From aec2260d10f8835b131e2884e0ec5252886b070a Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Wed, 6 Dec 2006 16:40:55 +0000
Subject: [PATCH] B() is a method of the quaternion class now
[[Imported from SVN: r1075]]
---
src/quaternion.hh | 30 ++++++++++++++++++++++++++++++
src/rodassembler.hh | 39 +++++++++------------------------------
2 files changed, 39 insertions(+), 30 deletions(-)
diff --git a/src/quaternion.hh b/src/quaternion.hh
index 846b5f0f..4e3a7076 100644
--- a/src/quaternion.hh
+++ b/src/quaternion.hh
@@ -223,6 +223,36 @@ public:
}
}
+
+ /** \brief Create three vectors which form an orthonormal basis of \mathbb{H} together
+ with this one.
+
+ This is used to compute the strain in rod problems.
+ See: Dichmann, Li, Maddocks, 'Hamiltonian Formulations and Symmetries in
+ Rod Mechanics', page 83
+ */
+ Quaternion<T> B(int m) const {
+ assert(m>=0 && m<3);
+ Quaternion<T> r;
+ if (m==0) {
+ r[0] = (*this)[3];
+ r[1] = (*this)[2];
+ r[2] = -(*this)[1];
+ r[3] = -(*this)[0];
+ } else if (m==1) {
+ r[0] = -(*this)[2];
+ r[1] = (*this)[3];
+ r[2] = (*this)[0];
+ r[3] = -(*this)[1];
+ } else {
+ r[0] = (*this)[1];
+ r[1] = -(*this)[0];
+ r[2] = (*this)[3];
+ r[3] = -(*this)[2];
+ }
+
+ return r;
+ }
};
#endif
diff --git a/src/rodassembler.hh b/src/rodassembler.hh
index bafe00bb..1f89df15 100644
--- a/src/rodassembler.hh
+++ b/src/rodassembler.hh
@@ -137,37 +137,12 @@ namespace Dune
const std::vector<Configuration>& globalSolution,
const int matSize, MatrixType& mat) const;
- template <class T>
- static Quaternion<T> B(int m, const Quaternion<T>& q) {
- assert(m>=0 && m<3);
- Quaternion<T> r;
- if (m==0) {
- r[0] = q[3];
- r[1] = q[2];
- r[2] = -q[1];
- r[3] = -q[0];
- } else if (m==1) {
- r[0] = -q[2];
- r[1] = q[3];
- r[2] = q[0];
- r[3] = -q[1];
- } else {
- r[0] = q[1];
- r[1] = -q[0];
- r[2] = q[3];
- r[3] = -q[2];
- }
-
- return r;
- }
+
template <class T>
static FieldVector<T,3> darboux(const Quaternion<T>& q, const FieldVector<T,4>& q_s)
{
- FieldVector<double,3> uCanonical; // The Darboux vector
- uCanonical[0] = 2 * ( q[3]*q_s[0] + q[2]*q_s[1] - q[1]*q_s[2] - q[0]*q_s[3]);
- uCanonical[1] = 2 * (-q[2]*q_s[0] + q[3]*q_s[1] + q[0]*q_s[2] - q[1]*q_s[3]);
- uCanonical[2] = 2 * ( q[1]*q_s[0] - q[0]*q_s[1] + q[3]*q_s[2] - q[2]*q_s[3]);
+ FieldVector<double,3> uCanonical = darbouxCanonical(q, q_s); // The Darboux vector
FieldVector<double,3> u;
u[0] = uCanonical*q.director(0);
@@ -180,9 +155,13 @@ namespace Dune
static FieldVector<T,3> darbouxCanonical(const Quaternion<T>& q, const FieldVector<T,4>& q_s)
{
FieldVector<double,3> uCanonical; // The Darboux vector
- uCanonical[0] = 2 * ( q[3]*q_s[0] + q[2]*q_s[1] - q[1]*q_s[2] - q[0]*q_s[3]);
- uCanonical[1] = 2 * (-q[2]*q_s[0] + q[3]*q_s[1] + q[0]*q_s[2] - q[1]*q_s[3]);
- uCanonical[2] = 2 * ( q[1]*q_s[0] - q[0]*q_s[1] + q[3]*q_s[2] - q[2]*q_s[3]);
+// uCanonical[0] = 2 * ( q[3]*q_s[0] + q[2]*q_s[1] - q[1]*q_s[2] - q[0]*q_s[3]);
+// uCanonical[1] = 2 * (-q[2]*q_s[0] + q[3]*q_s[1] + q[0]*q_s[2] - q[1]*q_s[3]);
+// uCanonical[2] = 2 * ( q[1]*q_s[0] - q[0]*q_s[1] + q[3]*q_s[2] - q[2]*q_s[3]);
+
+ uCanonical[0] = 2 * (q.B(0) * q_s);
+ uCanonical[1] = 2 * (q.B(1) * q_s);
+ uCanonical[2] = 2 * (q.B(2) * q_s);
return uCanonical;
}
--
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