Ah, the joys of math. So now I can ramble away with equations! (
Thanks to)
So, we can represent the symplectic part of the dynamics of an accelerator by a one turn map:
where
is the operator saying to take the Poisson bracket with its argument.
is the effective Hamiltonian and is a function of
and
. In the linear case,
is just a matrix
and if the Hamiltonian is
with
, then
where
is the symplectic inner product matrix and its multidimensional
extensions. Actually its kind of ugly. Ah well, I may or may not write more equations.
3 comments:
@#$$%@!??? - aka: I don't get it.
I never was very good at Math. I worked really hard on it in high school. School, private lessons, self-taught...
Now when I think of math I think of money. Ha - ha.
Yeah, a bunch of mumbo jumbo.
Funny, cause I'm the exact opposite. For all the math I've looked at, I seem to have a major block when it comes to money. Just doesn't compute.
I only like symplectic equations because it helps my little enzymes to conserve energy in a 160 nanosecond simulation. But sometimes, for reasons that I'm trying to track down now, the darn symplectic equation fails me!!!!! Whyyyyyy!
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