Kocaeli is a new university, is ranked 1841 in the world by webometrics and has over 52,000 students, founded in 1977. It is mainly technical but also has a fine arts faculty. UFT88 is a famous paper in scientific circles, and to the very large folloing of ECE theory, refutes the Einsteinian general relativity through consideration of torsion. It has been developed into UFT313, and should be read with UFT99 and UFT109, together with UFT354. It is the paper that epitomizes van der Merwe’s post Einsteinian paradigm shift, now widely accepted as mainstream physics. The Einstein theory has been replaced by ECE2, of which there are currently fifty six papers and books, all read around the world every day.

## Discussion of 371(4): Scheme of Computation for the 3D Orbit

OK many thanks, this Runge Kutta method is a very powerful Maxima algorithm, and can be applied now to give a large amount of new results for many problems of ECE2 theory. I will write out the equations of most interest. For spherical orbits it will be very interesting to plot the true orbit r = alpha / (1 + epsilon cos beta) obtained from the Hooke Newton inverse square law using spherical polar coordinates. No modelling assumption is made other than the usual inverse square law.

To: EMyrone@aol.com

Sent: 27/02/2017 17:38:36 GMT Standard Time

Subj: Re: 371(4): Scheme of Computation for the 3D OrbitBasically thre are two methods of solving the central motion in a spherical polar coordinate system: Either the full set of Lagrange equations without constants of motion or by predefining L and L_Z and solving (19-22). I will try the latter. These equations are only of first order for beta, theta, phi so they reduce the number of Hamilton equations used for the Runge-Kutta solution method.

Horst

Am 26.02.2017 um 14:19 schrieb EMyrone:

This note gives the scheme of computation that gives all information about a spherical orbit governed by an inverse square force law of attraction. Maxima can now be used to compute any type of information needed, notably the orbits r(beta), r(theta) and r(phi). Some of the analytical results from UFT270 to UFT276 on three dimensional orbits are reviewed. The planar orbit is recovered in the limit theta goes to pi / 2, theta dot goes to zero. The planar orbit is given by Eq. (33), and does not precess for an inverse square law as is well known. In three dimensions however it precesses in various ways. There is a typo in Eq. (31), which should read theta goes to pi / 2. We are now ready to use Maxima for the lagrangian in ECE2 relativity, both for planar and three dimensional orbits.

## Daily Report Sunday 26/2/17

The equivalent of 40,940 printed pages was downloaded (149.261 megabytes) from 1,676 memory files downloaded and 387 distinct visits each averaging 4.5 memory pages and 5 minutes, top referrals 2,213,162, printed pages to hits ratio of 24.43, main spiders Google, MSN and Yahoo. Collected ECE2 1191, Top ten 1120, Collected Evans / Morris 858(est), Collected scientometrics 540, F3(Sp) 371, Barddoniaeth 289, Principles of ECE 137, Eckardt / Lindstrom 131, Autrobiography volumes one and two 127, Collected Proofs 93, Engineering Model 83, Evans Equations 71, UFT88 70, PECE 50, CEFE 45, ECE2 43, UFT311 43, Self charging inverter 35, Llais 25, UFT321 25, PLENR 11(est), UFT313 21, UFT314 19, UFT315 17, UFT316 17, UFT317 28, UFT318 17, UFT319 20, UFT320 18, UFT322 22, UFT323 16, UFT324 18, UFT325 26, UFT326 18, UFT327 16, UFT328 27, UFT329 21, UFT330 15, UFT331 20, UFT332 14, UFT333 20, UFT334 15, UFT335 19, UFT336 14, UFT337 16, UFT338 13, UFT339 13, UFT340 13, UFT341 23, UFT342 11, UFT343 17, UFT344 22, UFT345 15, UFT346 15, UFT347 21, UFT348 15, UFT349 19, UFT351 20, UFT352 28, UFT353 26, UFT354 31, UFT355 17, UFT356 26, UFT357 27, UFT358 21, UFT359 20, UFT360 19, UFT361 12, UFT362 23, UFT363 22, UFT364 24, UFT365 16, UFT366 45, UFT367 42, UFT368 44, UFT369 46, UFT370 30 to date in February 2017. State University of New York Buffalo UFT213; University of Notre Dame UFT142; Ecole Superieure of Industrial Physics and Chemistry of the City of Paris (ESPCI) UFT330; Isfahan University of Technology Iran Essay 24; Bahria University Karachi Pakistan UFT41. Intense interest all sectors, updated usage file attached for February 2017.

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## ES and LENR Power Stations in Wales

These should come online as rapidly as possible. The ECE theory needed to understand ES power stations is available (UFT311), and the patented Osamu Ide circuit has been replicated by Horst Eckardt et al in UFT364. The Assembly should push ahead with raising the funds to develop all kinds of power devices based on ES, which has no moving parts and works on all scales, from microchips to major power stations. The ECE theory has been an international team effort, and was started here in Mawr. If a coal /oil cabal exists, it will shortly become extinct. The circuit can be demonstrated to the Assembly at any time.

## Daily Report Saturday 25/2/17

The equivalent of 68,953 printed pages was downloaded (251.401 megabytes) from 2158 downloaded memory files and 398 distinct visits each averaging 4.0 memory pages and 6 minutes, printed pages to hits ratio of 31.95, top ten referrals total 2,212,935, main spiders Google, MSN and Yahoo. Collected ECE2 1182, Top ten 1079, Collected Evans / Morris 825, Collected scientometrics 538, F3(Sp) 362, Barddoniaeth 269, Principles of ECE 155, Collected Eckardt / Lindstrom 130, Autobiography volumes one and two 123, Collected Proofs 90, Engineering Model 83, Evans Equations 70, UFT88 69, PECE 50, UFT311 43, ECE2 42, CEFE 35, Self charging inverter 30, Llais 23, UFT321 23, UFT313 21, UFT314 19, UFT315 16, UFT317 28, UFT318 17, UFT319 20, UFT320 18, UFT322 22, UFT323 16, UFT324 18, UFT325 26, UFT326 17, UFT327 16, UFT328 27, UFT329 21, UFT330 14, UFT331 20, UFT332 14, UFT333 20, UFT334 15, UFT335 19, UFT336 14, UFT337 16, UFT338 13, UFT339 13, UFT340 13, UFT341 23, UFT342 11, UFT343 17, UFT344 22, UFT345 14, UFT346 15, UFT347 21, UFT348 15, UFT349 19, UFT351 20, UFT352 28, UFT354 30, UFT355 17, UFT356 26, UFT357 27, UFT358 21, UFT359 20, UFT360 19, UFT361 12, UFT362 23, UFT363 22, UFT364 24, UFT365 16, UFT366 44, UFT367 42, UFT368 44, UFT369 43, UFT370 30 to date in February 2017. University of Oriente – Santiago de Cuba UFT169(sp), UFT170(Sp); Bracco Corporate Italy general; Kocaeli University Turkey UFT1, 10, 80, 87, 88. Intense interest all sectors, updated usage file attached for February 2017.

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## 371(5): The Planar and Three Dimensional Orbits of ECE2 Relativity

This is the Euler Lagrange theory of these orbits. From previous work in UFT328 for example they are known to produce precession. So the theoretical precession from this fundamental theory is matched with the experimental precessions of the perihelion. The Euler Lagrange method can also be used in quantization and relativistic quantization, for exaemple in the H atom, Sommerfeld, Schroedinger and Dirac theories. The Maxima code can solve essentially all these problems unless they get too complicated as in the description of orbits with Euler angles. Only a white haired raving maniac would attempt that by hand. The Euler Lagrange method can also be used to derive the ECE2 field equations of electrodynamics, gravitation, hydrodynamics and dynamics. The Hamilton Principle is the basis for much of physics, discovered by my Civil List predecessor Sir William Rowan Hamilton in the early nineteenth century. He was appointed full professor at Trinity College Dublin at the age of twenty three. He was never an F. R. S. because he could not afford the fees. The hamiltonian is the basis for all of quantum mechanics as is well known and the lagrangian is very similar to the hamiltonian in most problems, the sign of the potential energy being reversed. This is not always true however, an as usual, care must be taken. Horst Eckardt, Doug Lindstrom, others and I hammer out all technicalities in every UFT paper. These papers are now a central part of physics, having a huge and permanent worldwide readership in all the best universities.

## 371(4): Scheme of Computation for the 3D Orbit

This note gives the scheme of computation that gives all information about a spherical orbit governed by an inverse square force law of attraction. Maxima can now be used to compute any type of information needed, notably the orbits r(beta), r(theta) and r(phi). Some of the analytical results from UFT270 to UFT276 on three dimensional orbits are reviewed. The planar orbit is recovered in the limit theta goes to pi / 2, theta dot goes to zero. The planar orbit is given by Eq. (33), and does not precess for an inverse square law as is well known. In three dimensions however it precesses in various ways. There is a typo in Eq. (31), which should read theta goes to pi / 2. We are now ready to use Maxima for the lagrangian in ECE2 relativity, both for planar and three dimensional orbits.

## Euler Lagrange Equations for r1, r2 and r3

I agree that the complexity gets completely out of hand when using Eulerian angles for orbits. I think that it is sufficient just to note the simplest type of Euler Lagrange equations for r1, r2, and r3 in the final paper and evaluate spherical orbits using spherical polar coordinates, comparing with the results for UFT270 obtained about two years ago. The overall aim is to look for precession of the perihelion using spherical polar coordinates. I will proceed to your idea of adapting the gyroscope with fixed point for orbital theory. Tremendous progress is being made now because exceedingly complicated differential equations can be solved simultaneously with Maxima. If Lagrange had tried to solve the orbit problem his wig would have caught fire. Euler did not wear a wig.

To: EMyrone@aol.com

Sent: 25/02/2017 18:14:35 GMT Standard Time

Subj: Re: Further Discussion of Note 371(3) and 371(2)I have calculated the Lagrange equation (17) for r_1. It depends on the omega’s via (11-13). The omega’s depend on time so their time derivatives have to be evaluated. Omitting them gives a bit simpler expressions but seems not to be justified, see protocol file 371(2).pdf

When the full angular dependence (6-8) is introduced, the Lagrange equation for r_1,2,3 becomes extremely complicated, extending over more than one page in the protocol 371(2a).pdf. If the Euler angles are treated as Lagrange variables too, the equations have additionally to be resolved according to the second derivatives which was also done. Then there is a coupling of second derivatives across all equations. Trying to bring them into canonical form fails. Either the equations are too complicated or they are not resolvable. I guess that the latter is the case.

Horst

Am 25.02.2017 um 10:54 schrieb EMyrone:

The point mass M is placed at the origin and the point mass m is at (r1, r2, r3). The motion of the axes e1, e2, and e3 is defined with the dynamics of the Euler angles through the spin connection and equations (6) to (8). This gives six equations in six unknowns, Eqs. (17) to (22). That is an exactly determined problem therefore. The three degrees of freedom are the three dimensions of three dimensional space. Only three coordinates are being used, e sub 1, e sub 2 and e sub 3, and six Lagrange variables, r1, r2, r3, theta, phi and chi. The Euler equations for a rigid object are not being used, because there are no moments of inertia being used. Have you tried running these six simultaneous equations through Maxima, to find how the system behaves? If it gives reasonable results all looks OK. In spherical polar coordinates the mass M is at the origin and the mass m is at vector r. Solutions in the spherical polar system are also full of interest and much less complicated. It is also possible to use your idea of a unit vector by adapting the gyroscope with one point fixed. There are many interesting things to work on adn they will all create a lot of interest. It is best to work with spherical polar coordinates by Ockham’s Razor, but the Euler angles give a very large amount of new information. The important thing is the ability of Maxima so solve very complicated sets of simultaneous differential equations.

To: EMyrone

Sent: 25/02/2017 09:09:39 GMT Standard Time

Subj: Re: Discussion of Note 371(3) and 371(2)Your argument on time-dependence of the (e1, e2, e3) frame is correct. However it is not possble to describe a probelm with 3 degreees of freedom by 6 coordinates, at least not in Lagrange theory. Then you obtain an underdetermined system of equations, there is no unique solution.

A second point is to strictly discern if a masspoint or a rigid body is considered. You cannot use the Lagrange equations for a rigid body and apply it to a masspoint because then you have too many coordinates.

On the other hand it is possible to use Eulerian angles for masspoints. However you have already 3 coordinates so you cannot introduce additional translations. This type of application seems to be restricted to pure rotations on a unit sphere. The situation is different for a rigid body again.Horst

Am 25.02.2017 um 09:53 schrieb EMyrone:

It is a good idea to use the gyro with one point fixed for orbital theory, the mass M is at the fixed point of the gyro, and mass m is separated by a distance r from M. Unlike problem 10.10 of Marion and Thornton, however, the distance r is not constant. I will look in to this and go back to the basics of the derivation of the Euler equation from variational calculus, Marion and Thornton chapter five (Euler 1744). Howevber, I think that all is OK for the following reasons. It is true that the Euler angles relating frame (i, j, k) and (e1, e2, e3) are constants by definition, provided that frame (e1, e2, e3) always has the same orientation with respect to frame (i, j, k) and provided that the two frames are static. Then theta, phi and chi, being constants, cannot be used as variables. I agree about this point. However in Note 371(2), frame (e1, e2, e3) is moving with respect to (i. j. k), and so theta, phi and chi are also moving. This is because the Cartesain frame (i, jk, k) is static by definition, but frame (e1, e2, e3) is dynamic, i.e. e1, e2 and e3 depend on time, but i, j, and k do not depend on time. Similarly in spherical polars, (i, j, k) static, but (e sub r, e sub theta, e sub phi) is time dependent so r, theta and phi all depend on time. The lagrangian (1) of Note 371(2) is true for any definition of v, and Eq. (10) of that note is true for any definition of the spin connection (e.g. plane polar, spherical polar, Eulerian, and any curvilinear coordinate system in three dimensions). So Eqs. (11) to (16) of that note are correct. So it is correct to set up the lagrangian (16) using the Lagrange variables r1(t), r2(t), r3(t), theta(t), phi(t) and chi(t). It could also be set up with plane polar or spherical polar coordinates. We have already correctly solved those problems using the lagrangian method, The fundamental property of the spin connection is to show how the axes themselves move and it is valid to re express the angles of the plane polar and spherical polar coordinates as Eulerian angles. In the orbital problem, the Eulerian angles are all time dependent. So they vary in this sense, and can be used as Lagrange variables. The Euler variable x of chapter five of Marion and Thornton is t, x = t. To sum up, it is true that the Euler angles are constants when viewed as angles defining the orientation of a static (1, 2, 3) with respect to a static (X, Y, Z), but in Eq. (10) of Note 371(2), the components of the spin conenction are defined in terms of time dependent Euler angles, which are therefore Lagrange variables. This fact can be seen from Eqs. (6) to (8) of the note, in which appear phi dot, theta dot, and chi dot. These are in general non zero, i.e. they are all time dependent angular velocities.

To: EMyrone

Sent: 24/02/2017 18:35:19 GMT Standard Time

Subj: Re: Note 371(3) : Definition of Reference FramesThanks, this clarifies the subject. I think we must be careful in applying Lagrange theory. A mass point in 3D is described by 3 variables that are either [X. Y. Z] or [r1, r2,

r3]. The Eulerian angles describe the coordinate transformation between both frames of reference bold [i, j, k] and bold [e1, e2, e3]. The Eulerian angles are the sam for all points [r1, r2, r3]. So they cannot be subject to variation in the Lagrange mechanism. The degree of freedom must be the same in both frames, otherwise we are not dealing with generalized coordinates and Lagrange theory cannot be applied.A Lagrange approach in Eulerian coordinates can be made if we describe the motion of a mass point that is described as a unit vector in the [e1, e2, e3] frame. Then [r1, r2, r3] is fixed and the Eulerian angles can indeed be used for Lagrange variation. This is done for the gyro with one point fixed.

I calculated the transformation matrix A of the note and its inverse. The order of rotations is different from that in M&T.

Horst

Am 24.02.2017 um 15:11 schrieb EMyrone:

In this note the reference frames used in Note 371(2) are defined. The mass m orbits a mass M situated at the origin. The spherical polar coordinates are defined, and frame (X, Y, Z) is rotated into frame (1, 2, 3) with the matrix of Euler angles as in Eq. (11). The inverse of this matrix can be used to define r1, r2, and r3 in terms of X, Y, Z. In plane polar coordinates the orbit is a conic section with M at one focus as is well known.The planar elliptical orbit does not precess, but using spherical polar coordinates and Eulerian angles the orbit is no longer planar and precesses.

## Lagrange Mulipliers

This has been used in molecular dynamics computer simulation since the mid seventies, and the subject has become a major part of chemistry and physics.

To: EMyrone@aol.com

Sent: 25/02/2017 16:33:44 GMT Standard Time

Subj: Re: The Basics of the Euler Lagrange TheoryAgreed, the method of Lagrangian multipliers is more basic and can for example be applied when functions are not continuously differentiable. I will try a solution of eqs. (17-19) of note 371(2).

Horst

Am 25.02.2017 um 12:47 schrieb EMyrone:

I reviewed these basics as described by Marion and Thornton. The number of proper Lagrange variables is equal to the number of degrees of freedom, but it is also possible to use the method of undetermined multipliers when the number of Lagrange variables is greater than the number of degrees of freedom. However, a simple solution to the problem is to solve Eqs. (17) to (19) of Note 371(2) simultaneously, to give r1, r2 and r3 in terms of theta, phi and chi. These are the required orbits. There are three dimensions (degree of freedom) and three proper Lagrange variables, r1, r2, and r3. So there are three differential equations in three unknowns, an exactly determined problem. The orbits are r1(theta, phi, chi), r2(theta, phi, chi) and r3(theta, phi, chi). Finally use

r squared = r1 squared + r2 squared + r3 squared

to find r(theta, phi, chi) and its precessions. In the planar limit it should reduce to a conic section without precession.

## Daily Report 24/2/17

The equivalent of 77,180 printed pages was downloaded (281.397 megabytes) from 2,212 downloaded memory files and 474 distinct visits each averaging 3.1 memory pages and 6 minutes, printed pages to hits ratio of 43,68, total top ten referrals 2,212,438, main spiders Google, MSN and Yahoo. Collected ECE2 1142, Top ten 1004, Collected Evans / Morris 792 (est), Collected scientometrics 487, F3(Sp) 349, Barddoniaeth 259, Principles of ECE 150, Eckardt / Lindstrom 122, Autobiography volumes one and two 118, Collected Proofs 88, Engineering Model 83, UFT88 67, Evans Equations 63, PECE 48, CEFE 45, ECE2 41, UFT311 41, Self charging inverter 30, UFT321 23, Llais 20, PLENR 11, UFT313 20, UFT314 19, UFT315 16, UFT316 17, UFT317 28, UFT318 16, UFT319 19, UFT320 16, UFT322 20, UFT323 15, UFT324 16, UFT325 25, UFT326 17, UFT327 16, UFT328 27, UFT329 21, UFT330 13, UFT331 19, UFT332 14, UFT333 20, UFT334 14, UFT335 18, UFT336 14, UFT337 16, UFT338 13, UFT339 12, UFT340 12, UFT341 21, UFT342 11, UFT343 17, UFT344 21, UFT345 14, UFT346 15, UFT347 20, UFT348 15, UFT349 18, UFT351 19, UFT352 27, UFT353 25, UFT354 28, UFT355 16, UFT356 25, UFT357 26, UFT358 19, UFT359 20, UFT360 18, UFT361 13, UFT362 23, UFT363 22, UFT364 24, UFT365 16, UFT366 43, UFT367 42, UFT368 44, UFT369 42, UFT370 25 to date in February 2017. University of Antioquia Colombia UFT175(Sp); Deusu search engine home page; Chemistry University of Wisconsin Madison My page, Cumbric language. Intense interest all sectors, updated usage file attached for February 2017.

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