three-body problem

Started by John Larkin September 8, 2017
Apropos of nonlinear simulation, this is interesting:

https://en.wikipedia.org/wiki/Three-body_problem

The simplified case (point bodies in an ideal Newtonian universe) has
confounded mathematicians for centuries now. I was pleased to note the
the wiki article mentions the possibility of collisions, which make
things more interesting. They don't mention relativity, gravitional
waves, radiation pressure, or tidal effects.

If you include that stuff, even the two-body problem gets nasty.

LT Spice can have radically different runtimes and solutions if you
make tiny changes to circuit values or time steps or initial
conditions.


-- 

John Larkin         Highland Technology, Inc

lunatic fringe electronics 

On Fri, 08 Sep 2017 08:33:13 -0700, John Larkin
<jjlarkin@highlandtechnology.com> wrote:

>Apropos of nonlinear simulation, this is interesting: > >https://en.wikipedia.org/wiki/Three-body_problem > >The simplified case (point bodies in an ideal Newtonian universe) has >confounded mathematicians for centuries now. I was pleased to note the >the wiki article mentions the possibility of collisions, which make >things more interesting. They don't mention relativity, gravitional >waves, radiation pressure, or tidal effects. > >If you include that stuff, even the two-body problem gets nasty. > >LT Spice can have radically different runtimes and solutions if you >make tiny changes to circuit values or time steps or initial >conditions.
"radically different ... solutions"? Doesn't that make you suspicious/nervous? ...Jim Thompson -- | James E.Thompson | mens | | Analog Innovations | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | STV, Queen Creek, AZ 85142 Skype: skypeanalog | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | I'm looking for work... see my website. Thinking outside the box...producing elegant & economic solutions.
On 09/08/2017 11:33 AM, John Larkin wrote:
> Apropos of nonlinear simulation, this is interesting: > > https://en.wikipedia.org/wiki/Three-body_problem > > The simplified case (point bodies in an ideal Newtonian universe) has > confounded mathematicians for centuries now. I was pleased to note the > the wiki article mentions the possibility of collisions, which make > things more interesting. They don't mention relativity, gravitional > waves, radiation pressure, or tidal effects. > > If you include that stuff, even the two-body problem gets nasty.
Of course it's confounded mathematicians, they were looking for closed-form solutions but the overwhelming majority of real-world physics problems don't have them. You can't write an exact closed-form equation of how a nuclear weapon works either called "The Nuclear Bomb Equation" that gives an explicit answer in elementary functions for fireball diameter from first principles either. They seem to work OK though
> LT Spice can have radically different runtimes and solutions if you > make tiny changes to circuit values or time steps or initial > conditions.
Amazing but plz take a course in scientific computing/numerical methods prior to concluding that everything is a lie based on friggin' LTSpice behaving weird because you changed the timestep.
On 09/08/2017 12:36 PM, bitrex wrote:
> On 09/08/2017 11:33 AM, John Larkin wrote: >> Apropos of nonlinear simulation, this is interesting: >> >> https://en.wikipedia.org/wiki/Three-body_problem >> >> The simplified case (point bodies in an ideal Newtonian universe) has >> confounded mathematicians for centuries now. I was pleased to note the >> the wiki article mentions the possibility of collisions, which make >> things more interesting. They don't mention relativity, gravitional >> waves, radiation pressure, or tidal effects. >> >> If you include that stuff, even the two-body problem gets nasty. > > Of course it's confounded mathematicians, they were looking for > closed-form solutions but the overwhelming majority of real-world > physics problems don't have them.
Also even the general three-body problem isn't universally unboundedly chaotic; for any given phase-space volume it will have regions where the Hamiltonian is more sensitive to initial conditions and small perturbations from equilibrium, and others less so. <http://www.sciencemag.org/news/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem>
On Fri, 08 Sep 2017 08:52:35 -0700, Jim Thompson
<To-Email-Use-The-Envelope-Icon@On-My-Web-Site.com> wrote:

>On Fri, 08 Sep 2017 08:33:13 -0700, John Larkin ><jjlarkin@highlandtechnology.com> wrote: > >>Apropos of nonlinear simulation, this is interesting: >> >>https://en.wikipedia.org/wiki/Three-body_problem >> >>The simplified case (point bodies in an ideal Newtonian universe) has >>confounded mathematicians for centuries now. I was pleased to note the >>the wiki article mentions the possibility of collisions, which make >>things more interesting. They don't mention relativity, gravitional >>waves, radiation pressure, or tidal effects. >> >>If you include that stuff, even the two-body problem gets nasty. >> >>LT Spice can have radically different runtimes and solutions if you >>make tiny changes to circuit values or time steps or initial >>conditions. > >"radically different ... solutions"? Doesn't that make you >suspicious/nervous? > > ...Jim Thompson
No, I just fiddle until I see the solution that I want. -- John Larkin Highland Technology, Inc picosecond timing precision measurement jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
On Fri, 8 Sep 2017 12:36:01 -0400, bitrex
<bitrex@de.lete.earthlink.net> wrote:

>On 09/08/2017 11:33 AM, John Larkin wrote: >> Apropos of nonlinear simulation, this is interesting: >> >> https://en.wikipedia.org/wiki/Three-body_problem >> >> The simplified case (point bodies in an ideal Newtonian universe) has >> confounded mathematicians for centuries now. I was pleased to note the >> the wiki article mentions the possibility of collisions, which make >> things more interesting. They don't mention relativity, gravitional >> waves, radiation pressure, or tidal effects. >> >> If you include that stuff, even the two-body problem gets nasty. > >Of course it's confounded mathematicians, they were looking for >closed-form solutions but the overwhelming majority of real-world >physics problems don't have them.
Numerical solutions to the simplified 3-body probelm are just as intractable. The benign cases aren't very interesting.
> >You can't write an exact closed-form equation of how a nuclear weapon >works either called "The Nuclear Bomb Equation" that gives an explicit >answer in elementary functions for fireball diameter from first >principles either. They seem to work OK though > >> LT Spice can have radically different runtimes and solutions if you >> make tiny changes to circuit values or time steps or initial >> conditions. > >Amazing but plz take a course in scientific computing/numerical methods >prior to concluding that everything is a lie based on friggin' LTSpice >behaving weird because you changed the timestep. >
Did I say that everything is a lie? I don't remember doing that. -- John Larkin Highland Technology, Inc picosecond timing precision measurement jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
On 09/08/2017 11:52 AM, Jim Thompson wrote:
> On Fri, 08 Sep 2017 08:33:13 -0700, John Larkin > <jjlarkin@highlandtechnology.com> wrote: > >> Apropos of nonlinear simulation, this is interesting: >> >> https://en.wikipedia.org/wiki/Three-body_problem >> >> The simplified case (point bodies in an ideal Newtonian universe) has >> confounded mathematicians for centuries now. I was pleased to note the >> the wiki article mentions the possibility of collisions, which make >> things more interesting. They don't mention relativity, gravitional >> waves, radiation pressure, or tidal effects. >> >> If you include that stuff, even the two-body problem gets nasty. >> >> LT Spice can have radically different runtimes and solutions if you >> make tiny changes to circuit values or time steps or initial >> conditions. > > "radically different ... solutions"? Doesn't that make you > suspicious/nervous? > > ...Jim Thompson >
The whole world should make him nervous, then, because 100% deterministic physical systems only exist on the blackboards of mathematicians. And if LTSpice is giving radically different outcomes due to small changes in circuit values or timestep my money is that the circuit design itself has chaotic properties, not that there's anything intrinsically wrong with LTSpice. Or bumping up against roundoff/truncation error. <http://www.chaotic-circuits.com/8-simulating-chaus-circuit-with-ltspice/>
On 09/08/2017 12:58 PM, John Larkin wrote:
> On Fri, 8 Sep 2017 12:36:01 -0400, bitrex > <bitrex@de.lete.earthlink.net> wrote: > >> On 09/08/2017 11:33 AM, John Larkin wrote: >>> Apropos of nonlinear simulation, this is interesting: >>> >>> https://en.wikipedia.org/wiki/Three-body_problem >>> >>> The simplified case (point bodies in an ideal Newtonian universe) has >>> confounded mathematicians for centuries now. I was pleased to note the >>> the wiki article mentions the possibility of collisions, which make >>> things more interesting. They don't mention relativity, gravitional >>> waves, radiation pressure, or tidal effects. >>> >>> If you include that stuff, even the two-body problem gets nasty. >> >> Of course it's confounded mathematicians, they were looking for >> closed-form solutions but the overwhelming majority of real-world >> physics problems don't have them. > > Numerical solutions to the simplified 3-body probelm are just as > intractable. The benign cases aren't very interesting.
Nonsense, for any _specific_ set of initial conditions the three body problem is completely deterministic. You can write a computer program consisting of three idealized masses which are perfect spheres in empty space under the influence of gravity, set it up with some initial conditions, and the computer will predict the motion of three idealized masses which are perfect spheres in empty space under the influence of gravity perfectly down to the implied resolution of your numerical precision. What other kind of "numerical solution" are you looking for?
On Fri, 08 Sep 2017 09:55:41 -0700, John Larkin
<jjlarkin@highland_snip_technology.com> wrote:

>On Fri, 08 Sep 2017 08:52:35 -0700, Jim Thompson ><To-Email-Use-The-Envelope-Icon@On-My-Web-Site.com> wrote: > >>On Fri, 08 Sep 2017 08:33:13 -0700, John Larkin >><jjlarkin@highlandtechnology.com> wrote: >> >>>Apropos of nonlinear simulation, this is interesting: >>> >>>https://en.wikipedia.org/wiki/Three-body_problem >>> >>>The simplified case (point bodies in an ideal Newtonian universe) has >>>confounded mathematicians for centuries now. I was pleased to note the >>>the wiki article mentions the possibility of collisions, which make >>>things more interesting. They don't mention relativity, gravitional >>>waves, radiation pressure, or tidal effects. >>> >>>If you include that stuff, even the two-body problem gets nasty. >>> >>>LT Spice can have radically different runtimes and solutions if you >>>make tiny changes to circuit values or time steps or initial >>>conditions. >> >>"radically different ... solutions"? Doesn't that make you >>suspicious/nervous? >> >> ...Jim Thompson > >No, I just fiddle until I see the solution that I want.
Oh! I see! Optimization >:-} ...Jim Thompson -- | James E.Thompson | mens | | Analog Innovations | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | STV, Queen Creek, AZ 85142 Skype: skypeanalog | | | Voice:(480)460-2350 Fax: Available upon request | Brass Rat | | E-mail Icon at http://www.analog-innovations.com | 1962 | I'm looking for work... see my website. Thinking outside the box...producing elegant & economic solutions.
On Fri, 8 Sep 2017 13:07:59 -0400, bitrex
<bitrex@de.lete.earthlink.net> wrote:

>On 09/08/2017 12:58 PM, John Larkin wrote: >> On Fri, 8 Sep 2017 12:36:01 -0400, bitrex >> <bitrex@de.lete.earthlink.net> wrote: >> >>> On 09/08/2017 11:33 AM, John Larkin wrote: >>>> Apropos of nonlinear simulation, this is interesting: >>>> >>>> https://en.wikipedia.org/wiki/Three-body_problem >>>> >>>> The simplified case (point bodies in an ideal Newtonian universe) has >>>> confounded mathematicians for centuries now. I was pleased to note the >>>> the wiki article mentions the possibility of collisions, which make >>>> things more interesting. They don't mention relativity, gravitional >>>> waves, radiation pressure, or tidal effects. >>>> >>>> If you include that stuff, even the two-body problem gets nasty. >>> >>> Of course it's confounded mathematicians, they were looking for >>> closed-form solutions but the overwhelming majority of real-world >>> physics problems don't have them. >> >> Numerical solutions to the simplified 3-body probelm are just as >> intractable. The benign cases aren't very interesting. > >Nonsense, for any _specific_ set of initial conditions the three body >problem is completely deterministic.
Actually, in a quantum world, it's not. Or in a real world, with real objects in a real universe. You can write a computer program
>consisting of three idealized masses which are perfect spheres in empty >space under the influence of gravity, set it up with some initial >conditions, and the computer will predict the motion of three idealized >masses which are perfect spheres in empty space under the influence of >gravity perfectly down to the implied resolution of your numerical >precision.
Change the mass of one of those ideal spheres by 1 LSB of your float, sim a while, and one of those expensive perfect spheres might get flung out of the system. Or not. Before IEEE floats, different computers would round slightly differently, or compute transcendentals a tiny bit differently, so nonlinear sims like weather would produce wildly different results if run on different machines. Now, everyone has agreed on a uniformly incorrect result.
> >What other kind of "numerical solution" are you looking for?
As an engineer, I care if a numerical solution is predictive of the future state of the system to some useful sort of accuracy... like maybe, let's get the sign right. Some systems can be simulated to parts per million over any time span. Chaotic systems can't. -- John Larkin Highland Technology, Inc picosecond timing precision measurement jlarkin att highlandtechnology dott com http://www.highlandtechnology.com