this is for holding javascript data
Jacob Stevenson edited Trajectory spawning.tex
about 9 years ago
Commit id: 12c07d02d8624e729704d12f4f0838f7887bb0d9
deletions | additions
diff --git a/Trajectory spawning.tex b/Trajectory spawning.tex
index b3637be..13b371a 100644
--- a/Trajectory spawning.tex
+++ b/Trajectory spawning.tex
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note:
At first I had the projection part, that includes the term $\vec{n}(x(0))$ as part of the factor node. It seemed logical because it is evaluated at the spawning surface (which is the factor). But I think computationally it will be simpler this way because the messages that are passed are simply numbers and all the computation involving the potential and high dimensional vectors can be done at runtime during the trajectory.
note on units: The end result should not depend on energy, so all units with energy should cancel. This means that $\left| \vec{n}(x(0)) \cdot \vec{\nabla} U(x(0)) \right|$ should actually be $\left| \vec{n}(x(0)) \cdot \vec{\nabla} U(x(0)) \right| / \left| \vec{\nabla} U(x(0)) \right| $.
Additionally $Tr(H) dt$ must be unitless. That means that either $dt$ has units length$^2$ / energy, or there is a term missing.