Deterministic Mechanism of Irreversibility

2018 ◽  
Vol 14 (3) ◽  
pp. 5708-5733 ◽  
Author(s):  
Vyacheslav Michailovich Somsikov

The analytical review of the papers devoted to the deterministic mechanism of irreversibility (DMI) is presented. The history of solving of the irreversibility problem is briefly described. It is shown, how the DMI was found basing on the motion equation for a structured body. The structured body was given by a set of potentially interacting material points. The taking into account of the body’s structure led to the possibility of describing dissipative processes. This possibility caused by the transformation of the body’s motion energy into internal energy. It is shown, that the condition of holonomic constraints, which used for obtaining of the canonical formalisms of classical mechanics, is excluding the DMI in Hamiltonian systems. The concepts of D-entropy and evolutionary non-linearity are discussed. The connection between thermodynamics and the laws of classical mechanics is shown. Extended forms of the Lagrange, Hamilton, Liouville, and Schrödinger equations, which describe dissipative processes, are presented.

2016 ◽  
Vol 30 (04) ◽  
pp. 1650018 ◽  
Author(s):  
V. M. Somsikov

In this paper, necessity of creation of mechanics of structured particles is discussed. The way to create this mechanics within the laws of classical mechanics with the use of energy equation is shown. The occurrence of breaking of time symmetry within the mechanics of structured particles is shown, as well as the introduction of concept of entropy in the framework of classical mechanics. The way to create the mechanics of non-equilibrium systems in the thermodynamic approach is shown. It is also shown that the use of hypothesis of holonomic constraints while deriving the canonical Lagrange equation made it impossible to describe irreversible dynamics. The difference between the mechanics of structured particles and the mechanics of material points is discussed. It is also shown that the matter is infinitely divisible according to the laws of classical mechanics.


1969 ◽  
Vol 12 (2) ◽  
pp. 209-212 ◽  
Author(s):  
J. E. Marsden

As is well known, there is an intimate connection between geodesic flows and Hamiltonian systems. In fact, if g is a Riemannian, or pseudo-Riemannian metric on a manifold M (we think of M as q-space or the configuration space), we may define a smooth function Tg on the cotangent bundle T*M (q-p-space, or the phase space). This function is the kinetic energy of q, and locally is given by


Author(s):  
Hiroaki Yoshimura ◽  
Kenji Soya

This paper develops a discrete Hamiltonian system with holonomic constraints with Geometric Constraint Stabilization. It is first shown that constrained mechanical systems with nonconservative external forces can be formulated by using canonical symplectic structures in the context of Hamiltonian systems. Second, it is shown that discrete holonomic Hamiltonian systems can be developed via the discretization based on the Backward Differentiation Formula and also that geometric constraint stabilization can be incorporated into the discrete Hamiltonian systems. It is demonstrated that the proposed method enables one to stabilize constraint violations effectively in comparison with conventional methods such as Baumgarte Stabilization and Gear–Gupta–Leimkuhler Stabilization, together with an illustrative example of linkage mechanisms.


2019 ◽  
pp. 142-148
Author(s):  
Valentina Shakula

The article deals with the peculiarities of the activity of Pereyaslav-Khmelnytsky bakery in the period from 1977 to 1985, when Pereyaslav-Khmelnytsky bakery at the food factory was reorganized into an independent enterprise. This theme has been studied already fragmentarily by such scholars as M. Sikorsky, D. Shvydky, I. Goncharenko, O. Goncharenko, N. Onoprienko, but fundamentally is developed for the first time. In the process of work, the author used methods of search, analysis, synthesis and generalization, which allowed to investigate the problem and find out some facts from the history of the enterprises. The purpose of this study was to establish the peculiarities of the production activity of Pereyaslav-Khmelnytsky bakery in the period of its establishment as an independent food enterprise through an analytical review of archival sources, publications of periodicals and systematization of the information received. According to the intended purpose, the following tasks are set: to investigate the history of the functioning of the Pereyaslav-Khmelnytsky bread factory in 1977-1985, to establish the main directions of the development of production and personnel policy, to identify the features of the range, directions and problems of its implementation. It was revealed that during this period of its production, Pereyaslav-Khmelnytsky bakery has undergone a long path of formation and development: from a small half-baked of Pereyaslav-Khmelnytsky foodstuff factory, that baked bread in brick burning stoves on solid fuels to a powerful enterprise, that works on high-tech equipment and provides high-quality bakery products, not only to the population of the city of Pereyaslav-Khmelnytsky and the district, but also to the nearest settlements of Boryspil, Baryshiv, Yagotyn districts of the Kyiv region, Zolotonosha and Drabiv districts of Cherkasy region. It is important that the gross output figures increase each year. The range of bakery products and the quality of products have increased significantly, despite the periodic problems associated with providing the bakery with quality raw materials and fuel materials for continuous operation. This influenced positively the economic performance of the enterprise and the entire region. It was also established that the administration of the bakery in the specified period paid special attention to the increase of professional qualifications of its employees, improvement of conditions and safety of their work, legal education and social security of people, which significantly reduced the percentage of personnel turnover. It was emphasized, that the important point of the backery's activity was the re-equipment of sanitary rooms and food units, because of the duration of work shift on bakery department was 24 hours for workers. Workers were provided by quality rest during lunch breaks. It has been proved, that the modernization of industrial baking equipment was not actually carried out at this time, if not taking into account the annual fragmentary and cosmetic repairs, because it was built also a new premises with the latest at that time technical equipment with a production capacity of 65 tons per day. The administration and the team of the bakery were seriously preparing themselves for work under the new conditions, as new mechanisms required not only experience, but also knowledge of the technical characteristics of the equipment and the release of new types of bakery products. Pereyaslav-Khmelnytsky bakery played an important role in the economy of the city and the region during the first half of the 80's. XX century, as it was one of the leading enterprises of the food industry in the region.


1998 ◽  
Vol 12 (03) ◽  
pp. 309-360
Author(s):  
Toshio Kawai

The Titius–Bode law governs the planet distribution in our Solar system. In this paper a possible explanation is proposed based on inelastic collision effects among planetessimals during the evolution of the Solar system. The main purpose of this paper is, however, to introduce a strategy to study phenomena driven by rare but drastic events such as colllisions in the planetary problem. Many complex systems evolve through rare but violent events, so that an efficient strategy to simulate such systems is desirable. An event-driven strategy is proposed in this article, and is used to produce many runs of 108 year evolution history of planetary systems. I have found that the Titius–Bode law holds approximately, if the gravitational effect (scattering) and the collisions are taken into account. The result illustrates the importance of inelastic collisions, which are often neglected in the standard classical mechanics courses. Therefore, for completeness, other simpler particle systems under the effect of inelastc collisions, such as one-dimensional systems, are also included.


1976 ◽  
Vol 63 (2) ◽  
pp. 53-62 ◽  
Author(s):  
C. Truesdell

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2959
Author(s):  
Lili Xia ◽  
Mengmeng Wu ◽  
Xinsheng Ge

Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference type of symmetry preserving invariants are constructed based on the three points of the lattice and the characteristic equations. The difference scheme is constructed by using these discrete invariants. An example is presented to illustrate the applications of the results. The solutions of the invariant numerical schemes are compared to the noninvariant ones, the standard and the exact solutions.


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