Re: Wilsonian EM Control Frames.

On Jun 2, 3:34 am, HW@....(Henri Wilson) wrote:
On Fri, 01 Jun 2007 17:30:16 -0700, Jerry <Cephalobus_alie...@xxxxxxxxxxx>
wrote:

Henri, according to your notion, the predicted bending of light
around the Sun, visible during a solar eclipse, would be several
orders of magnitude greater than what is observed AND IN THE
OPPOSITE DIRECTION TO WHAT IS OBSERVED.

Show me the maths.

For a completely accurate solution, I would need to perform a
numerical solution to the differential equations describing
the change in a "packet" of light's velocity (i.e. acceleration),
as a function of its position and direction in the solar wind.

AN ESSENTIAL PIECE OF INFORMATION IS MISSING from your description
of your theory, namely, what is the coupling constant between
a light beam and the solar wind, i.e. what is the extinction
distance, and how does it vary as the density of the Solar Wind?
To a first approximation, we can assume the speed of the wind
to be more or less constant whether reasonably close to the Sun
or reasonably distant from the Sun; what varies strongly is the
density of particles. If we want better figures, we need better
data.

I would plug the differential equations into a C++ function that
matches the following typedef pattern (courtesy of my brother):

// function pointer typedef defining the system of differential
// equations
typedef void (*diffEQ)(double &, // time
double [], // input variables
double [], // output variables
void * // parameters
);

Input variables would be t, x, y, z, vx, vy, vz, the output
variables would be vx, vy, vz, ax, ay, az, and the void pointer
cab be used to point to a variable or "struct" of relevant
input parameters required for the specific computation.

----- EXAMPLE -----
My brother was playing around with a celestial mechanics
program, and he wrote the following function following the
diffEQ typedef

#include <cmath>
// Equations of motion for a Keplerian orbit (pure elliptical)

// Let r represent the position vector of an orbiting body
// |r| represent its magnitude
// then r/|r| represents a unit vector in the direction of
// the orbiting body
// Let m represent the mass of the orbiting body
// M represent the mass of the central body
// r: represent the second derivative of the position vector

// F = -GmM/|r|^2 * r/|r|
// F/m = -GMr/|r|^3
// Let mu = GM.
// r: = -mu*r/|r|^3

void KeplerEquationsOfMotion(double &, double x[], double z[],
void * parms)
{
double r, r3;
double mu = *(double*)parms;

z[0] = x[3];
z[1] = x[4];
z[2] = x[5];

r = sqrt(x[0]*x[0] + x[1]*x[1] + x[2]*x[2]);
r3 = r*r*r;

z[3] = -mu*x[0]/r3;
z[4] = -mu*x[1]/r3;
z[5] = -mu*x[2]/r3;
}
----- END OF EXAMPLE -----

Once I have sufficient information to "fill in" the blanks and
write a function following the diffEQ typedef, I can use Runge-Kutta
integration to work out the path of an arbitrary packet of light
passing through the Solar System.

Again, courtesy of my brother, since I really don't do any
programming (I have a mental blank that prevents me from writing
decent code, although I can -use- code that others have written),
here is a Runge-Kutta routine. Note the diffEQ input parameter.
The History object would hold the complete (t,x,y,z) set the light
packets path through space, and is written to either use memory, or
to write out to disk, if memory is believed to be insuffient.

----- FIFTH ORDER RUNGE-KUTTA -----
// for NQ simultaneous first-order equations
void RungeKutta(double x[NQ], History &history, double t, double tf,
diffEQ diffeq, double h, double tl, void * parms,
double& h_min )
{
PositionCoordinates c;
double z[NQ];
double xt[NQ], te[NQ], f[ORDER+1][NQ] = {0};
double tt, tm, ht;
int n, k, k_1, l;
bool oneLastIteration = false;

history.clear();
addToHistory(t, x, history);
h_min = h;

do // repeat while (t < tf)
{
tt = t;
diffeq(t, x, z, parms);
for (n = 0; n < NQ; n++)
{
f[0][n] = z[n];
xt[n] = x[n];
}

do // repeat while (tm > tl)
{
for (k = 1; k <= ORDER; k++)
{
t = tt + A[k]*h;

for (n = 0; n < NQ; n++)
{
x[n] = xt[n]; k_1 = k - 1;
for (l = 0; l <= k_1; l++)
{
x[n] = x[n] + h*B[k][l]*f[l][n];
}
}

diffeq(t, x, z, parms);

for (n = 0; n < NQ; n++)
{
f[k][n] = z[n];
}
}

for (n = 0; n < NQ; n++)
{
te[n] = 0; x[n] = xt[n];
for (k = 0; k <= ORDER; k++)
{
x[n] += h*CH[k]*f[k][n];
te[n] += h*CT[k]*f[k][n];
}

te[n] = fabs(te[n]);
}

tm = 0.0;
for (n = 0; n < NQ; n++)
{
if (tm > te[n]) continue;
tm = te[n];
}

ht = h;
h = CHICKEN_FACTOR*h*pow(tl/tm, 0.2);

} while (tm > tl); // The step must be repeated with
// the new, reduced h

t = tt + ht;
// A successful step has been completed

if (h < 0)
{
c.t = t;
c.x = x[0]; c.y = x[1]; c.z = x[2];
// c.vx = x[3]; c.vy = x[4]; c.vz = x[5];
history.back() = c;
return; // the final step has been taken
}
else
{
addToHistory(t, x, history);
if (h < h_min) h_min = h;
}

if ( t > tf )
{
h = tf - t; // Ready for the final step.
// Stepsize h will be negative
oneLastIteration = true;
}
} while ( t < tf || oneLastIteration);
}
----- END FIFTH ORDER RUNGE-KUTTA -----

Since you HAVEN'T described your theory in sufficient detail
for a function to be written following the diffEQ typedef, an
order-of-magnitude estimate is all that is possible.

BZ has given you a completely satisfactory order-of-magnitude
estimate in his earlier post today. I don't need to repeat
what he wrote.

Jerry

Henri Wilson's Faked Diploma
http://mysite.verizon.net/cephalobus_alienus/henri_diploma.htm


Henri Wilson's Use of Deceptive Language or,
Would You Buy A Used Ballistic Theory From This Man?
http://mysite.verizon.net/cephalobus_alienus/henri_deception.htm


RT Aurigae versus Emission Theory or,
Henri Wilson's Faked Program Output
http://mysite.verizon.net/cephalobus_alienus/rt_aurigae.htm


Henri Wilson Attempts to Rewrite the Historical Record
http://mysite.verizon.net/cephalobus_alienus/henri_history.htm


.

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