From cc8699f9bbdd8b10043771cb0b01c197e3225a31 Mon Sep 17 00:00:00 2001
From: ralfulrich <ralf.ulrich@kit.edu>
Date: Fri, 11 Jun 2021 10:41:27 +0200
Subject: [PATCH] more docs
---
corsika/framework/geometry/LeapFrogTrajectory.hpp | 13 ++++++++++++-
1 file changed, 12 insertions(+), 1 deletion(-)
diff --git a/corsika/framework/geometry/LeapFrogTrajectory.hpp b/corsika/framework/geometry/LeapFrogTrajectory.hpp
index ec281e5f7..e1c2bff3b 100644
--- a/corsika/framework/geometry/LeapFrogTrajectory.hpp
+++ b/corsika/framework/geometry/LeapFrogTrajectory.hpp
@@ -19,7 +19,7 @@ namespace corsika {
/**
* The LeapFrogTrajectory stores information on one leap-frog step.
*
- * The leap-frog algorithm uses a half-step and is used in magnetic
+ * The leap-frog algorithm uses two half-steps and is used in magnetic
* field tracking. The LeapFrogTrajectory will solve the leap-frog
* algorithm equation for a given constant $k$ that has to be
* specified during construction (essentially fixing the magnetic
@@ -28,6 +28,17 @@ namespace corsika {
* direction as calculated by the algorithm for any steplength, or
* intermediate position.
*
+ * One complete leap-frog step is
+ * $
+ * \vec{x}(t_{i+0.5}) = \vec{x}(t_{i}) + \vec{v(t_{i})} * \Delta t / 2 \\
+ * \vec{v}(t_{i+1}) = \vec{v}(t_{i}) + \vec{v}(t_{i})\cross\vec{B}(x_{i}, t_{i}) *
+ *\Delta t \\
+ * \vec{x}(t_{i+1}) = \vec{x}(t_{i+0.5}) + \vec{v}(t_{i+1}) * \Delta t /2 \\
+ * $
+ *
+ * The volocity update has the characteristics $|\vec{v}(t_{i+1})|>1$, thus final
+ * velocities are renormalised. The full leap-frog steplength is thus
+ * $L = |\vec{v}(t_{i+1})| * \Delta t / 2 + |\vec{v}(t_{i+1})| *\Delta t / 2$
**/
class LeapFrogTrajectory : public BaseTrajectory {
--
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