Sir William Rowan Hamilton is known as Rowan Hamilton in Trinity College Dublin, of which I am sometime Visiting Academic. He was appointed to the Civil List on April 27th 1844 with a pension of £200 a year (about £22,319 a year today). My Civil List Pension is £2,400 a year, so it has been eroded a lot in value since 1844. It is now an honorarium rather than a salary to live on. The Civil List Pension is akin to Order of Merit. Hamilton was appointed Professor of Astronomy in Dublin at the age of twenty two and was considered to be one of the best mathematicians in the world at the age of 18. His papers “On a General Method of Dynamics” (1834 and 1835) gave the Hamilton Principle of Least Action and also what are known now as the Euler Lagrange equations. These were actually discovered by Hamilton using the Euler principle of 1744 and using some of Lagrange’s ideas of 1760. He also inferred the Hamilton or canonical equations, defined the lagrangian and inferred the hamiltonian, the basis of quantum mechanics. In UFT176, (www.aias.us and www.upitec.org) the Quantum Hamilton Equations are inferred, in what has become a classic paper. The Hamilton Principle of Least Action can be used in many branches of physics and mathematics.

## Computations of 374(2) and 374(3): Precession Confirmed

This is an important remark, precession is still present. These will be very interesting as usual, there are many possible advances that can be made by using the equations of fluid dynamics in orbital theory: the continuity equation (conservation of matter); Navier Stokes equation; conservation of energy equation and vorticity equation. All of these add new equations to the set of simultaneous differential equations. I will write new notes on this theme.

To: EMyrone@aol.com

Sent: 31/03/2017 08:35:03 GMT Daylight Time

Subj: Re: Discussion of 374(2)

Many thanks for these clarifications, I fully agree that fluid dynamic effects must be handled like a potential (i.e. as given properties) for the Lagrange mechanism. Using the correct momentum (28) will not give qualitative changes in the numerical solution because I used a constant spin connection, only the numbers will change.

Eqs. 43-44 c an be solved for any assumed radial function R_r(r). Eq. 45 does not enter the calculation, it would be interesting to see if the angular momentum is really conserved for non-constant functions R_r.Horst

Am 29.03.2017 um 10:42 schrieb EMyrone:

These are interesting comments. This note is based entirely on standard equations of the Lagrange and Hamilton dynamics applied to vectors, notably Eq. (3), which gives the correct momentum p from the Lagrangian (2), these are all contained in Marion and Thornton. The vector Euler Lagrange equation is Eq. (11), and leads correctly to the well known equations (20) and (21), the Leibniz equation and the equation of constraint (21). The kinetic energy is p dot p / (2m). The primary purpose of the note is to show that the correct momentum must be defined by p bold = partial lagrangian / partial r dot bold (see for example Marion and Thornton). Eqs. (22) – (24) work correctly for classical dynamics, but no longer work correctly for fluid dynamics. The correct momentum of fluid dynamics must be calculated from eq. (3) using the lagrangian (35). The correct momentum is p bold = m v bold, where v bold is given by Eq. (26). This is the same as the momentum used in UFT363, and leads to Eqs. (33) and (34). The spin connection partial R sub r / partial r must be regarded in the same way as the potential energy U(r). Neither is a Lagrange variable. The key point is that the momentum p bold can be obtained correctly from the lagrangian (2) if and only if Eq. (3) is used. This is checked from the fact that p bold is r bold dot in Eq.(2). Then use the rules of differentiation with r dot bold. For classical dynamics, Eqns (22) to (24) happen to work fortuitously, and these are of course the equations used by Marion and Thornton in their chapter seven. However, for fluid dynamics they no longer work, because the complete momentum is now:

p bold = x r dot e sub r bold + r theta dot e sub theta bold

where

x = (1 + partial R sub r / partial r)Using this in Eqs. (2) and (3) gives the correct momentum from the correct lagrangian, containing the correct kinetic energy. The correct momentum is Eq. (28) multiplied by m. When used in Eq. (29) it leads to to Eqs. (33) and (34). Eq. (33) is different from that found in UFT363, because in UFT363, the correct factor x in Eq. (33) turned out to be x squared, as in Eq. (39) of this note. Therefore the lagrangian (35) cannot be used with Eq. (38). This result is by no means obvious. It shows that there is a certain amount of subjectivity in the Lagrange method as is well known. It is by no means obvious how to choose the Lagrange variables, and the choice of lagrangian is also subjective to some degree. These things emerge in for example quantum field theory. Fortunately the answer is simple, use Eq. (13), in which there is only one Lagrange variable, vector r bold. This leads to Eqs. (33) and (34). I suggest putting Eqs. (43) to (45) through Maxima to see how the orbital precession behaves. I do not think that the replacement of x sqaured of UFT363 by the correct x of this note will make any qualitative difference to the precession that you have already inferred numerically. It might affect the details of the precession, but the precession will remain.

To: EMyrone

Sent: 28/03/2017 14:40:47 GMT Daylight Time

Subj: Re: 374(2): Complete Analysis of UFT363It is difficult for me to understand this note for principal reasons. My interpretation is the following:

The Lagrangian method is based on the kinetic energy and generalized coordinates. The Euler-Lagrange equations are based on the kinetic energy of the generalized coordinates. These coordinates are found by coordinate transformations. In our case the radial coordinate is transformed by

r –> r + R_r(r)

where R_r(r) is a “distortion” of radial motion of a particle inferred by fluid dynamics. For the Lagrange mechanism this function has to be known a priori, it cannot result from the Euler-Lagrange equations. If we assume that the R_r function is to be determined dynamically by the dynamics, we need an additional equation of motion or state or whatever. In Lagrange theory, energy conservation is fulfilled. This is not necessarily the case if a “free floating” function is introduced. I guess that you had this in mind when saying that a Hamiltonian formulation is needed in addition to the Lagrangian formulation to determined the dynamics consistently.

So the question is where to take the conditions for R_r that must appear as a constraint in the Lagrange mechanism. The generalized coordinates should be r and theta, but what is the kinetic energy? Let’s assmume that the velocity, eqs.(26,27) of the note, is that derived from the coordinate transformation. Then the Euler-Lagrange equations (33,34) are correct, although they contain an unspecified function R_r (which is not time dependent).

I do not understand the part of the note after eqs.(33,34). Why do you introduce the Lagrangian (35)? Obviously this belongs to a different problem to be solved. And why should it be re-expressed to (36)? The momentum in Lagrange theory is a generalized momentum and needs not have the form (37).

On page 6 of the manuscript I cannot decipher the sentence “It is not possible to choose … as Lagrange varibles”. Which variables do you mean?

Eqs. (44) and (45) are derived from the same Euler-Lagrange equation and are not independent. It is true that (45) is a constant of motion but this is not suited for solving the equations because it is only of first order. What about usingH = 1/2 m v^2 + U(r) = const.

instead? Then we can determine partial R_r/partial r , and replace it in (43,44) so that we have only derivatives of time and the equation system could be solved by Maxima for example. In general, combination of Lagrange theory (which is for mass points primarily) and fluid dynamics (which is for distributed fields) may be a bit tricky.

Sorry for having written such a long sermon today.

HorstAm 28.03.2017 um 10:44 schrieb EMyrone:

This note shows that the complete Lagrangian and Hamiltonian formulations are needed to describe fluid dynamics self consistently. When this is done UFT363 is slighly corrected to Eqs. (43) to (45), which can be solved simultaneously using Maxima to give the orbit and spin connection.

## Bosch Corporation Studying Energy from Spacetime Devices

This interest can be seen on the daily reports for today and yesterday. These can be based on the replicated and patented Osami Ide circuit (UFT311, UFT321 UFT364, Self Charging Inverter), which will bring in the second industrial revolution described by AIAS Fellow Dr. Steve Bannister in his Ph. D. Thesis on www.aias.us (Department of Economics, University of Utah). See also www.et3m.net and www.upitec.org. The Alex Hill company has recently signed a joint venture agreement with a company in the United States. I think that investment managers should be interested in this new industry. It should return a spectacular amount on investment. ECE theory describes the Osamu Ide circuit with precision (UFT311), whereas the obsolete standard model fails completely. See also the pulsed LENR report by AIAS Director Douglas Lindstrom on www.aias.us and his Idaho lecture. He is currently on a business trip to China, where there has been intense interest in ECE theory for some years. There are potentially huge new markets for spacetime devices all over the world. They could be used to power domestic appliances of the type manufactured by Bosch. They could also be made into power stations, large power plants, power devices for electric vehicles, power plants for ships and also aircraft and spacecraft, and should make the chemical battery industry obsolete. That is why Prof. Bannister describes them as powering the second industrial revolution. Wind turbines are already obsolete as well as completely useless. Governments should implement energy from spacetime devices as quickly as they can. They can also be distributed to the starving poor of many countries.

## Daily Report 29/3/17

The equivalent of 81,576 printed pages was downloaded (297.426 megabytes) from 2,239 downloaded memory files and 406 distinct visits each averaging 3.9 memory pages and 6 minutes, printed pages to hits ratio of 36.43, to referrals total of 2,223,687, main spiders Google, MSN and Yahoo. Collected ECE2 1686, Top ten 1484, Collected Evans / Morris 957(est), F3(Sp) 630, Collected scientometrics 542, Principles of ECE 398, Barddoniaeth 232, Evans Equations 194, Collected Eckardt / Lindstrom papers 151(est), Autobiography volumes one and two 125, Collected Proofs 104, UFT88 89, Self charging inverter 84, Engineering Model 78, UFT311 76, Mann Johnson ECE 73, PLENR 59, ECE2 59, CEFE 54, Llais 44, Idaho 29, UFT321 22, UFT313 29, UFT314 19, UFT315 22, UFT316 17, UFT317 19, UFT318 13, UFT319 22, UFT320 16, UFT322 35, UFT323 20, UFT324 25, UFT325 32, UFT326 16, UFT327 21, UFT328 23, UFT329 20, UFT330 15, UFT331 20, UFT332 19, UFT333 16, UFT334 14, UFT335 36, UFT336 15, UFT337 14, UFT338 17, UFT339 16, UFT340 15, UFT341 31, UFT342 26, UFT343 31, UFT344 30, UFT345 27, UFT346 24, UFT347 46, UFT348 27, UFT349 25, UFT351 41, UFT352 52, UFT353 35, UFT354 63, UFT355 39, UFT356 42, UFT357 37, UFT358 38, UFT359 39, UFT360 31, UFT361 13, UFT362 25, UFT363 40, UFT364 36, UFT365 22, UFT366 59, UFT367 35, UFT368 35, UFT369 44, UFT370 48, UFT371 59, UFT372 31, UFT373 9 to date in March 2017. University of Adelaide Proof One; University of Oriente Santiago de Cuba UFT169(Sp); Bosch Company Germany Spacetime Devices; Deusu search engine Home Page; University of Baguio Philippines (on edu) general; Marine Hydrographic and Oceanographic Service France UFT351, UFT353, UFT357, UFT358; The Campaign for the Protection of Rural Wales Home Page; National Electrification authority Philippines general. Intense interest all sectors, updated usage file attached for March 2017.

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## 374(3): Equations for the Precessing Orbit of Fluid Gravitation

In the first instance, Eqs. (27) to (29) can be solved numerically using Maxima to check that the method gives the correct orbit (18). Then the algorithm can be modified to solve Eqs. (37), (38) and (40 numerically using a model for the function x defined in Eq. (31). Finally Eq. (44) can be added if the fluid is assumed to be incompressible, so both the orbit and x can be found. The caveat of this note explains why the note slightly corrects the equations of UFT363. The lagrangian method of UFT363 gives Eq. (47), which is different from the correct Eq. (37). The reason is that the kinetic energy of fluid gravitation, Eq. (48), is not in the required format (49) demanded by the Hamilton Principle of Least Action. The kinetic energy must be T(r bold dot, r bold). Sometimes it is simpler and clearer to derive results without the Lagrange method using both the Lagrange and Hamilton equations of motion.

## Basics of the Lagrangian Method

The fundamental reason for the last note is that the Hamilton Principle of Least Action, from which is follows that the lagrangian must be defined as T(r bold dot) – U(r bold). I will explain this in another note to be distributed shortly. This method holds for any r bold dot. The method used in UFT363 did not satisfy the fundamental criterion for a lagrangian, which is why it did not lead to the correct momentum. The new method of UFT374 corrects this and leads to soluble sets of simultaneous partial differential equations. The new advance is that these can be tied in with the equations of hydrodynamics in many interesting ways. for background reading I suggest Marion and Thornton chapter five. So UFT374 will develop in this way. I recommend Marion and Thornton as far as it goes. It is now known that its section on the Einstein theory is wildly wrong. This was again shown by Horst’s numerical methods combined with analytical methods. Marion and Thornton is not easy, but is recommended reading. I remember doing lagrangian theory in the second year mathematics course at UCW Aberystwyth. It i snot easy, but sometimes useful. I have used it many times throughput my research career. Sometimes it is better to use other methods. The method of UFT374 uses all the available dynamics, Lagrangian and Hamiltonian. UFT176 on the discovery of the quantum Hamilton equations, is now a famous paper, a classic by any standards. There is a hugely successful combination of analytical and numerical techniques in each UFT paper, mainly by Horst Eckardt, Douglas Lindstrom and myself, and many contributions by other Fellows.

## UFT88 read at Pierre et Marie Curie Astrophysics Institute

Universite Pierre et Marie Curie (Paris 6) is the best university in France at present. It is ranked 39 in the world by Shanghai, 121 by Times, 141 by QS and 175 by webometrics. It has 32,000 students on the Jussieu Campus of the Latin Quarter of Paris. The University of Paris is the second oldest on mainland Europe after Bologna founded in the second half of the twelfth century by Robert de Sorbon. The oldest university in Europe was Bangor Tewdos, founded in the fourth or fifth centuries, but completely destroyed by raiders. The Astrophysics Institute is situated next to the famous Paris Observatory and was founded in 1936, opening in 1952. UPMC is affiliated with the Sorbonne and CNRS. It includes the Institute Henri Poincare, where Jean-Pierre Vigier , co author of “The Enigmatic Photon”, Omnia Opera of www.aias.us) was a professor for many years, starting as an assistant to the Nobel Laureate Louis de Broglie. Vigier immediately accepted B(3) and probably nominated it for a Nobel Prize, or used his influence to have it recognized and nominated. UPMC has produced several famous Nobel Laureates, including Pierre Curie, Marie Curie (two Nobel Prizes), Henri Bequerel, Louis de Broglie, Frederic Joliot, Irene Joliot-Curie and Pierre Gilles de Gennes, whom I heard lecture on liquid crystals at Aberystwyth during a conference I helped organize. In the student risings of 1968 to 1970 there were prolonged clashes between the students and the police. The students occupied the Sorbonne and declared it an autonomous People’s Republic. This occurred when I was an undergraduate at Aberystwyth (1968 to 1971) as described in Autobiography Volume Two. The radical atmosphere of the Parisian student Rising pervaded the campus at Aberystwyth and also all the Campi in the United States after the Kent State shootings. UFT88 is a famous classic paper by now, it was published in 2007 and corrects the second Bianchi identity for torsion, leading to the complete geometrical refutation of the Einstein relativity and another revolution, the post Einsteinian paradigm shift in natural philosophy. So www.aias.us and www.upitec.org are read continuously at all the best universities in the world. The authorities of the old Ministry of Truth in physics try not to notice.

## Daily Report 28/3/17

The equivalent of 93,405 printed pages was downloaded (340.556 megabytes) from 2,108 downloaded memory files (hits) and 424 distinct visits each averaging 4.4 memory pages and 6 minutes, printed pages to hits ratio of 44.31, top referrals total 2,223,504, main spiders Google, MSN and Yahoo. Collected ECE2 1606, Top ten 1546, Collected Evans / Morris 924(est), F3(Sp) 622, Collected scientometrics 520, Principles of ECE 394, Barddoniaeth 230, Evans Equations 191, Collected Eckardt / Lindstrom 151, Autobiography volumes one and two 124, Collected Proofs 98, UFT88 89, Self charging inverter 78, Engineering Model 77, Mann Johnson ECE 72, PLENR 58, ECE2 57, CEFE 51, Llais 43, UFT311 39, UFT321 21, UFT313 29, UFT314 16, UFT315 19, UFT316 15, UFT317 19, UFT318 12, UFT319 20, UFT320 15, UFT322 33, UFT323 19, UFT324 25, UFT325 32, UFT326 14, UFT327 21, UFT328 20, UFT329 19, UFT330 15, UFT331 20, UFT332 17, UFT333 16, UFT334 13, UFT335 32, UFT336 13, UFT337 14, UFT338 17, UFT339 14, UFT340 15, UFT341 31, UFT342 24, UFT343 28, UFT344 28, UFT345 25, UFT346 22, UFT347 43, UFT348 26, UFT349 23, UFT351 39, UFT352 50, UFT353 32, UFT354 61, UFT355 37, UFT356 40, UFT357 35, UFT358 35, UFT359 37, UFT360 30, UFT361 12, UFT362 25, UFT363 40, UFT364 33, UFT365 21, UFT366 57, UFT367 35, UFT368 33, UFT369 44, UFT370 48, UFT371 59, UFT372 31, UFT373 8 to date in March 2017. University of Adelaide UFT142; University of Quebec Trois Rivieres UFT366 – UFT373; Bosch Company Germany ECE Devices; Steinbuch Centre for Computing Karlsruhe Institute for Technology Home page, Three World records by MWE, Nomination, B. Sc. Degree Ceremony; Stanford University general; Institut d’Astrophysique de Paris (Astrohysics Institute of Paris, Joint research centre of Pierre and Marie Curie University and the National Centre for Scientific Research (CNRS)) UFT88; French National Hydrographic Service (SHOM) UFT349, UFT370, ECE2 preprint; Campaign fro the Protection of Rural Wales home page; Pakistan Education and Research Network general; University of Warwick Newspaper cuttings. Intense interest all sectors, updated usage file attached for March 2017.

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## Discussion of 374(2)

These are interesting comments. This note is based entirely on standard equations of the Lagrange and Hamilton dynamics applied to vectors, notably Eq. (3), which gives the correct momentum p from the Lagrangian (2), these are all contained in Marion and Thornton. The vector Euler Lagrange equation is Eq. (11), and leads correctly to the well known equations (20) and (21), the Leibniz equation and the equation of constraint (21). The kinetic energy is p dot p / (2m). The primary purpose of the note is to show that the correct momentum must be defined by p bold = partial lagrangian / partial r dot bold (see for example Marion and Thornton). Eqs. (22) – (24) work correctly for classical dynamics, but no longer work correctly for fluid dynamics. The correct momentum of fluid dynamics must be calculated from eq. (3) using the lagrangian (35). The correct momentum is p bold = m v bold, where v bold is given by Eq. (26). This is the same as the momentum used in UFT363, and leads to Eqs. (33) and (34). The spin connection partial R sub r / partial r must be regarded in the same way as the potential energy U(r). Neither is a Lagrange variable. The key point is that the momentum p bold can be obtained correctly from the lagrangian (2) if and only if Eq. (3) is used. This is checked from the fact that p bold is r bold dot in Eq.(2). Then use the rules of differentiation with r dot bold. For classical dynamics, Eqns (22) to (24) happen to work fortuitously, and these are of course the equations used by Marion and Thornton in their chapter seven. However, for fluid dynamics they no longer work, because the complete momentum is now:

p bold = x r dot e sub r bold + r theta dot e sub theta bold

where

x = (1 + partial R sub r / partial r)

Using this in Eqs. (2) and (3) gives the correct momentum from the correct lagrangian, containing the correct kinetic energy. The correct momentum is Eq. (28) multiplied by m. When used in Eq. (29) it leads to to Eqs. (33) and (34). Eq. (33) is different from that found in UFT363, because in UFT363, the correct factor x in Eq. (33) turned out to be x squared, as in Eq. (39) of this note. Therefore the lagrangian (35) cannot be used with Eq. (38). This result is by no means obvious. It shows that there is a certain amount of subjectivity in the Lagrange method as is well known. It is by no means obvious how to choose the Lagrange variables, and the choice of lagrangian is also subjective to some degree. These things emerge in for example quantum field theory. Fortunately the answer is simple, use Eq. (13), in which there is only one Lagrange variable, vector r bold. This leads to Eqs. (33) and (34). I suggest putting Eqs. (43) to (45) through Maxima to see how the orbital precession behaves. I do not think that the replacement of x sqaured of UFT363 by the correct x of this note will make any qualitative difference to the precession that you have already inferred numerically. It might affect the details of the precession, but the precession will remain.

To: EMyrone@aol.com

Sent: 28/03/2017 14:40:47 GMT Daylight Time

Subj: Re: 374(2): Complete Analysis of UFT363It is difficult for me to understand this note for principal reasons. My interpretation is the following:

The Lagrangian method is based on the kinetic energy and generalized coordinates. The Euler-Lagrange equations are based on the kinetic energy of the generalized coordinates. These coordinates are found by coordinate transformations. In our case the radial coordinate is transformed by

r –> r + R_r(r)

where R_r(r) is a “distortion” of radial motion of a particle inferred by fluid dynamics. For the Lagrange mechanism this function has to be known a priori, it cannot result from the Euler-Lagrange equations. If we assume that the R_r function is to be determined dynamically by the dynamics, we need an additional equation of motion or state or whatever. In Lagrange theory, energy conservation is fulfilled. This is not necessarily the case if a “free floating” function is introduced. I guess that you had this in mind when saying that a Hamiltonian formulation is needed in addition to the Lagrangian formulation to determined the dynamics consistently.

So the question is where to take the conditions for R_r that must appear as a constraint in the Lagrange mechanism. The generalized coordinates should be r and theta, but what is the kinetic energy? Let’s assmume that the velocity, eqs.(26,27) of the note, is that derived from the coordinate transformation. Then the Euler-Lagrange equations (33,34) are correct, although they contain an unspecified function R_r (which is not time dependent).

I do not understand the part of the note after eqs.(33,34). Why do you introduce the Lagrangian (35)? Obviously this belongs to a different problem to be solved. And why should it be re-expressed to (36)? The momentum in Lagrange theory is a generalized momentum and needs not have the form (37).

On page 6 of the manuscript I cannot decipher the sentence “It is not possible to choose … as Lagrange varibles”. Which variables do you mean?

Eqs. (44) and (45) are derived from the same Euler-Lagrange equation and are not independent. It is true that (45) is a constant of motion but this is not suited for solving the equations because it is only of first order. What about usingH = 1/2 m v^2 + U(r) = const.

instead? Then we can determine partial R_r/partial r , and replace it in (43,44) so that we have only derivatives of time and the equation system could be solved by Maxima for example. In general, combination of Lagrange theory (which is for mass points primarily) and fluid dynamics (which is for distributed fields) may be a bit tricky.

Sorry for having written such a long sermon today.

HorstAm 28.03.2017 um 10:44 schrieb EMyrone:

This note shows that the complete Lagrangian and Hamiltonian formulations are needed to describe fluid dynamics self consistently. When this is done UFT363 is slighly corrected to Eqs. (43) to (45), which can be solved simultaneously using Maxima to give the orbit and spin connection.

## Chapter 5 of ECE2 and UFT373 in Spanish

Many thanks again!

In a message dated 28/03/2017 21:16:10 GMT Daylight Time, burleigh.personal@gmail.com writes:

Done today

Dave

On 3/26/2017 12:36 PM, Alex Hill (ET3M) wrote:

Hello Dave,

Please find enclosed the Spanish version of Chapter 5 of the ECE2 book in pdf file, which I hope you can attach to the existing ECE2 Ch 1 to 4 pdf file in Spanish, since all five chapters are too heavy a file to mail by Yahoo.

I am also enclosing the recent UFT373 file in Spanish, for posting.

Thanks.

Regards,