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Re: [Phys-l] Phys-l Digest, Vol 36, Issue 1



If you change the initial conditions, you must get a different stable orbit,
I think. There is no reason why it should decay back to the original initial
conditions before you perturbed it. It seems to me you are solving two
different problems. Regards,

Alfredo Louro

On Jan 1, 2008 10:00 AM, <phys-l-request@carnot.physics.buffalo.edu> wrote:

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Today's Topics:

1. Re: Simulating a disturbance of a stable planetary system.
(LaMontagne, Bob)
2. Re: Simulating a disturbance of a stable planetary system.
(John Mallinckrodt)
3. Re: Simulating a disturbance of a stable planetary system.
(Ludwik Kowalski)


----------------------------------------------------------------------

Message: 1
Date: Mon, 31 Dec 2007 12:39:58 -0500
From: "LaMontagne, Bob" <RLAMONT@providence.edu>
Subject: Re: [Phys-l] Simulating a disturbance of a stable planetary
system.
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Message-ID:
<16D2F020BC8FA2419680166FB97CF7AE3F7438@post1.providence.col>
Content-Type: text/plain; charset="iso-8859-1"

Ludwik,

You seem to be repeating the same thing over and over expecting hoping to
get different results.

Personally, I don't trust Interactive Physics - I prefer to program a
problem in Fortran or C. However, try using the random number generator in
I.P. to produce a series of small disturbances at random times and random
directions. A single disturbance has to change the orbit. Real orbits are
subject to both random and periodic disturbances.

Bob at PC

________________________________

From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Ludwik
Kowalski
Sent: Sun 12/30/2007 9:45 PM
To: Forum for Physics Educators
Subject: [Phys-l] Simulating a disturbance of a stable planetary system.



On Dec 30, 2007, at 7:16 PM, John Mallinckrodt wrote:

. . . An IP simulation will easily demonstrate this fact in a
minute or two and it will not be a computational artifact. . . .

That issue emerged from my failure to demonstrate stability of a simple
two body system (a single planet revolving the sun along a circular
trajectory). We expect such system to be stable (persistent). Using the
I.P. (Interactive Physics) I simulated the system and a short
disturbance. Someone wrote that stability means ability to recover
after a disturbance. In my simulation the new orbit (after the
disturbance) was significantly different from the orbit before the
disturbance. The period of revolution of the new (elliptical) orbit
turned out to be longer that period of revolution of the initial
(circular) orbit. In other words, the disturbance I applied was not
self-correcting.

The idea was to show that a disturbance applied to a two-body system is
self-correcting while the same disturbance applied to the three-body
system is not self-correcting. How to implement an I.P. disturbance
whose consequences disappear after the disturbance is over? I changed
the subject line of the thread because this question has nearly nothing
to do with what has been discussed earlier today.
P.S. To trust results of an experiment one often tests instruments by
performing control experiments. The two-body simulation was to be a
control experiment before the three-body simulation. But I was stuck,
as described in a message posted two days ago.
________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/<http://csam.montclair.edu/%7Ekowalski/cf/>
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l



------------------------------

Message: 2
Date: Mon, 31 Dec 2007 10:04:45 -0800
From: John Mallinckrodt <ajm@csupomona.edu>
Subject: Re: [Phys-l] Simulating a disturbance of a stable planetary
system.
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Message-ID: <CFFC462F-F24A-4E9D-A6CC-0C859665C0AE@csupomona.edu>
Content-Type: text/plain; charset=US-ASCII; delsp=yes;
format=flowed

Because every instant of time is exactly the same as the initial
instant of time in terms of the dynamics of this system. There is no
need to go to any lengths to apply a perturbation "at some later
time" or "periodically" or "for a while" or anything else. Simply
change any ONE of the 12 initial conditions (i.e., the 2-d position
and velocity components of the three particles) by a miniscule
amount, push the start button, and watch the ensuing chaos!

John Mallinckrodt
Cal Poly Pomona

On Dec 31, 2007, at 9:39 AM, LaMontagne, Bob wrote:

Ludwik,

You seem to be repeating the same thing over and over expecting
hoping to get different results.

Personally, I don't trust Interactive Physics - I prefer to program
a problem in Fortran or C. However, try using the random number
generator in I.P. to produce a series of small disturbances at
random times and random directions. A single disturbance has to
change the orbit. Real orbits are subject to both random and
periodic disturbances.

Bob at PC

________________________________

From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Ludwik
Kowalski
Sent: Sun 12/30/2007 9:45 PM
To: Forum for Physics Educators
Subject: [Phys-l] Simulating a disturbance of a stable planetary
system.



On Dec 30, 2007, at 7:16 PM, John Mallinckrodt wrote:

. . . An IP simulation will easily demonstrate this fact in a
minute or two and it will not be a computational artifact. . . .

That issue emerged from my failure to demonstrate stability of a
simple
two body system (a single planet revolving the sun along a circular
trajectory). We expect such system to be stable (persistent). Using
the
I.P. (Interactive Physics) I simulated the system and a short
disturbance. Someone wrote that stability means ability to recover
after a disturbance. In my simulation the new orbit (after the
disturbance) was significantly different from the orbit before the
disturbance. The period of revolution of the new (elliptical) orbit
turned out to be longer that period of revolution of the initial
(circular) orbit. In other words, the disturbance I applied was not
self-correcting.

The idea was to show that a disturbance applied to a two-body
system is
self-correcting while the same disturbance applied to the three-body
system is not self-correcting. How to implement an I.P. disturbance
whose consequences disappear after the disturbance is over? I changed
the subject line of the thread because this question has nearly
nothing
to do with what has been discussed earlier today.
P.S. To trust results of an experiment one often tests instruments by
performing control experiments. The two-body simulation was to be a
control experiment before the three-body simulation. But I was stuck,
as described in a message posted two days ago.
________________________________
Ludwik Kowalski, a retired physicist
5 Horizon Road, apt. 2702, Fort Lee, NJ, 07024, USA
Also an amateur journalist at http://csam.montclair.edu/~kowalski/cf/<http://csam.montclair.edu/%7Ekowalski/cf/>
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


<mime-attachment.txt>

A. JOHN MALLINCKRODT
Professor of Physics, Cal Poly Pomona
http://www.csupomona.edu/~ajm <http://www.csupomona.edu/%7Eajm>
Acting Editor, AMERICAN JOURNAL of PHYSICS
http://www.kzoo.edu/ajp

Professional/Personal email: ajm@csupomona.edu
Journal-related email: ajp@csupomona.edu
Phone: 909-869-4054
FAX: 909-869-5090

Physics Department
Building 8, Room 223
Cal Poly Pomona
3801 W. Temple Ave.
Pomona, CA 91768-4031




------------------------------

Message: 3
Date: Mon, 31 Dec 2007 16:16:02 -0500
From: Ludwik Kowalski <kowalskil@mail.montclair.edu>
Subject: Re: [Phys-l] Simulating a disturbance of a stable planetary
system.
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Message-ID: <b229926577eae589310aea920c161398@mail.montclair.edu>
Content-Type: text/plain; charset=US-ASCII; format=flowed

On Dec 31, 2007, at 1:04 PM, John Mallinckrodt wrote:

Because every instant of time is exactly the same as the initial
instant of time in terms of the dynamics of this system. There is no
need to go to any lengths to apply a perturbation "at some later
time" or "periodically" or "for a while" or anything else. Simply
change any ONE of the 12 initial conditions (i.e., the 2-d position
and velocity components of the three particles) by a miniscule
amount, push the start button, and watch the ensuing chaos!

1) That is true, except that the chaos is perfectly reproducible from
run to run, unless one of the initial conditions was changed before
each run. There is nothing unexpected in this.

2) What I would like to do, but do not know how, is the following:

a) Watch the undisturbed initial trajectory for a while to show that
cycles are identical.
b) Disturb the system, during the same run, and observe the consequence.

The expectation is that for a two-body system (planet of mass m and the
star of mass M>>m) the cycles after the disturbance will eventually
become identical to cycles before the disturbance, for example, in term
of periods of repetition. (That would by like disturbing a vertical
harmonic oscillator by changing g. Increase g and T becomes shorter,
restore the original g and the original T will restored, after some
time). For a three body system, such as three stars of equal mass, the
undisturbed trajectory is also cyclic. But effect of the disturbance is
expected to be dramatically different, as it is clear to me now.

I would like to be able to perform (a) and (b) using exactly the same
disturbance. I tried this with one kind of disturbance and it did not
work very well. However, one thing became clear; for the two-body
system the motion after the disturbance was still cyclic (an elliptical
orbit instead of the original circular orbit, as expected). For the
three-body system, on the other hand, the motion after the disturbance
became dramatically non-cyclic. It did behave as described by JohnD
yesterday. That is the best I could do so far. I cannot imagine a
single-parameter disturbance, for a two-body system, after which the
original circular motion is restored.

Why am I repeating myself? To be sure that nuances are either clear or
nonsensical. If stability is defined as resistance to changes resulting
from disturbances, then I failed to demonstrate stability of the
two-body system. What I was able to do, by using the I.P., was to show
that the cyclic nature of motion of two-body system was not destroyed
by the disturbance while the cyclic nature was destroyed by exactly the
same disturbance applied to a three-body system. That would be OK if
stability was defined in terms non-chaotic versus chaotic consequences.
But this is not OK when stability is defined in terms of absence of
permanent consequences of a disturbance.

What is the acceptable definition of stability for a system composed of
two or three particles interacting via central forces?







------------------------------

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


End of Phys-l Digest, Vol 36, Issue 1
*************************************