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Re: Lagranian Method Revisited

Newsgroups sci.physics.relativity
Date 2016-01-27 13:33 -0800
References (2 earlier) <75fd0393-a156-4a6c-baee-196aae4ecbd9@googlegroups.com> <836942bc-ee40-4819-945c-e7393ad79101@googlegroups.com> <43869d3f-8262-4973-b07b-bb693129e684@googlegroups.com> <53ae9124-a95c-42d3-97e7-fe69c9cbd876@googlegroups.com> <2e7282bb-7aaa-4a23-9d76-fab600a59124@googlegroups.com>
Message-ID <d361c92b-e565-452c-ac70-e516019ef611@googlegroups.com> (permalink)
Subject Re: Lagranian Method Revisited
From JanPB <filmart@gmail.com>

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On Wednesday, January 27, 2016 at 10:27:25 AM UTC-8, al...@interia.pl wrote:
> W dniu środa, 27 stycznia 2016 08:29:24 UTC+1 użytkownik JanPB napisał:
> > On Tuesday, January 26, 2016 at 10:37:30 PM UTC-8, Koobee Wublee wrote:
> > > On Tuesday, January 26, 2016 at 12:36:35 AM UTC-8, JanPB wrote:
> > > > Koobee Wublee wrote:
> > > 
> > > > > The Euler-Lagrange equations are pretty much what govern the
> > > > > physical laws discovered by the self-claimed scientists.  The
> > > > > Lagrangian method (to derive the special equations) was
> > > > > discovered during Euler's time that was slightly before Newton.
> > > > > <shrug>
> > > >
> > > > > It starts with the following action as an integral of a
> > > > > Lagrangian (density to this action) with respect to instances
> > > > > (time).  <shrug>
> > > >
> > > > > **  A = Integral(T1, T2)[L dt]
> > > >
> > > > > Where
> > > >
> > > > > **  A = action accumulated from T1 to T2
> > > > > **  T1 = starting instance
> > > > > **  T2 = ending instance
> > > > > **  L = Lagrangian
> > > > > **  dt = discrete instance
> > > >
> > > > > For a special path, s, there exists a stationary condition to
> > > > > this action from T1 to T2 along this path.  So,
> > > >
> > > > > **  dA/ds = 0, definition of stationary action (min, max, saddle)
> > > >
> > > > > Or
> > > >
> > > > > **  Integral(T1, T2)[@L/@s dt] = 0
> > > >
> > > > > Where
> > > >
> > > > > **  @ = partial derivative operator
> > > >
> > > > > Now, you can choose to describe L in an observer's coordinate
> > > > >  system, [q], instead of invariant geometry, s.  If L is also a
> > > > > function of (ds/dt), the above can be rewritten as follows.
> > > > > <shrug>
> > > >
> > > > > **  Integral(T1, T2)[(@L/@s+ @L/@(ds/dt)) dt] = 0
> > > >
> > > > > Applying integration by parts, we have
> > > >
> > > > > **  @L/@(ds/dt)[T1, T2] +
> > > > >      Integral(T1, T2)[(@L/@s - d(@L/@(ds/dt))/dt) dt] = 0
> > > >
> > > > > The fixed points at T1 and T2 are just nonsense.  In reality, the
> > > > > mathematics says when (@L/@(ds/dt) at T1) = (@L/@(ds/dt) at T2),
> > > > > the above equation simplify into the equation below.  <shrug>
> > > >
> > > > > **  Integral(T1, T2)[(@L/@s - d(@L/@(ds/dt))/dt) dt] = 0
> > > >
> > > > > Where
> > > >
> > > > > **  @L/@(ds/dt)[T1, T2] = 0
> > > >
> > > > > Thus, the Euler-Lagrange equation can be derived as follows where
> > > > > it is true between T1 and T2 that the specific condition
> > > > > described above must be met.  It is not the fixed end points as
> > > > > the self-styled physicists have proclaimed.  <shrug>
> > > >
> > > > > **  @L/@s - d(@L/@(ds/dt))/dt = 0
> > > >
> > > > > Where
> > > >
> > > > > **  @L/@(ds/dt) at T1 = @L/@(ds/dt) at T2
> > > >
> > > > > So, when dealing with Mercury's perihelion advance, the
> > > > > Euler-Lagrange equation cannot possibly apply since with
> > > > > advancing perihelion, there is no way to establish the condition
> > > > > required of the Euler-Lagrange equation.  The whole fixed,
> > > > > coherent derivation of Mercury's perihelion advance is just a
> > > > > SCAM!  <shrug>
> > > 
> > > > No. It's the LSD version of it :-)
> > > 
> > > This is a ridiculous comment from an imbecile who knows no math about differential geometry but myths.  It is the same imbecile who raises objection when Koobee Wublee declared to use the polar coordinate system to describe a geometry.  What an imbecile whether on LSD or not!  <shrug>
> > 
> > You can use polar coordinates but they are not the whole story. Before solving
> > Einstein's equation one makes more coordinate changes to make the metric diagonal.
> > (The Einstein equation itself does not necessarily guarantee the diagonal form.)
> > 
> > It is this extra coordinate change that introduces certain new artifacts:
> > 
> > 1. a radial coordinate shift so that Schwarzschild's "r=0' no longer refers to the origin
> > but is a locus of points forming a sphere, see https://drive.google.com/open?id=0B2N1X7SgQnLRV1otWnE2T2F6aEk 
> 
> Another stupid nonsense...
> 
> a transform type of;
> r = r - a, is just a spimple translation alnog r in the polar coord...
> 
> therefore the so-called standard Schwarzchild's solution
> is just a translated version of the oryginal solution,
> where the r parameter is limited: r > rs.

The extra coordinate change I'm talking about is not just a shift in r.
It also involves a logarithmic-like transformation of the time coordinate
with the logarithm blowing up at the horizon (that's why the coordinate
singularity ends up there).

> the region r < 2m, simply doesnt exists in the solution,
> and the point r = 2m is just the place of the mass m,
> which is in standard polar cood. for r = 0.

False.

--
Jan

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Thread

Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-25 00:27 -0800
  Re: Lagranian Method Revisited Gertrude Kräuter <gertk@bundesadler.org> - 2016-01-25 16:59 +0000
    Re: Lagranian Method Revisited Dirk Van de moortel <dirkvandemoortel@hotspam.not> - 2016-01-25 23:03 +0100
      Re: Lagranian Method Revisited Odd Bodkin <bodkinodd@gmail.com> - 2016-01-25 16:44 -0600
      Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-25 17:24 -0800
  Re: Lagranian Method Revisited alsor@interia.pl - 2016-01-25 09:05 -0800
  Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-25 21:44 -0800
    Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-25 22:10 -0800
      Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-26 00:36 -0800
        Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-26 22:37 -0800
          Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-26 23:29 -0800
            Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-26 23:57 -0800
              Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-27 01:55 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-27 09:50 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-27 13:30 -0800
                Re: Lagranian Method Revisited Juan Sebastián <jseb@montserrat.info> - 2016-01-27 22:06 +0000
                Re: Lagranian Method Revisited Juan Sebastián <jseb@montserrat.info> - 2016-01-27 22:16 +0000
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-27 23:17 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-27 23:49 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-28 13:56 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-28 17:45 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-29 13:19 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-29 14:54 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-29 15:32 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-29 15:59 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-29 17:57 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-29 22:24 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-31 13:38 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-01-31 21:39 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-02-01 09:01 -0800
                Re: Lagranian Method Revisited shan <shan@enterapps.org> - 2016-02-01 18:46 +0000
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-01 11:27 -0800
                Re: Lagranian Method Revisited dancouriann@gmail.com - 2016-01-30 09:41 -0800
                Re: Lagranian Method Revisited Polikwaptiwa <polikw@polikwamail.org> - 2016-01-30 17:49 +0000
                Re: Lagranian Method Revisited David Fuller <fuller.david@hotmail.com> - 2016-02-09 15:28 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-02-09 15:52 -0800
                Re: Lagranian Method Revisited Tom Roberts <tjroberts137@sbcglobal.net> - 2016-01-29 12:46 -0600
                Re: Lagranian Method Revisited Tom Roberts <tjroberts137@sbcglobal.net> - 2016-01-29 12:56 -0600
                Re: Lagranian Method Revisited Juan Sebastián <jseb@montserrat.info> - 2016-01-29 19:02 +0000
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-29 11:08 -0800
                Re: Lagranian Method Revisited Juan Sebastián <jseb@montserrat.info> - 2016-01-29 18:58 +0000
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-29 11:17 -0800
            Re: Lagranian Method Revisited alsor@interia.pl - 2016-01-27 10:27 -0800
              Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-27 13:33 -0800
                Re: Lagranian Method Revisited alsor@interia.pl - 2016-01-31 15:16 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-31 15:29 -0800
                Re: Lagranian Method Revisited alsor@interia.pl - 2016-01-31 16:41 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-01-31 18:42 -0800
                Re: Lagranian Method Revisited alsor@interia.pl - 2016-02-03 10:31 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-08 23:20 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-02-09 11:20 -0800
                Re: Lagranian Method Revisited alsor@interia.pl - 2016-02-09 16:02 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-02-09 16:21 -0800
                Re: Lagranian Method Revisited alsor@interia.pl - 2016-02-10 10:18 -0800
                Re: Lagranian Method Revisited oriel36 <kelleher.gerald@gmail.com> - 2016-02-10 10:32 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-02-10 22:28 -0800
                Re: Lagranian Method Revisited alsor@interia.pl - 2016-02-11 09:39 -0800
                Re: Lagranian Method Revisited oriel36 <kelleher.gerald@gmail.com> - 2016-02-11 09:45 -0800
                Re: Lagranian Method Revisited alsor@interia.pl - 2016-02-12 11:36 -0800
                Re: Lagranian Method Revisited oriel36 <kelleher.gerald@gmail.com> - 2016-02-14 00:47 -0800
                Re: Lagranian Method Revisited Odd Bodkin <bodkinodd@gmail.com> - 2016-02-14 15:18 -0600
                Re: Lagranian Method Revisited Céline Desirée Hedwig <celinedh@bernhardine.org> - 2016-02-14 22:19 +0000
                Re: Lagranian Method Revisited alsor@interia.pl - 2016-02-14 14:37 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-02-23 17:06 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-01 12:54 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-03-01 13:00 -0800
                Re: Lagranian Method Revisited Koobee Wublee <koobee.wublee@gmail.com> - 2016-03-01 17:57 -0800
                Re: Lagranian Method Revisited JanPB <filmart@gmail.com> - 2016-03-01 19:03 -0800
  Re: Lagranian Method Revisited David Waite <waitedavid1618@yahoo.com> - 2016-01-27 02:03 -0800

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