Subject: Re: Problem: Gravity simulator
From: Marcus
Date: Wed, 18 Dec 1996 23:22:42 -0500
Wayne Schlitt wrote:
>
> In Mattias Bryntesson writes:
> >
> > I guess you have just discovered the slingshot effect, [ ... ]
> >
> > So if you think your results are unphysical, don't worry! It's
> > reality!
>
> No, the slingshot effect _requires_ at least 3 bodies to be involved.
> If there are only two bodies involved, the paths are always one of the
> conic sections.
>
> -wayne
>
> --
> Wayne Schlitt can not assert the truth of all statements in this
> article and still be consistent.
But conic sections also include hyperbolas and parabolas. If your
statement holds that only two bodies are required for conic section
paths, then the slingshot could result.
Marc
Subject: Re: Problem: Gravity simulator
From: Peter Teuben
Date: Wed, 18 Dec 1996 23:33:38 -0500
Marcus wrote:
>
> Wayne Schlitt wrote:
> >
> > In Mattias Bryntesson writes:
> > >
> > > I guess you have just discovered the slingshot effect, [ ... ]
> > >
> > > So if you think your results are unphysical, don't worry! It's
> > > reality!
> >
> > No, the slingshot effect _requires_ at least 3 bodies to be involved.
> > If there are only two bodies involved, the paths are always one of the
> > conic sections.
> >
> > -wayne
> >
> > --
> > Wayne Schlitt can not assert the truth of all statements in this
> > article and still be consistent.
>
> But conic sections also include hyperbolas and parabolas. If your
> statement holds that only two bodies are required for conic section
> paths, then the slingshot could result.
>
> Marc
I've been listening to this interesting thread for the past days.
What I think is meant here is that the parabolas and hyperbolas
are solutions of the two body problem (with 0 or positive energy),
however in those cases the incoming velocity equals the outgoing
velocity, and although the direction of the particle has changed, it is
not a slingshot where you've increased the velocity (if that is what
you mean by slingshot).
Indeed (as somebody already remarked) it takes 3 bodies (minimum) to
slingshot/eject a particle at high velocity (in fact, there are stars
found in the halo of our galaxy which appear to have been created
in a close encounter of 3 bodies (mostly a double star encountering
a single star). The "exchange" can be anything (remember, the 3 body
problem has chaotic properties): any of the 3 particles can be
ejected at high velocity.
There is a wonderful site where you can run these simulations yourself:
http://einstein.drexel.edu/~mcmillan/starlab_demo_2.html
- peter
--
Peter Teuben http://www.astro.umd.edu/~teuben
Astronomy Department mailto:teuben@astro.umd.edu
University of Maryland ftp://ftp.astro.umd.edu/pub/teuben
College Park, MD 20742 audio:301-405-1540
Subject: Re: numerical integration
From: j.groenenboom@mp.tudelft.nl (Jeroen Groenenboom)
Date: 19 Dec 1996 09:12:00 GMT
In article <596ru8$11n2@service.polymtl.ca>, charron@grbb.polymtl.ca (Guy Charron) writes:
> Salut everyone,
>
Salut to you too Guy,
> I have a problem I'm sure I am not the first one to encounter, so I would appreciate a little feedback on this. To solve a differential equation in an electromagnetic
> problem, I am using Green functions. The solution is known, but expressed in the form
> of a complicated multidimensional integral. I have to perform an integral from
> zero to infinity of a product of two bessel functions and a rational fonction. As the
> variable tend toward infinity, the integrand tend toward zero.
>
> For some values of parameters, the function may need to be integrated to around 10
> before the integral converges, some other cases require that it has to
> be integrated up until 100 000 or so. What would be the best way to minimise
> computation time in such a case.
>
> There is also the problem of how many points should be used to perform the
> integral. The main problem is that the integrand oscillate, and that there is
> a slight difference between the positive part and the negative part of the function
> that slowly add up to give me the result. What would be a good way to tackle this
> problem?
>
> Currently, I'm working with Matlab. I am using a Gauss rule, ( Can anyone point
> me some reference on this) where basically the algorithm chooses points and calculate
> a weigth for them so that the integral is exact for a polynom of order 2*n-1 if I
> use n points. To tackle both problem, I do the integral on 0 to 100, then on 100 to 200 etc, until the new contribution becomes sufficently small. I have to check the
> integrande before though, because in some cases, to evaluate it I multiply large number
> by small number, and the programm doesn't know what to do exactly with that ( but I
> am sure that the small number is way smaller than 1/(large number)).
>
> So basically, that is where I am. Any comments anyone?
Although I do not know the exact form of your integral, but maybe you could split
the integration in different parts. Integrate the contribution of a positive and
negative part together, since they tend to cancel. So, in that case you need to
determine the zeros of the bessel functions. Might be a better way to determine
convergence to infinity. You can determine the high zeros with an asymptotic
series expansion.
Good Luck
Jeroen
*************************************************
* Jeroen Groenenboom *
* Delft University of Technology *
* The Netherlands *
* *
* Faculty of Applied Earth Sciences *
* Section of Applied Geophysics *
* Centre of Technical Geoscience *
* DelFrac Consortium *
* E:J.Groenenboom@MP.TUDelft.nl *
* T:31-15-2786028 *
* F:31-15-2781189 *
* *
* "De Geest moet waaien", *
* Johnny "the selfkicker" van Doorn *
*************************************************
