It is shown straightforwardly in this note that the orbits of a mass m around a mass M in the frame (1, 2, 3) of the Euler angles can be found by solving simultaneously six Euler Lagrange equaions in six Lagrange variables. The problem is far too complicated to be solved by hand but can be solved numerically using Maxima to give twenty one new types of orbit described on page 4. There are nutations and precessions in the Euler angles phi, theta and chi. The usual assumption made in orbital theory is that the orbit is planar. Note carefully that the inverse square law is still being used for the force of attraction between m and M, but the Eulerian orbits contain far more information than the theory of planar orbits. The inverse square law does not give precession of a planar orbit as is well known. However the same inverse square law gives rise to many types of nutation and precession in the twenty one types of orbit described by the Euler angles. This isa completely new discovery, and it should be noted carefully that it is based on classical rotational dynamics found in any good textbook. It could have been defined in the eighteenth century, but orbital theory became ossified in planar orbits. This theory is part of ECE2 generally covariant unified field theory because all of rotational dynamics are described by a spin connection of Cartan geometry. Eq. (10) of this note is a special case of the definition of the Cartan covariant derivative. This is another major discovery. An art gallery full of graphics can be prepared based on these results, of greatest interest are plots of the twenty one types of orbit, looking for precessions of a point in the orbit such as the perihelion.

a371stpapernotes2.pdf

Many thanks again. This is just a typo, the equation should be the same as Eq. (25) of UFT270. The rest of the note is the same. The great advantage of UFT371 over UFT270 is that Maxima is able to solve all the relevant equations numerically in UFT371, so the laborious hand calculations in UFT270 no longer have to be done. A close control over the use of the computer is still needed of course, but an array of new possibilities opens up. I will proceed now to develop the same problem in terms of the Eulerian angles. ECE2 relativity is still needed of course in other situations, but it would be interesting to see whether classical rotational dynamics gives planetary precessions. That would mean that one of the most famous experiments of Einsteinian general relativity EGR, the precession of the perihelion would be refuted. We have refuted EGR in many ways, and there have been no valid objections to these refutations. The lagrangian (1) of Note 371(1) gives precessions in the angles of the spherical polar coordinates. When Eulerian angles are used, more precessions appear on the classical level. Furthermore, we now know clearly that classical rotational dynamcis are governed by a well defined spin connection of Cartan geometry. Finally, all these calculations can be quantized. Again, Maxima removes all the laborious calculations.

To: EMyrone@aol.com
Sent: 22/02/2017 13:48:28 GMT Standard Time
Subj: Re: Note 371(1): Precession of the Perihelion on the Classical Level

Anything seems to go wrong with beta. Inserting beta dot squared from (6) does not give (1), there are additional terms then.

Horst

Am 21.02.2017 um 12:31 schrieb EMyrone:

This note looks afresh at the precession of the perihelion by setting up the classical lagrangian (1) and solving Eqs. (3), (4), (5), (9) and (13) simultaneously for the orbit r = alpha / (1 + epsilon cos beta) where beta is defined in Eq. (6). This method is a development of one used originally in UFT270. The power of the Maxima program now allows the relevant equations to be solved for beta in terms of the angles theta and phi if the spherical polar coordinates system. There are precessions in theta and phi. The precession of the perihelion is usually thought of as a precession of phi in a planar orbit, using the incorrect Einsteinian general relativity. In the UFT papers ECE2 relativity has been used to describe the precession. However it may be that it can be described on the classical level with the use of spherical polar coordinates. If this supposition is true, and if Eq. (8) is a precessing ellipse, then other precessions can also be developed in this way. The theory can also be developed with the Eulerian angles. In general there are precessions in theta and phi. There is no reason why an orbit should be planar. In general it must be described by a three dimensional theory.

The equivalent of 203,818 printed pages was downloaded (743.122 megabytes) from 2,734 downloaded memory files and 546 distinct visits each averaging 3.6 memory pages and 8 minutes, printed pages to hits ratio of 74.56, top ten referrals total 2,211,593, main spiders Google, MSN and Yahoo. Collected ECE2 1019, Top ten 835, Collected Evans / Morris 693, Collected scientometrics 453, F3(Sp) 285, Barddoniaeth 198, Principles of ECE 142, Collected Eckardt / Lindstrom 113, Autobiography volumes one and two 89, Collected Proofs 76, Engineering Model 73, Evans Equations 52, UFT88 59, PECE 43, CEFE 41, UFT311 39, ECE2 36, Self charging inverter 26, UFT321 21, Llais 18, PLENR 10, UFT313 20, UFT314 16, UFT315 14, UFT316 14, UFT317 28, UFT318 15, UFT319 18, UFT320 15, UFT322 19, UFT323 15, UFT324 16, UFT325 22, UFT326 15, UFT327 15, UFT328 23, UFT329 20, UFT330 13, UFT331 17, UFT332 12, UFT333 18, UFT334 13, UFT335 18, UFT336 11, UFT337 15, UFT338 11, UFT339 10, UFT340 11, UFT341 19, UFT342 10, UFT343 14, UFT344 20, UFT345 13, UFT346 12, UFT347 17, UFT348 13, UFT349 17, UFT351 19, UFT352 23, UFT353 23, UFT354 27, UFT355 12, UFT356 22, UFT357 22, UFT358 17, UFT359 18, UFT360 15, UFT361 13, UFT362 20, UFT363 19, UFT364 22, UFT365 14, UFT366 36, UFT367 37, UFT368 39, UFT369 38, UFT370 14 to date in February 2017. Deusu search engine AIAS staff; University of Paderborn home page; University of the Bundeswehr (Armed Forces) Munich Engineering Model; University of Oulu Finland UFT265; Science Museum National Autonomous University of Mexico UFT166(Sp); City Government of Taguig Philippines general; Punjab Industrial Estates general; Stockholm Institute of Education UFT84; University of Durham Foundations of Physics Leaflet. Intense interest all sectors, updated usage file atatched for February 2017.

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The University is ranked 119 in the world by webometrics, 106 by Times, 54 by Shanghai and 85 by QS. It was founded as a merger in 1525 of the Carolinum and other faculties, and became the university in 1833. Albert Einstein submitted his Ph. D. Thesis to the university in 1905, on Brownian motion. He had studied from 1896 to 1900 at ETH, across the road from the University. In 1909 the university created an associate professorship for Einstein, and he was promoted full professor at Prague in 1911. From 1912 – 1914 he was a professor at ETH, and in 1914 left for Berlin to become Director of the Kaiser Wilhelm Institute with no teaching duties. In 1933 he was forced to emigrate to the Princeton Institute for Advanced Studies and never returned to Europe. In 1915 Einstein proposed his famous field equation of general relativity, based directly on the 1902 second Bianchi identity. UFT88 corrects this identity for torsion, and it has been developed into the Jacobi Cartan Evans identity of UFT313. The latter was read two days ago at the Simons Center for Geometry and Physics at Stonybrook University on Long Island. UFT88 is a classic by any standard, having been studied at least ten thousand times in a decade, without objection. It is based directly on Cartan geometry, and greatly improves the Einstein theory of general relativity, developing it into ECE2. All fifty six ECE2 papers and books to date are studied every day around the world. I was a Guest of the University of Zuerich from 1990 to 1991 on leave from Cornell Theory Center, studying with the Dean, Georges Wagniere. I also worked at ETH on the IBM 3096 supercomputer. The results are in the Omnia Opera section of www.aias.us.

The equivalent of 92,429 printed pages was downloaded (336.995 megabytes) from 2.391 downloaded memory files (hits) and 477 distinct visits each averaging 4.3 memory pages and 7 minutes, printed pages to hits ratio of 38.66, top ten referrals total 2,211,396, main spiders Google, MSN and Yahoo. Collected ECE2 991, Top ten 785, Evans Morris 660(est), Collected scientometrics 436, F3(Sp) 260, Barddoniaeth 191, Principles of ECE 139, Eckardt Lindstrom 112, Autobiography volumes one and two 85, Collected Proofs 70, Engineering Model (Collected Equations) 68, UFT88 57, PECE 42, CEFE 40, UFT311 36, Self charging inverter 25, UFT321 21, Llais 18, PLENR 10, UFT313 19, UFT314 16, UFT315 14, UFT316 14, UFT317 27, UFT318 15, UFT319 18, UFT320 15, UFT322 19, UFT323 14, UFT324 15, UFT325 22, UFT326 15, UFT327 15, UFT328 22, UFT329 20, UFT330 12, UFT331 17, UFT332 12, UFT333 18, UFT334 13, UFT335 16, UFT336 11, UFT337 14, UFT338 11, UFT339 10, UFT340 11, UFT341 19, UFT342 9, UFT343 14, UFT344 19, UFT345 13, UFT346 12, UFT347 16, UFT348 12, UFT349 17, UFT351 18, UFT352 23, UFT353 23, UFT354 23, UFT355 12, UFT356 21, UFT357 22, UFT358 16, UFT359 18, UFT360 15, UFT361 13, UFT362 20, UFT363 18, UFT364 21, UFT365 13, UFT366 35, UFT367 36, UFT368 39, UFT369 36, UFT370 13 to date in February 2017. Argentine Research Institute for Defence Science and Technology (CITEFA) general; Catholic University Leuven Potential Waves; Telematic Educational Network of Catalonia (Xtec) F3(Sp); University of Quebec Trois Rivieres UFT366 to UFT370; Swiss Federal Institute Zurich (ETH) general; University of Zurich UFT88; University of Paderborn UFT theory, Devices, CV, Autobiography, extensive download of UFT papers; University of Wuppertal UFT33, UFT128; Universit of Aarhus Denmark LCR Resonant; University of Pittsburgh Home Page; University of Stonybrook Simons Center for Geometry and Physics UFT313; University of Vermont Extensive download; Indian National Institute for Science and Technology UFT158; Unite the Union, Britain Latest Family History; Philippine National Electrification Administration UFT158; University of Luton CV, historical source documents, UNCC Saga; University of St Andrews UFT239. Intense interest all sectors, updated usage file attached for February 2017.

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This note looks afresh at the precession of the perihelion by setting up the classical lagrangian (1) and solving Eqs. (3), (4), (5), (9) and (13) simultaneously for the orbit r = alpha / (1 + epsilon cos beta) where beta is defined in Eq. (6). This method is a development of one used originally in UFT270. The power of the Maxima program now allows the relevant equations to be solved for beta in terms of the angles theta and phi if the spherical polar coordinates system. There are precessions in theta and phi. The precession of the perihelion is usually thought of as a precession of phi in a planar orbit, using the incorrect Einsteinian general relativity. In the UFT papers ECE2 relativity has been used to describe the precession. However it may be that it can be described on the classical level with the use of spherical polar coordinates. If this supposition is true, and if Eq. (8) is a precessing ellipse, then other precessions can also be developed in this way. The theory can also be developed with the Eulerian angles. In general there are precessions in theta and phi. There is no reason why an orbit should be planar. In general it must be described by a three dimensional theory.

a371stpapernotes1.pdf

This took place last Sunday with interest from Mathematics at Harvard, Umea University Sweden, and Academia Sinica Taiwan. UFT213 gives simple proofs of the antisymmetry of the connection. Definitive Proofs based on UFT99 have been read thousands of times without objection. They mean the end of the Einstein era in general relativity, and the introduction of a torsion based unified field theory, ECE and ECE2. Other parts of Einstein’s work are still acceptable with some modification. Much of the standard mdoel pf physics is obsolete and obsolescence should not be publicy funded. Einstein’s theory of relativity was initially influential, but now it has been shown conclusively that it is riddled with errors. that’s how real progress in ideas is made. All this is well known to the ECE School of Physics, which is independent of vested interest, and which replaces dogma by Baconian science. Last Sunday there was also interest from Physics Oxford in UFT158, which challenges standard particle physics, and from St Peter’s College Oxford in UFT216. There about five hundred UFT papers and books available in English and Spanish, and they are all archived on the Wayback Machine. For some years I have been the most prolific contemporary physicist in the world having produced about two thousand papers, books and essays, and over twenty six thousand diary entries (the well known blog of www.aias.su and www.upitec.org) in nearly forty four years of much higher than average productivity. All my work back to 1973 is read all the time, and it is all archived. Many thanks to all concerned!

The circuit needed to build a power station using energy from spacetime (ES), the patented Osamu Ide circuit, is already available (UFT311), it has been explained exactly by ECE theory (UFT311) and replicated exactly (UFT364) with independent testing apparatus. The ES power stations adn power plants of all kinds, would be by far the best answer for energy needs, because they contain no moving parts, are entirely free of any kind of pollution, and easy and cheap to manufacture. They could serve as power plants on ships, heavy vehicles and cars. They would put fossil burning cabals out of business, and coal and gas and so on could be conserved for the manufacture of clothes, medicine and so on. LENR (low energy nuclear reaction) is explained qualitatively in UFT226 ff. and is another proven technology. Combined with hydroelectricity, these would solve all the energy problems of humankind very easily. Wind turbines are a total disaster which humankind cannot afford.

This is a clear and incisive section as usual from co author Horst Eckardt, especially figure four and the development of a simple dumb bell model for the nutations and precessions of the earth in orbit around the sun. This could lead to a model of the Milankovitch cycles. The computation of the free rotation of the asymmetric top is also full of interest. It is carried out in spherical polar coordinates, and this is much simpler than the use of the Eulerian angles. Both spherical polar coordinates and Eulerian angles should be used for any given problem in order to extract the maximum possible information. The key advance in recent papers is the use of Maxima to solve simultaneous differential equations ( Euler Lagrange equations) without approximation. This gives a huge amount of new information about gyroscope dynamics of all kinds, and more generally, classical rotational dynamics. UFT370 shows that the latter subject is part of Cartan geometry and ECE2 unified field theory.

Sent: 20/02/2017 17:40:06 GMT Standard Time
Subj: Paper 370, section 3

I finished section 3 with the dumbbell model and a calculation of a
freely rotating body in spherical coordinates.

Horst

paper370-3.pdf

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