][1][2] = 2; dd_dq_dq[2][1][2][1] = 2; dd_dq_dq[2][1][3][0] = -2;
+ dd_dq_dq[2][2][0][0] = -2; dd_dq_dq[2][2][1][1] = -2; dd_dq_dq[2][2][2][2] = 2; dd_dq_dq[2][2][3][3] = 2;
+
+ }
+
/** \brief Compute the derivative of the squared distance function with respect to the second argument
*
* The squared distance function is
--
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