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Re: Lagranian Method Revisited

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On January 31, 2016, 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>

> you are not completely wrong and I was not completely right.

No, Jan, you are still wrong since you have been an arm-chair amateur physicist.  Koobee Wublee, on the other hand, had personally derived the field equations.  Koobee Wublee understands it is absolutely impossible to write down the set of field equations in a coordinate system other than the polar coordinate system.  If you want, Koobee Wublee can write down the null Einstein tensor for you to verify that the following solution, not the only ones, satisfy as solutions.  <shrug>

**  dS^2 = c^2 (1 + K / R) dt^2 - dr^2 (dR/dr)^2 / (1 + K / R) - R^2 dO^2

Where

**  dO^2 = cos^2(Latitude) dLongitude^2 + dLatitude^2
**  K = integration constant
**  R = any function of r 

> On certain issues we can meet in the middle (details coming up soon).

This is not a political compromise but a scientific debate.  There can only be right or wrong.  Koobee Wublee is not willing to meet you in the middle.  <shrug>

> But the final conclusions remain unchanged: Schwarzschild's solution
> as derived in his paper is the same solution as the one from modern
> textbooks.

No, this is not the case.  After Nordstrom has introduced the null Ricci tensor as the more general form of the Laplace equation, Schwarzschild had already solved it well before 1915, and the solution is exactly what the Schwarzschild metric is.  <shrug>

However, Hilbert had derived the Einstein tensor with this added trace term.  Schwarzschild needed to eliminate this trace term in which he did not know that the null Einstein tensor is the same as the null Ricci tensor.  So, he needed to transform the polar coordinate system into one that yields a metric with the determinant of -1 to eliminate the trace term and then transform it back to the polar coordinate system.  Schwarzschild unknowingly to himself has presented an infinite such type of solutions to the field equations.  Unfortunately, this brilliant man died with a few months of deriving the original metric.  <shrug>

> In other words the claim of Schwarzschild's paper containing a different
> solution (without a black hole) is _false_.

You will start to understand how right Koobee Wublee has been if you actually derived the field equations.  There is no other way.  <shrug>

> The delicacy I mentioned above also includes the standard thorn:
> extending a tensor field over a (removable) singularity.

Don't worry about the singularity.  Just solve the field equations.  <shrug>

> This is actually not always what it seems. Again, final
> conclusions remain unchanged.

Again, you need to experience how the field equations are derived and solved.  Then, show Koobee Wublee how you can achieve so without using a set of coordinate system.  This is not a delicate matter but cut and dry one.  <shrug>

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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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