The Great Beal's Conjecture  The Last Fermat's Theorem (proof) MATHEMATICAL JOURNALS and GREAT BEAL'S CONJECTURE  FERMAT'S LAST THEOREM
New Scientific Paper of Rotor Dynamics, June 1821, 2007 New Theory of Rotor Dynamics: Dynamics of Jeffcott Rotor with Moment Unbalance
Scientific Paper of Rotor Dynamics, 2528 September 2006 Dynamics of Vertical Rotor with Arbitrary Arrangement of Static and Moment Unbalances
New Scientific Paper of Rotor Dynamics (2006) Dynamics of an Outboard Rotor with a Quasi  Static Unbalance Papers about evolution Inertial Mechanics and New Theory of Rotor Dynamics Inertial Mechanics: Base Laws of Rotational Motion of a Free Body; (PDF, 2005, July 4) Base Laws of Translation Motion of a Body (PDF, 2005); The Bounded Rotational and Translation Motion of a Body (a Material Point as Physical Point) on a Circle; (PDF, 2005, July 4) Problems in Classical Mechanics (2005). New Theory of Rotor Dynamics: Disk Rotor Dynamics with Static Unbalance (PDF, 2002); Disk Rotor Dynamics with Static Unbalance Taking into Account Aerodynamic Drag Forces (PDF); Rotor Dynamics with Moment Unbalance (PDF, 2003); Dynamics of UmbrellaType Rotor with Flexible Support (ISCORMA2). For engineers and experts on vibration of machines: Autobalancing (equilibration) of Centrifuges Rotors.
The site is created: May, 16, 2002. The site is regularly updated! Last updating of a site: April, 08, 2009. This site will be useful to everyone who works in the field of rotor dynamics. First of all, the site is created for engineers who project and serve rotors of the machines. Site also represents the big interest for students, postgraduate students and young scientists. For you we have created the correct, clear and simple theory and suggest you to take part in her development. This theory will open for you real opportunities and new prospects. 

Any course of Physics or Engineering Mechanics includes Dynamics of Rigid Body, because the dynamics plays an important role in manufacturing engineering. General merits of basis dynamics creation belong to Galileo Galilei and Isaac Newton. Euler, d'Alamber and Lagrange played a general role in development of analytic methods of body dynamics study using differential and integral calculus. Founders of analytic methods considered the dynamics issues of absolutely rigid body rotation in absolutely rigid supports. Also, they studied the rigid body motion about fixed point and rotation of free body. An approximate theory of gyroscopic effects appeared far later. However, appearance of gyroscope approximate theory based on dynamics of rigid body motion about a support point showed that dynamics problems are more complicated than motion founders of the analytic methods had been studied. Experimentally detected rotor deflection from the rotation axis beginning from some speeds delivered a heavy blow to understanding of gyrodynamics. The classical dynamics theory turns out to be verdant to resonance and rotor selfalignment effects. Unavailability of acceptable theory and insufficient analysis of the gyroprocess physics resulted in vibration theory application to study the rotor dynamics. In 1869, Renkin pioneered the analysis of "vibration" motion of the flexible shaft with rotor. Since then, the rotor dynamics became a part of vibration theory and a proving ground to use the fundamental equations of vibration theory. Over the all time, the vibration theory equations tailored artificially to describe the rotor dynamics, even to the detriment of the process physics. The terms used in the literature reflected superior role of the vibration theory. So, the rotor dynamics had been considering as "bending vibrations of flexible rotors". Due to vagueness of the process physics, the Lagrange method found a wide application in the vibration theory of the rotor dynamics. On of Lagrange method advantages is an opportunity of mechanical approach to problems. However, the Lagrange method provides solutions even if initial data are erroneous. Certainly, highscale application of the vibration theory to solve inappropriate problems could not provide a positive result. When the fundamental equation of the rigid rotor dynamics on flexible shaft is examined carefully, it is clear that these equations are erroneous (see the critical review of rotor dynamics "vibration" theory). It is unlikely that study used erroneous equations is true. We turned back to origins of Physics and Engineering Mechanics and attempted to find what fell within the view of Newton, Euler and Lagrange during gyrodynamics study. We discovered vary important feature and created new "inertial" theory of the rotor dynamics. Ground of the "inertial" theory is new hypothesis and proper understanding of the process physics. The theory provides construction of the acting forces diagram according to requirements of the classical physics and engineering mechanics. Possibility of error reduces to zero and is easy to check by comprehensive analysis of the diagram of acting forces. New "inertial" theory exists already and solves successfully the rotor dynamics issues. The "vibration" theory would be applied within the "inertial" theory as means to solve the typical problems dedicated to the vibration. If classical physics and engineering mechanics include Newtoncreated dynamics theory of rigid body in rigid supports, so "inertial" theory is a further development of the classical theory of rotor dynamics in case of rotor or shaft is not a rigid body. New insight into physics of the rotating body impelled us temporarily refusing differential and integral calculus, and we took successfully a short at solving most problems of dynamics using algebraic equations including Newton's forces and moments. This is not a backward step of mathematics, but forward step of physics. We are just aware that most progressive methods of the mathematical analysis lead to no positive results without sharply defined and accurate selected initial data. Just our understanding of gyrodynamics we attempt to present in our studies, using as simple mathematical tool as possible. It is a satisfaction to note that most of gyrodynamics issues are solved by means of algebraic equations of no more than thirdorder. Such is indeed the example how important to correct insight into the process from the physics point of view. Therefore, our "inertial theory" is comprehensible to anyone.
Rotation of bodies with the variable moments of inertia
We ask to excuse us for a delay of preparation of "Results". A small vacation was very useful.
"Another's"? Do not approach!
Dear colleagues! Has passed three years as the new inertial theory of dynamics of a rotor became accessible to foreign scientists and experts. Six scientific papers have been (in English) offered to scientists for discussion at international conference IFToMM on dynamics of rotors (Sydney  2002), on an international symposium "ISCORMA2" (Gdansk  2003) and on congress IFToMM  2003. Huge on volume the scientific material is submitted in scientific papers in the compressed concise form. The material will bring in updating to bases of such sciences, as: Physics, Theoretical mechanics, the Theory of machines and mechanisms, Dynamics of machines, the Theory of a gyroscope, the Rotor dynamics. Carried out scientific researches supplement existing understanding of rotary motion of material points, rotary motion of bodies, give new understanding of rotation of bodies with variable inertia moments. Acceleration of Coriolis has received an explanation from the point of view of physics. Eller's classical problem about rotation of a body with one point of a support is solved. Bases for creation of new technologies of balancing of rotors are submitted. Circumstances, which have not been noticed by such scientists, as Newton, Eller, Lagrange, underlie researches. Circumstances have essentially changed representation about rotation of bodies, and words " the New theory " has appeared in our scientific papers. We are convinced, that the classical mechanics comes in new stage. All directions of mechanics will be updated. There has stepped time when Everyone should reflect on change of curriculums in average and higher educational institutions. Education, which receives youth, should be correct and correspond to modern fundamental (academic) achievements in a science. Past three years have been allocated on acquaintance of the scientific world with some our researches. It is the first stage. At this stage we aspired to show position of a body concerning a motionless point or a motionless axis at rotary motion. We aspired to give the general method of the solution of similar problems. The first stage has ended. In this connection we bring results of our external activity and the first reaction of the scientific world to our researches. We have prepared the first scientific paper "New Theory of Rotors Dynamics: Disk Rotor Dynamics with Static Unbalance" to take part in work IFToMM Sixth International Conference on Rotor Dynamics. Comments of reviewers were sad. Two reviewers from three reviewers gave a negative response on a scientific paper without any comment. The solution on the publication of the abstract of a scientific paper was accepted. The foreign audience has remained without the full text of a scientific paper. Today we consider, that organizers of conference and the critical review of scientific papers have exerted high moral qualities and courage when have made the solution on the publication of the resume in the collection of works of conference at existence of two negative reviews. We compensated information famine by means of the publication of the full text of a scientific paper on this Site. We have prepared two scientific papers to take part in work The 11th World Congress in Mechanism and Machine Science (IFToMM 2003): "New Theory of Rotor Dynamics: Disk Rotor Dynamics with Static Unbalance Taking info Account Aerodynamic Drag Forces";"New Theory of Rotor Dynamics: Rotor Dynamics with Moment Unbalance". We have been amazed, when IFToMM has made possible and impossible steps for isolation of our scientific papers from a foreign audience (We have in detail enough published correspondence on this question on the Site). We hope, that CHAIR OF THE TECHNICAL COMMITTEE ON ROTOR DYNAMICS Dr. Neville F. Rieger in the survey report will inform about existence of the new theory of a rotor dynamics and will consider and will assess the new inertial theory of a rotor dynamics. At last, we have prepared three scientific papers for participation in symposium ISCORMA2: "New Theory of Rotor Dynamics: Dynamics of a Rotor Having Hinge Support and Elastic Support"; "New Theory of Rotor Dynamics: Dynamics of UmbrellaType Rotor with Flexible Support "; "New Theory of Rotor Dynamics: Dynamics of Vertically Suspended Rotor ". The general method of the solution of problems of dynamics is the important advantage of the new inertial theory. However, the general method has played a negative role. Organizers of a symposium have allowed us to make presentation only one scientific paper ("New Theory of Rotor Dynamics: Dynamics of UmbrellaType Rotor with Flexible Support"). They have explained to us, that we have operated the general method at the solution of other problems of a rotor dynamics. Therefore it is not meaningful to publish solutions of other problems (for example, dynamics of an overhand rotor). In a result the foreign audience could not familiarize with two scientific papers. We emphasize, that foreign scientists have suffered first of all. We have received indemnification for "loss" of two other reports as friendly discussion of a scientific paper.
The founder of the new inertial theory of rotation of a body with variable inertia moments A. Zhivotov and the legendary theorist of vibrating theory Donald E. Bently. Different views on the theory of a rotor dynamics are not a handicap for dialogue.
1. All six scientific
papers have passed the critical review. Reviewers, who considered scientific
papers, have not found mistakes in our inertial theory of a rotor dynamics.
More than 2400 scientists and experts have familiarized with the first
scientific paper, which has been published on our Site in full. Scientists
and experts also have not found out mistakes in the new theory of a rotor
dynamics. It is elements of our inertial theory of a rotor dynamics. However we confirm, that These circumstances of a rotor dynamics are incompatible with the vibrating theory. Scientific magazines have suggested publishing our scientific papers. In our opinion it confirms a scientific solvency of the inertial theory of a rotor dynamics.
2. We have worked hard, that our scientific researches became available to foreign scientists. We bore expenses, which exceeded our incomes in the basic place of work. Despite of our the efforts, only one scientific article from six scientific papers has been published in the foreign official collection in English. Other five scientific papers have not reached a foreign audience because of opinions of reviewers which "have overlooked" to prove these opinions. It is very low efficiency. We do all necessary for correction of a situation. Now translation quality of scientific articles on the English language is checked. All six scientific papers become available to foreign experts and scientists in the near future. In a stage of end there is a monograph in which the complex of questions on dynamics and balancing of a disk rotor will be stated. We reflect on necessity of creation of courses on studying a new rotor dynamics. However we are going to change our economic policy and to refuse gratuitous transfer of the scientific information in English. We had an impression, that some scientists underestimate our information, as it is gratuitous. Moreover, we carry charges to acquaint all with the new theory. Therefore the opinion can be created, that we thrust the unnecessary theory. We wish scientists who think thus, to not get in outsiders.
3. Some scientists ask us. What problems the new theory can solve, which have not been solved with the help of the vibrating theory? Such question is not correct. We declare, that the vibrating theory of a rotor dynamics has not solved correctly any problem. In the scientific papers we already gave the solution of some important problems with the help of the inertial theory. In our opinion more correct the question would be. Whether it is possible to apply the inertial theory to the solution of practical problems? We answer this question. In part Yes. For wide application of the theory it is necessary to get acquainted with our third basic equation of a rotor dynamics. It is possible to create new ways of balancing of rotors, it is possible to create new diagnostic programs, it is possible to learn to define precisely reactions of support if our third basic equation of a rotor dynamics will be known. We prepare for such scientific paper for presentation at the international conference. We are always ready for teamwork on practical application of the new theory if you will make such offer. We wait for your offers. We ask you to support our projects, which we shall prepare for The Science and Technology Center in Ukraine. We hope to get from them financial support. We hope to receive from you such letters. We wait for your letters.
4. Some scientists ask us. In what novelty of the inertial theory will consist? Others declare, that we have deformed the vibrating theory of a rotor dynamics. We hope, that these second scientists can explain the first scientists of the cause who have caused in them negative opinion. The answer to a question on novelty of new theory A. Zhivotov has given repeatedly in the report, which has been read on symposium ISCORMA  2. The quotation from the report below is resulted. 1.Rotorsuspender (rotorbearing) system deflection results in inertial properties changes of general system. We consider these changes as disturbing factor opposing the rotor rotation. 2.To overcome the disturbing factor it is need to apply an additional torque. 3.The rotorbearings system has constraint of rotation and geometrical axes by means of the rotor shaft. The rotor and all its points rotate about the rotation axis with equal angular velocity. However, the shaft deflection results in appearance of system additional degree of freedom allowing turn of the rotor about its own geometrical axis. 4.We think that shaft longitudinal fibers bending stiffness factor (at cross deflection) is significantly less than shaft fibers offsetting stiffness factor. 5. The additional torque results in additional force moment. This force moment is called additional inertial moment (accelerative moment) as distinct from a moment of inertia. Additional inertial moment (accelerative moment) (taking into account the system additional degree of freedom) attempts to turn the rotor about its geometrical axis in direction opposite to the rotor rotation. 6. Also, we believe that rotor dynamics should be studied at rotating coordinates.
5. Questions of education of youth are very important questions from the economic point of view. We count, that universities should not train youth in erroneous theories. It is unprofitable for any state, as the state will be compelled to spend means to retrain youth for the new theory. Therefore we again address to the scientific world. We ask to find mistakes in the inertial theory of rotary motion or to recognize this theory.
6. Thus, the past stage has shown:  scientists have not found out mistakes in the inertial theory  interest to the new theory steadily increases, and
it will gradually obtain recognition.
The best regards, Yu. Zhivotov
XXVI International Readings on astronautic in memory of Academician S.P. Koroliov and other outstanding scientists  pioneers of space exploration. February 27 to March 3, 2002, Moscow, Russia
Sixth International Conference on Rotor Dynamics (IFToMM) September 30 to October 3, 2002, Sydney, Australia
The 11th World Congress in Mechanism and Machine Science August 1821, 2003, Tianjin, China
Second International Symposium on Stability Control of Rotating Machinery, 48 August, 2003, Gdansk, Poland
IUTAM XXI International Congress of Theoretical and Applied Mechanics 15  21 August, 2004, Warsaw, Poland
We are grateful to all who has answered our letters!
We plan participation in the following scientific conferences:
IUTAM XXI International Congress of Theoretical and Applied Mechanics 15  21 August 2004, Warsaw, Poland; Paper: "New theory of rotor dynamics: the equation of the torque"
Second International Symposium on Stability Control of Rotating Machinery, 48 August, 2003, Gdansk, Poland;
The 11th World Congress in Mechanism and Machine Science August 1821, 2003, Tianjin, China;
IFToMM Sixth International Conference on Rotor Dynamics September 30 to October 4, 2002 SYDNEY, AUSTRALIA
ATTENTION! Please contact Yu.G. Zhivotov on the issues connected with organization, copyrights, copying of scientific articles, incorporation of scientific articles into composite and educational books or other technical literature.
Scientific articles written in English.
New theory of rotor dynamics:
1. Disk Rotor Dynamics with Static Unbalance. Abstract. Paper. 2. Disk Rotor Dynamics with Static Unbalance Taking into Account Aerodynamic Drag Forces. Abstract. Paper. 3. Rotor Dynamics with Moment Unbalance. Abstract. Paper. 4. Dynamics of a Rotor Having Hinged Support and Elastic Support. Abstract. Paper. 5. Dynamics of Vertically Suspended Rotor. Abstract. Paper. 6. Dynamics of a Rotor of "Umbrella" Type, with Elastic Support. Abstract. Paper. 7. Disk Rotor Dynamics with Static Unbalance in RealLife Environment. Abstract. Paper.
Scientific articles written in Russian.
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