Thie note expresses any three dimensional orbital motion of m around M in terms of the orbital spherical polar coordinates, Eqs. (18) to (22), and in terms of orbital Euler angles, Eqs. (24) to (28). These equations give the nutations and precessions of the centre of mass of the orbiting object. A three dimensional orbit is much more intricate than a two dimensional orbit. In addition to the orbital kinetic energy there is a spin kinetic energy due to the internal nutations and precessions of the object in orbit. This internal or rotational kinetic energy is 1/2 sigma I sub i omega squared sub i, i = 1, 2, 3, where I sub i are the three principal moments of inertia and omega sub i the angular velocities in the internal frame of the object (e.g. the planet Earth in orbit around the sun). Either the spherical polar coordinates or the Euler angles can be used. In the former case tehre are five Lagrange variables in general, three for the orbit, and two for the rotational kinetic energy. In the latter case there are seven Lagrange variables, four for the orbit and three for the internal or rotational kinetic energy. If the orbit is considered to be planar the number of Lagrange variables is reduced because plane polar coordinates can be used for the orbit. These sets of simultaneous differential equations can be solved by Maxima, giving all the information needed for any problem, for example the Milankovitch cycles, and a gyroscope subjected to an external force or torque. It is matter of setting up and defining the lagrangian, and identifying the Lagrange variables. In principle this is straightforward, and the Maxima code gives all the solutions in tems of various trajectories. This is the great advantage of the code.
Many thanks indeed to Alex Hill, and also Dave Burleigh for posting.
ent: 17/02/2017 19:33:23 GMT Standard Time
Subj: Spanish version of Chapter 4 of ECE2 book
I was planning to send you a chapters 1 to 4 of the Spanish version of the ECE2 book, but it seems to be too heavy to be emailed by Yahoo.
Therefore, I hope you can attach it to the 1 to 3 file you have already posted with little trouble.
The average wind speed in the Betws area now is 7 mph, not enough to start the rotting monuments to corruption known as “wind turbines”. They need 9 mph to start. This area of Mawr is administered by remote and utterly corrupt government which has almost completely destroyed the language, culture and environment over the past sixty years. This is a violation of human rights and I hereby make a formal protest to UNESCO. The latter has warned against the extinction of the Welsh language as a spoken tongue. There are a few of us who still fight for the language in Mawr and fight against overdevelopment and unrestricted monoglot immigration into what used to be a wholly Welsh speaking area. The Welsh Assembly is responsible for the destruction of Betws and Mynydd y Gwair and the Minister responsible did not carry out a simple study of this type, every day for six months. The almost unanimous opinion in Mawr and Gower is that these turbines are the result of a dangerous level of corruption, the frenzied greed for subsidies and rent. This is why a Land Act is necessary to eliminate foreign landlords, and another Act is needed to demolish all turbine plants known to be useless. In Wales they are all essentially useless because of lack of wind, and already decaying into ugly junk. As people wake up one morning to see the destruction of Mynydd y Gwair, they will become enraged by betrayal. I have fought these turbines for twenty five years, many people still do not know that Mynydd y Gwair will be completely destroyed. Being descended from the Princes I describe this destruction as treason, or another assault on Wales. Another Act is needed to set up Broydd Iaith along the lines of the Gealtachti in Ireland. No immigration would be allowed into a Bro Iaith without a severe Welsh language test. All harmful overdevelopment would be prohibited completely, and Welsh language schools reestablished. Otherwise the entire heartland of Welsh speaking Wales will be cynically destroyed.
The equivalent of 86,888 printed pages was downloaded (316.795 megabytes) from 2,515 downloaded memory files (hits) and 497 distinct visits each averaging 3.9 memory pages and 6 minutes, printed pages to hits ratio of 34.55, top ten referrals total 2,210,042, main spiders Google, MSN and Yahoo. Collected ECE2 752, Top ten 629, Evans / Morris 528(est), Collected scientometrics 369, F3(Sp) 206, Barddoniaeth 153, Principles of ECE 105, Eckardt / Lindstrom 87, Collected Proofs 58, Engineering Model 52, UFT88 41, PECE 34, UFT311 33, CEFE 31, Evans Equations 28, ECE2 27, Self charging inverter 23, Llais 14, UFT321 14, PLENR 10, UFT313 15, UFT314 12, UFT315 10, UFT316 12, UFT317 19, UFT318 11, UFT319 14, UFT320 11, UFT322 13, UFT323 8, UFT324 11, UFT325 14, UFT326 12, UFT327 12, UFT328 20, UFT329 16, UFT330 8, UFT331 13, UFT332 10, UFT333 14, UFT334 9, UFT335 11, UFT336 8, UFT337 11, UFT338 6, UFT339 8, UFT340 9, UFT341 14, UFT342 7, UFT343 11, UFT344 15, UFT345 9, UFT346 10, UFT347 11, UFT348 9, UFT349 11, UFT351 14, UFT352 20, UFT353 15, UFT354 19, UFT355 8, UFT356 17, UFT357 17, UFT358 12, UFT359 16, UFT360 10, UFT361 10, UFT362 17, UFT363 15, UFT364 17, UFT365 11, UFT366 27, UFT367 27, UFT368 31, UFT369 29 to date in February 2017. City of Winnipeg UFT section, University of Quebec Trois Rivieres UFT366 – UFT369; University of Aarhus Denmark UFT114; Arizona State University Homopolar; Cornell University UFT42; Pennsylvania State University general; Texas A and M University UFT128; University of Chicago general; United States Naval Academy UFT149; Institute for Advanced Scientific Studies University of Paris Saclay Criticism of Vacuum Big Bang by Stephen Crothers; City University of Hong Kong UFT4; Bose Institute Calcutta UFT88; INFN Padua UFT175 (Italian National Institute for Nuclear Physics); Sony Corporation general; Philippines National Electrification Administration general. Intense interest all sectors, updated usage file attached for February 2017.
This is an extension of the dumb bell model resulting in six simultaneous differential equations giving all the information about the dynamics of a dumbbell in orbit about a mass M. The axis of the dumbbell can be thought of as a diameter of the earth in orbit about the sun. The nutations and precessions of the axis can be linked to the Milankovitch cycles. This model can be extended to any number n of masses given the necessary computer power to solve 3n equations in 3n unknowns. It is clear why the Milankowitch cycles are intricate, and why weather patterns and climate patterns are also intricate.
I intend to write up Horst’s calculation as a Note, and develop frame transformations with the novel spin connection matrix discovered in UFT369 and UFT370, then write up my Sections 1 and 2. Those who can read the access report every morning can see hundreds of UFT papers all being studied, including all fifty five UFT books and papers to date. There is no further strategic impediment to the advance of ECE and ECE2. Indeed they are familiar mainstream ideas in physics. ” ……..on ne resist pas a l’invasion des idees” (Victor Hugo). As General Patton was fond of saying something as follows: a static defence is one of the follies of mankind. It can be outflanked and small pockets of resistance left behind. He was descended from General Hugh Mercer of the Revolutionary War. I know that Patton was wild and difficult and careless of lives, but this saying shows how futile it is to try to order the tide not to come in. Your boots just fill with obsolete water – yesterday’s snow.
In the first half of February 2017 there was the usual intense international interest, including interest from the following universities in the world’s top twenty (* denotes repeat visits): Caltech, Harvard*, Princeton, Penn State, Stanford, Texas A and M, Univ. California San Diego, EPF Lausanne, Cambridge and Imperial. There was also a visit from the U.S. Joint Chiefs of Staff at the Pentagon. Ivy League visits were from: Harvard, Dartmouth, Princeton and Stanford. Harvard and Stanford are often ranked the world’s number one. Essentially all the university visits were from the top two hundred or so, and this has been a steady pattern since 2003. The best in the world are open minded about new ideas and accept our distance methods of research and teaching. Otherwise they would not study our work, which consists of the development of a perfect unified field theory checked all the time by computer. Our work exists alongside the standard model of physics, and that is how it should be, that is how ideas progress.
Texas Dallas was founded in 1961 and is ranked 273 in the world by Webometrics, 469 by Times, 300 by Shanghai and 380 by QS. It has 26,793 students. Texas Austin and Texas A and M are both in the world’s top twenty and staff and students from Texas have regularly studied ECE theory since inception in March 2003. UFT88 has been studied tens of thousands of times without objection and is generally accepted as the paper that ends the Einstein era of gravitational physics. It is part of Alwyn van der Merwe’s “post Einsteinian paradigm shift” now being studied worldwide every day, in all the best universities, as ECE and ECE2 theories. The final version of UFT88 is UFT313, the Jacobi Cartan Evans identity, the 1902 second Bianchi identity corrected for torsion. The obsolete Einstein field equation was based directly on the 1902 second Bianchi identity of geometry. The understanding of physics in terms of geometry goes back to ancient times. The Greeks thought of geometry as beauty, and made a deliberate flaw in the Parthenon so as not to offend the gods with microscopic human vanity. The Periclean Parthenon was constructed on a geometrical basis and became the blueprint for architecture for two thousand five hundred years. Cartan’s geometry is also a perfect construct, and will be the same in two thousand five hundred years more. This makes the dubious assumption that humankind will not blow itself to pieces or completely destroy the planet.
The average wind speed in the Betws area is now 2 mph, well below the 9 mph needed to start the useless wind turbines. The political will is needed to demolish all wind turbines in Wales at developer expense and to re establish some semblance of democracy. This means that developers will have to pay back millions in subsidies, repair the tremendous damage done to rare ecologies, and also be prosecuted. I think that the appropriate sentence for directors is twenty years hard labour down a reopened drift mine, producing steam coal for use as a source of many useful products. Ministers could be employed as colliers.
The equivalent of 120,782 printed pages was downloaded (440.376 megabytes) from 2,202 downloaded memory files (hits) and 440 distinct visits each averaging 4.3 memory pages and 7 minutes, printed pages to hits ratio of 54.85, top ten referrals total 2,209,535, main spiders Google, MSN and Yahoo. Collected ECE2 702, Top ten 594, Evans / Morris 495(est), Collected Scientometrics 319, F3(Sp) 186, Barddoniaeth 153, Principles of ECE 99, Eckardt / Lindstrom 84, Collected Proofs 58, Engineering Model 49, Autobiography volumes one and two 41, UFT88 38, PECE 33, UFT311 32, CEFE 31, ECE2 25, Self charging inverter 22, UFT321 14, Llais 10, PLENR 8, UFT313 12, UFT314 12, UFT315 9, UFT316 12, UFT317 18, UFT318 11, UFT319 14, UFT320 9, UFT322 12, UFT323 8, UFT324 9, UFT325 12, UFT326 12, UFT327 12, UFT328 20, UFT329 16, UFT330 8, UFT331 12, UFT332 8, UFT333 14, UFT334 9, UFT335 11, UFT336 8, UFT337 9, UFT338 6, UFT339 7, UFT340 8, UFT341 13, UFT342 7, UFT343 11, UFT344 14, UFT345 9, UFT346 10, UFT347 9, UFT348 8, UFT349 11, UFT351 13, UFT352 18, UFT353 15, UFT354 17, UFT355 7, UFT356 17, UFT357 15, UFT358 10, UFT359 15, UFT360 9, UFT361 10, UFT362 15, UFT363 14, UFT364 16, UFT365 11, UFT366 25, UFT367 25, UFT368 28, UFT369 25 to date in February 2017. Students University of Waterloo UFT213; Deusu search engine Omnia Opera; Students Harvard University publications; University of Pittsburg UFT283; Stanford University UFT239; Fujitsu Spain general; School of Telecommunications Engineering Polytechnic University of Madrid AIAS Fellows; Italian National Agency for New Technologies, Energy and Sustainable Development Cassaccia Research Centre general; Stur Institute of Linguistics Slovak Academy of Sciences general. Intense interest all sectors, updated usage file attached for February 2017.