48 research outputs found
Landscape planning for Ukrainian rural communities: challenges, outputs, prospects
A significant number of economic, social and environmental problems have accumulated in all areas of Ukraine and pose a serious obstacle to sustainable development. Those problems are particularly acute in the rural areas. The local rural communities in Ukraine have the lowest indicators of economic development, significant social problems, including particularly acute demographic and employment problems, and an unfavorable ecological situation caused by poor municipal infrastructure, land degradation, etc. The vast majority of the rural communities in Ukraine have no plans for their own territoriesβ development. In such circumstances, the introduction of landscape planning tools is an effective means of identifying the existing development problems and environmental management issues, as well as of defining the best ways for the integrated development of the local rural communities. A number of reasons prevents introduction of such planning in Ukraine, including the flaws in the legislation, lack of interest among managers of rural communities and low activity of local people on the issues which determine the future of their settlements.
However, there are examples of successful implementation of landscape planning tools in designing of the plans of rural communitiesβ development. The authors were a part of the team which, for the first time in Ukraine, undertook this research in the Stepanetsky rural council in Cherkassy region. The results of the research have been welcomed by the management, the residence and the members of the village council and they are being practically implemented.
The foregoing demonstrates the relevance and feasibility of landscape planning tools implementation in Ukraine directed at addressing and resolving the problems of the rural communities
Das KernkraftwerksunglΓΌck von Tschernobyl: geographische Aspekte der Folgen in der Ukraine
On April 26, 1986 the most serious accident in the history of the peaceful use of nuclear energy took place in the Chernobyl nuclear power plant in the immediate vicinity of the town of Pripet. Especially the surrounding areas that now belong to the republics of Byelorussia, Ukraine and Russia were affected. Within a radius of 30 to 50 km around the power plant human life, plants and animals, soils and water were most severely affected by radioactivity. The population had to be evacuated from this area rapidly. Economic activities had to be reduced in a much larger area. Like many other scientists and technicians, geographers also participated in the research on the consequences and on damage reduction. In spite of the contamination, vegetation became an "ally" of man, surprisingly fast. Pioneer plants supported the attempts to minimize the spread of radioactively contaminated substances by their reoccupation of former agricultural land. Observing this development, trees were planted purposively, to stabilize the radio-ecological situation. Extensive geomorphological, geochemical and geoecological research allowed to determine areas of further output and accumulation of radionuclides and their transportation routes. The economy in the contaminated areas was affected to different degrees. Seriously affected were agriculture and forestry in the Ukrainian Polesye. There is virtually no more production in the industrial towns of Pripet, Poleskoe, Chernobyl and Narodichi. Other areas and sites have changes in their production and their functions. The management has to mind constantly the danger of a further spreading of radionuclides and of the contamination of products. The most serious result of radioactive contamination is the worsening of the ecological conditions of life of the population. Additional dangers, on which little research has been done, result from the combination of "normal" pollution and the nuclear accident. The life styles of millions of people were deformed, thousands became ill and the constant expectation of additional diseases led to an enormous psychiological stress. The relief provided by the state is not insignificant, but because of the recession it encounters diverse limitations. The regeneration of the conditions of life is a great task for spatial research and regional planning. Especially the alleged mutual interdependencies between physical and social environmental conditions and developmental measures have to be examined, in spite of the urgent need for action. It is necessary to coordinate the projects of all the affected republics: Ukraine, Byelorussia and Russia
Die RelativitΓ€t des Strukturbegriffs "peripherer Raum" in den Nachfolgestaaten der Sowjetunion
1959 von R. PREBISCH im Rahmen globaler WirtschaftsraumerΓΆrterungen β IndustrielΓ€nder hier, βEntwicklungslΓ€nderβ dort β erstmals in der Geographie gebraucht, wurden die Begriffe ,Peripherieβ und ,periphere RΓ€umeβ vom Ende der 1960er Jahre an vor allem bei der Charakterisierung der wirtschaftsrΓ€umlichen VerhΓ€ltnisse eines Landes benutzt. Sie stehen in abstrahierender Ansprache den Begriffen ,Zentrumβ und ,Ballungsraumβ gegenΓΌber und damit fΓΌr lΓ€ndliche und andere von der Landesentwicklung vernachlΓ€ssigte ,Passivβ-RΓ€ume. In jΓΌngerer Zeit tauchen diese Begriffe hΓ€ufig in Arbeiten zur Wirtschaftstransformation in den LΓ€ndern des ΓΆstlichen Europa auf. Obwohl ihr Gebrauch dabei generell nicht zu VerstΓ€ndnisschwierigkeiten fΓΌhrt, empfiehlt es sich, bei Untersuchungen der VerhΓ€ltnisse in den Nachfolgestaaten der ehemaligen Sowjetunion die Besonderheit zu beachten, dass in sowjetischer Zeit auch Zentren und Ballungsgebiete Merkmale der Peripherie zwangslΓ€ufig angenommen haben. Durch diverse ideologisch bestimmte politische, ΓΆkonomische und administrative MaΓnahmen entstanden RΓ€ume, die hier als ,relativ peripherβ bezeichnet werden und deren Charaktreistika auch die gegenwΓ€rtigen Prozesse beeinflussen. In der Ukraine, die im vorliegenden Artikel als Beispiel dient, kam es unter anderem dazu, dass (1) selbst in StΓ€dten wie Kiew, Dnipropetrowsk oder Lwiw (Lemberg) infrastrukturelle und institutionelle Eigenentwicklungen nur eingeschrΓ€nkt mΓΆglich ware, dass (2) Industriegebiete wie das Donbass oder die ErdΓΆlfΓΆrdergebiete in den Vorkarpaten und im Dnjeper-Tiefland technologisch und strukturell zurΓΌckbleiben mussten, dass (3) Industriezentren und -gebiete wegen bewusster unvollendeter Produktionszyklen in ihrer Bedeutung beschnitten wurden. Sie alle gerieten in die relative Peripherie und sind deshalb heute eine Ursache fΓΌr die wirt schaftliche Krise und die generellen Schwierigkeiten im Transformationsprozess in der Ukraine. Nur mit Hilfe neuartiger Initiativen und allmΓ€hlicher Modernisierung von Strukturen, Verfahren und Beziehungen (z.B. in Euroregionen) kΓΆnnen die entstandenen Nachteile β Monostrukturen, Unterentwicklung, fehlende industrielle Endfertigung, geringe Anbindung β sowohl der relativen wie der wirklichen peripheren RΓ€ume ΓΌberwunden bzw. bis zu einem bestimmten Grad ΓΌberwunden werden
βNEWβ GEOGRAPHY IN UKRAINIAN REALITY: MISSION AND DEVELOPMENT TRENDS
It is a well-known fact that science is international in nature and has no national boundaries. The authors of the paper presented herein used the combination of the words βnew geographyβ and βUkrainian realityβ in attempt to focus attention on the complexities of geography in a fundamental change of social development objectives and methods of management. The authors are concerned about the decrease in the degree of influence of geography on various spheres of human life and consider the distinctive characteristics of geographical science through the presentation of the features of its construction methods (object-oriented, subject-oriented, and problem-solving methods). The weakness of geography is manifested in the lack of knowledge refined to natural laws. But it is precisely a geographer who forms a specific individual model matrix of relations using geographic logic his/her perceptions.Given the current transformation processes taking place in Ukraine, there is now a new international challenge in complex conditions of development: limited resources; environmental, demographic, and financial problems; and much moreββre-discovering of the world.β It is natural that each country meets challenges in its own ways. Therefore, by using the combination of the words βnew geographyβ and βUkrainian realities,β the authors attempt, on the one hand, to focus attention on the complexities of the modern formation and development of geography and, on the other hand, to emphasize the advantages of geographical studies of various spheres of human activity. They demonstrate that in Ukraine, own vectors and the development trends of geography were formed and brought real results that were positively valued not only by the scientific community, but also by society as a whole. There is a large gap between scientific and educational geography. Two possible options to reduce this gap are suggested. Examples of the implementation in Ukraine of some projects based on achieving βnew geographyβ are provided
Die ΓΆkologische Situation in der Ukraine und GrundsΓ€tze einer ΓΆkologischen Landesentwicklungspolitik
The marked deterioration of the state of the environment in the Uk raine in the course of the last twenty years and its increasingly negative affects on broad areas of the private and social life has lead to a close scientific connection between geography and ecology. In this context and at the same time as concrete, region-related examinations, theoretic studies have also been carried out. This lead to a differentiation and definition of a whole range of terms and research aspects, which will be elaborated on in the introductory phase. As a term with a particular importance for the characterisation of the geographic-ecological situation, the ecological safety will be given special, closer attention. The background for the widespread and deeply-rooted reduction in the ecological safety is formed by the large extent of population density, the high level of agricultural development, the intensive extraction of natural resources and rocks, the widespread employment of obsolete technology with high energy consumption and huge quantities of exhaust substances and the catastrophe from Chernobyl. The ecological situation is extremely critical -given conventional pollution- in the industrial areas of Krivoi Rog-Dnepropet rovsk, Donetsk, Lugansk-Lysytshansk and Cis-Carpathian, as well as in the agglomerations and/or urban centres of Kiev, Lvov (Lemberg), Kharkov, Zaporozhye, Odessa, Mariupol and Mikolayiv. In order to ensure improvements, it is necessary for the economy to be reformed, for fundamental technological changes to be made and for the social and intellectual recovery to be implemented. This design of life in the Ukrainian society to comply with ecological principles occurs at the same time and in the same contents as the international efforts for the long-term development of national economies
State Institution Β«Romodanov Neurosurgery Institute of the National Academy of Medical Sciences of UkraineΒ» celebrates the 70th anniversary!
In 2020, State Institution βRomodanov Neurosurgery Institute of NAMS of Ukraineβ occupies the glorious anniversary β 70 years since its foundation. By order of the Minister of Health of the USSR No. 439 of July 3, 1950, the structure and staffing of the Kyiv Research Institute of Neurosurgery were approved in the amount of 291 units. The regulations on the Institute were approved by the Ministry of Health of Ukraine on August 4, 1950.Departments of Neuro-oncology, Acute Trauma of the Central and Peripheral Nervous System, Neurovascular Pathology, Restorative Neurosurgery and Pediatric Neurosurgery were established in the structure of the Institute.The Neurosurgery Institute in different years was headed by: O.I. Arutiunov (1951β1964), A.P. Romodanov (1964β1993), Yu.P. Zozulia (1993β2013), E.G. Pedachenko (since February 2013).Today, the Instituteβs clinical base consists of 15 specialized departments with 361 beds, where up to 7,000 patients are treated annually. In the out-patient department, from 30,000 to 40,000 patients receive counseling every year. In 15 operating rooms, more than 5,000 operations of the highest complexity are performed per year. Comprehensive examination and treatment of patients are provided by the scientific and diagnostic departments and laboratories.Currently, the Neurosurgery Institute staff amounts for 1,008 employees, including 38 doctors of medicine, 14 professors, and 80 candidates of sciences.Currently, the State Institution βRomodanov Neurosurgery Institute of NAMS of Ukraineβ occupies a leading position in the diagnosing and treatment of neurosurgical pathology in Ukraine. The Institute has established and operates scientific schools on neurotrauma, neuro-oncology, vascular pathology of the brain and spinal cord, minimally invasive spinal neurosurgery, neurotransplantation, and neuroimmunology, which are headed and developed by leading specialists of the Institute. Throughout the existence of the Institute, training of scientific personnel is constantly carried out.The prospects for further development of the Neurosurgery Institute are intended in wide implementation of neuromodulation method, the development of gene therapy, the use of invasive electrophysiological studies and modern neuroimaging, the improvement and widespread adoption of endoscopic techniques in the neurosurgical practice, the development and implementation of methods of reconstructive neurosurgery and the treatment of chronic pain syndromes. It is extremely important for Ukraine to create a scientific and practical center for neurotrauma and a modern rehabilitation center on the basis of the Institute
Π‘ΠΈΠ½ΡΠ΅Π· ΡΠ° ΠΊΠ»Π°ΡΠΈΡΡΠΊΠ°ΡΡΡ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΈΡ ΡΡΠ°ΡΠΊΡΠΎΡΡΠΉ ΡΡΡ Ρ Π²Π°Π½ΡΠ°ΠΆΡ Ρ ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ
The study of possibilities of geometric modeling of non-chaotic periodic paths of motion of a load of a swinging spring and its variants has been continued. In literature, a swinging spring is considered as a kind of mathematical pendulum which consists of a point load attached to a massless spring. The second end of the spring is fixed motionless. Pendular oscillations of the spring in a vertical plane are considered in conditions of maintaining straightness of its axis. The searched path of the spring load was modeled using Lagrange second-degree equations.Urgency of the topic is determined by the need to study conditions of dissociation from chaotic oscillations of elements of mechanical structures including springs, namely definition of rational parameter values to provide periodic paths of their oscillations. Swinging springs can be used as mechanical illustrations in the study of complex technological processes of dynamic systems when nonlinearly coupled oscillatory components of the system exchange energy with each other.The obtained results make it possible to add periodic curves as Β«parametersΒ» in a graphic form to the list of numerical parameters of the swinging spring. That is, to determine numerical values of the parameters that would ensure existence of a predetermined form of the periodic path of motion of the spring load. An example of calculation of the load mass was considered based on the known stiffness of the spring, its length without load, initial conditions of initialization of oscillations as well as (attention!) the form of periodic path of this load. Periodic paths of the load motion for the swinging spring modifications (such as suspension to the movable carriage whose axis coincides with the mathematical pendulum) and two swinging springs with a common moving load and with different mounting points were obtained.The obtained results are illustrated by computer animation of oscillations of corresponding swinging springs and their varieties.The results can be used as a paradigm for studying nonlinear coupled systems as well as for calculation of variants of mechanical devices where springs influence oscillation of their elements and in cases when it is necessary to separate from chaotic motions of loads and provide periodic paths of their motion in technologies using mechanical devicesΠΡΠΎΠ΄ΠΎΠ»ΠΆΠ΅Π½ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠ΅ΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π΅Ρ
Π°ΠΎΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΉ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ Π³ΡΡΠ·Π° ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ ΠΈ Π΅Π΅ ΡΠ°Π·Π½ΠΎΠ²ΠΈΠ΄Π½ΠΎΡΡΠ΅ΠΉ. Π Π»ΠΈΡΠ΅ΡΠ°ΡΡΡΠ΅ ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½ΠΎΠΉ (swinging spring) Π½Π°Π·ΡΠ²Π°ΡΡ ΡΠ°Π·Π½ΠΎΠ²ΠΈΠ΄Π½ΠΎΡΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ°, ΡΠΎΡΡΠΎΡΡΠ΅Π³ΠΎ ΠΈΠ· ΡΠΎΡΠ΅ΡΠ½ΠΎΠ³ΠΎ Π³ΡΡΠ·Π°, ΠΏΡΠΈΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½Π½ΠΎΠ³ΠΎ ΠΊ Π½Π΅Π²Π΅ΡΠΎΠΌΠΎΠΉ ΠΏΡΡΠΆΠΈΠ½Π΅. ΠΡΠΎΡΠΎΠΉ ΠΊΠΎΠ½Π΅Ρ ΠΏΡΡΠΆΠΈΠ½Ρ ΡΠΈΠΊΡΠΈΡΡΠ΅ΡΡΡ Π½Π΅ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎ. Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠΎΠ²ΡΠ΅ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΡ ΠΏΡΡΠΆΠΈΠ½Ρ Π² Π²Π΅ΡΡΠΈΠΊΠ°Π»ΡΠ½ΠΎΠΉ ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠΈ ΠΏΡΠΈ ΡΡΠ»ΠΎΠ²ΠΈΠΈ ΡΠΎΡ
ΡΠ°Π½Π΅Π½ΠΈΡ ΠΏΡΡΠΌΠΎΠ»ΠΈΠ½Π΅ΠΉΠ½ΠΎΡΡΠΈ Π΅Π΅ ΠΎΡΠΈ. ΠΡΠΊΠΎΠΌΠ°Ρ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΡ Π³ΡΡΠ·Π° ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΡΠ΅ΡΡΡ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ°Π³ΡΠ°Π½ΠΆΠ° Π²ΡΠΎΡΠΎΠ³ΠΎ ΡΠΎΠ΄Π°.ΠΠΊΡΡΠ°Π»ΡΠ½ΠΎΡΡΡ ΡΠ΅ΠΌΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΡΡΡ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΠΎΡΠΌΠ΅ΠΆΠ΅Π²Π°Π½ΠΈΡ ΠΎΡ Ρ
Π°ΠΎΡΠΈΡΠ½ΡΡ
ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ² ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ, Π² ΡΠΎΡΡΠ°Π² ΠΊΠΎΡΠΎΡΡΡ
Π²Ρ
ΠΎΠ΄ΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ, Π° ΠΈΠΌΠ΅Π½Π½ΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ°ΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² Π΄Π»Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΉ ΠΈΡ
ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ. ΠΠ°ΡΠ°ΡΡΠΈΠ΅ΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ ΠΊΠ°ΠΊ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈΠ»Π»ΡΡΡΡΠ°ΡΠΈΠΈ ΠΏΡΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ»ΠΎΠΆΠ½ΡΡ
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ, ΠΊΠΎΠ³Π΄Π° Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎ ΡΠ²ΡΠ·Π°Π½Π½ΡΠ΅ ΠΊΠΎΠ»Π΅Π±Π°ΡΠ΅Π»ΡΠ½ΡΠ΅ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΠΎΠ±ΠΌΠ΅Π½ΠΈΠ²Π°ΡΡΡΡ ΡΠ½Π΅ΡΠ³ΠΈΠ΅ΠΉ ΠΌΠ΅ΠΆΠ΄Ρ ΡΠΎΠ±ΠΎΠΉ.ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ ΠΏΡΠΈΠΎΠ±ΡΠΈΡΡ ΠΊ ΠΏΠ΅ΡΠ΅ΡΠ½Ρ ΡΠΈΡΠ»ΠΎΠ²ΡΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ Π΅ΡΠ΅ ΠΈ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΊΡΠΈΠ²ΡΠ΅ ΠΊΠ°ΠΊ "ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡ" Π² Π³ΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠΎΡΠΌΠ΅. Π’. Π΅. ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΡΡ ΡΠΈΡΠ»ΠΎΠ²ΡΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ², ΠΊΠΎΡΠΎΡΡΠ΅ Π±Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ»ΠΈ ΡΡΡΠ΅ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΠ΅ Π·Π°Π²Π΅Π΄ΠΎΠΌΠΎ Π·Π°Π΄Π°Π½Π½ΠΎΠΉ ΡΠΎΡΠΌΡ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΈ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ Π³ΡΡΠ·Π° ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½ ΠΏΡΠΈΠΌΠ΅Ρ Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΡ ΠΌΠ°ΡΡΡ Π³ΡΡΠ·Π° ΠΏΠΎ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΠΌ ΠΆΠ΅ΡΡΠΊΠΎΡΡΠΈ ΠΏΡΡΠΆΠΈΠ½Ρ, Π΅Π΅ Π΄Π»ΠΈΠ½Π΅ Π±Π΅Π· Π½Π°Π³ΡΡΠ·ΠΊΠΈ, Π½Π°ΡΠ°Π»ΡΠ½ΡΠΌ ΡΡΠ»ΠΎΠ²ΠΈΡΠΌ ΠΈΠ½ΠΈΡΠΈΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ, Π° ΡΠ°ΠΊΠΆΠ΅ (Π²Π½ΠΈΠΌΠ°Π½ΠΈΠ΅) ΡΠΎΡΠΌΠ΅ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΈ ΡΡΠΎΠ³ΠΎ Π³ΡΡΠ·Π°. ΠΠΎΠ»ΡΡΠ΅Π½Ρ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΈ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ Π³ΡΡΠ·Π° Π΄Π»Ρ ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΠΉ ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ,, ΡΠ°ΠΊΠΈΡ
ΠΊΠ°ΠΊ ΠΏΠΎΠ΄Π²Π΅ΡΠ΅Π½Π½ΠΎΠΉ ΠΊ ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎΠΉ ΡΠ΅Π»Π΅ΠΆΠΊΠ΅, ΠΎΡΡ ΠΊΠΎΡΠΎΡΠΎΠΉ ΡΠΎΠ²ΠΏΠ°Π΄Π°Π΅Ρ Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΌ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠΎΠΌ. Π ΡΠ°ΠΊΠΆΠ΅ Π΄Π²ΡΡ
ΠΊΠ°ΡΠ°ΡΡΠΈΡ
ΡΡ ΠΏΡΡΠΆΠΈΠ½ Ρ ΠΎΠ±ΡΠΈΠΌ ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΡΠΌ Π³ΡΡΠ·ΠΎΠΌ ΠΈ Ρ ΡΠ°Π·Π½ΡΠΌΠΈ ΡΠΎΡΠΊΠ°ΠΌΠΈ ΠΊΡΠ΅ΠΏΠ»Π΅Π½ΠΈΡ.ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΡΠΎΠΈΠ»Π»ΡΡΡΡΠΈΡΠΎΠ²Π°Π½Ρ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΡΠΌΠΈ Π°Π½ΠΈΠΌΠ°ΡΠΈΡΠΌΠΈ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΡ
ΠΊΠ°ΡΠ°ΡΡΠΈΡ
ΡΡ ΠΏΡΡΠΆΠΈΠ½ ΠΈ ΠΈΡ
ΡΠ°Π·Π½ΠΎΠ²ΠΈΠ΄Π½ΠΎΡΡΠ΅ΠΉ.Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ ΠΊΠ°ΠΊ ΠΏΠ°ΡΠ°Π΄ΠΈΠ³ΠΌΡ Π΄Π»Ρ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ
ΡΠ²ΡΠ·Π°Π½Π½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ, Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠΈ ΡΠ°ΡΡΠ΅ΡΠ°Ρ
Π²Π°ΡΠΈΠ°Π½ΡΠΎΠ² ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΡΡΠΎΠΉΡΡΠ², Π³Π΄Π΅ ΠΏΡΡΠΆΠΈΠ½Ρ Π²Π»ΠΈΡΡΡ Π½Π° ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠ΅ ΠΈΡ
ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ². Π ΡΠ°ΠΊΠΆΠ΅ Π² ΡΠ»ΡΡΠ°ΡΡ
, ΠΊΠΎΠ³Π΄Π° Π² ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΡ
ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΡΡΠΎΠΉΡΡΠ² Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎ ΠΎΡΠΌΠ΅ΠΆΠ΅Π²Π°ΡΡΡΡ ΠΎΡ Ρ
Π°ΠΎΡΠΈΡΠ½ΡΡ
ΠΏΠ΅ΡΠ΅ΠΌΠ΅ΡΠ΅Π½ΠΈΠΉ Π³ΡΡΠ·ΠΎΠ² ΠΈ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΡΡ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΈ ΠΈΡ
Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡΠΡΠΎΠ΄ΠΎΠ²ΠΆΠ΅Π½ΠΎ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΌΠΎΠΆΠ»ΠΈΠ²ΠΎΡΡΠ΅ΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΡΠ²Π°Π½Π½Ρ Π½Π΅Ρ
Π°ΠΎΡΠΈΡΠ½ΠΈΡ
ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΈΡ
ΡΡΠ°ΡΠΊΡΠΎΡΡΠΉ ΡΡΡ
Ρ Π²Π°Π½ΡΠ°ΠΆΡ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΡΠ° ΡΡ ΡΡΠ·Π½ΠΎΠ²ΠΈΠ΄ΡΠ². Π Π»ΡΡΠ΅ΡΠ°ΡΡΡΡ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΎΡ (swinging spring) Π½Π°Π·ΠΈΠ²Π°ΡΡΡ ΡΡΠ·Π½ΠΎΠ²ΠΈΠ΄ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ½ΠΎΠ³ΠΎ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ°, ΡΠΊΠΈΠΉ ΡΠΊΠ»Π°Π΄Π°ΡΡΡΡΡ Π· ΡΠΎΡΠΊΠΎΠ²ΠΎΠ³ΠΎ Π²Π°Π½ΡΠ°ΠΆΡ, ΠΏΡΠΈΡΠ΄Π½Π°Π½ΠΎΠ³ΠΎ Π΄ΠΎ Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ. ΠΡΡΠ³ΠΈΠΉ ΠΊΡΠ½Π΅ΡΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΡΡΠΊΡΡΡΡΡΡΡ Π½Π΅ΡΡΡ
ΠΎΠΌΠΎ. Π ΠΎΠ·Π³Π»ΡΠ΄Π°ΡΡΡΡΡ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠΎΠ²Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Π½Ρ ΠΏΡΡΠΆΠΈΠ½ΠΈ Ρ Π²Π΅ΡΡΠΈΠΊΠ°Π»ΡΠ½ΡΠΉ ΠΏΠ»ΠΎΡΠΈΠ½Ρ Π·Π° ΡΠΌΠΎΠ²ΠΈ Π·Π±Π΅ΡΠ΅ΠΆΠ΅Π½Π½Ρ ΠΏΡΡΠΌΠΎΠ»ΡΠ½ΡΠΉΠ½ΠΎΡΡΡ ΡΡ ΠΎΡΡ. Π¨ΡΠΊΠ°Π½Π° ΡΡΠ°ΡΠΊΡΠΎΡΡΡ Π²Π°Π½ΡΠ°ΠΆΡ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΠΌΠΎΠ΄Π΅Π»ΡΡΡΡΡΡ Π· Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½ΡΠΌ ΡΡΠ²Π½ΡΠ½Ρ ΠΠ°Π³ΡΠ°Π½ΠΆΠ° Π΄ΡΡΠ³ΠΎΠ³ΠΎ ΡΠΎΠ΄Ρ.ΠΠΊΡΡΠ°Π»ΡΠ½ΡΡΡΡ ΡΠ΅ΠΌΠΈ Π²ΠΈΠ·Π½Π°ΡΠ°ΡΡΡΡΡ Π½Π΅ΠΎΠ±Ρ
ΡΠ΄Π½ΡΡΡΡ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΡΠΌΠΎΠ² Π²ΡΠ΄ΠΌΠ΅ΠΆΡΠ²Π°Π½Π½Ρ Π²ΡΠ΄ Ρ
Π°ΠΎΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ Π΅Π»Π΅ΠΌΠ΅Π½ΡΡΠ² ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΠΉ, Π΄ΠΎ ΡΠΊΠ»Π°Π΄Ρ ΡΠΊΠΈΡ
Π²Ρ
ΠΎΠ΄ΡΡΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ, Π° ΡΠ°ΠΌΠ΅ Π²ΠΈΠ·Π½Π°ΡΠ΅Π½Π½Ρ ΡΠ°ΡΡΠΎΠ½Π°Π»ΡΠ½ΠΈΡ
Π·Π½Π°ΡΠ΅Π½Ρ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ² Π΄Π»Ρ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΈΡ
ΡΡΠ°ΡΠΊΡΠΎΡΡΠΉ ΡΡ
ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ. Π₯ΠΈΡΠ½Ρ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΠΌΠΎΠΆΠ½Π° Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°ΡΠΈ ΡΠΊ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½Ρ ΡΠ»ΡΡΡΡΠ°ΡΡΡ ΠΏΡΠΈ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΡΠΊΠ»Π°Π΄Π½ΠΈΡ
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΡΡΠ½ΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠ² Π΄ΠΈΠ½Π°ΠΌΡΡΠ½ΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ, ΠΊΠΎΠ»ΠΈ Π½Π΅Π»ΡΠ½ΡΠΉΠ½ΠΎ Π·Π²'ΡΠ·Π°Π½Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π»ΡΠ½Ρ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠΈ ΡΠΈΡΡΠ΅ΠΌΠΈ ΠΎΠ±ΠΌΡΠ½ΡΡΡΡΡΡ Π΅Π½Π΅ΡΠ³ΡΡΡ ΠΌΡΠΆ ΡΠΎΠ±ΠΎΡ.ΠΠ΄Π΅ΡΠΆΠ°Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡΡΡ Π΄ΠΎΠ»ΡΡΠΈΡΠΈ Π΄ΠΎ ΠΏΠ΅ΡΠ΅Π»ΡΠΊΡ ΡΠΈΡΠ»ΠΎΠ²ΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ² Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΡΠ΅ ΠΉ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½Ρ ΠΊΡΠΈΠ²Ρ ΡΠΊ "ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈ" Π² Π³ΡΠ°ΡΡΡΠ½ΡΠΉ ΡΠΎΡΠΌΡ. Π’ΠΎΠ±ΡΠΎ Π²ΠΈΠ·Π½Π°ΡΠΈΡΠΈ ΡΠΈΡΠ»ΠΎΠ²Ρ Π·Π½Π°ΡΠ΅Π½Π½Ρ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ², ΡΠΊΡ Π± Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠΈΠ»ΠΈ ΡΡΠ½ΡΠ²Π°Π½Π½Ρ Π½Π°ΠΏΠ΅ΡΠ΅Π΄ Π·Π°Π΄Π°Π½ΠΎΡ ΡΠΎΡΠΌΠΈ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΎΡ ΡΡΠ°ΡΠΊΡΠΎΡΡΡ ΡΡΡ
Ρ Π²Π°Π½ΡΠ°ΠΆΡ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ. Π ΠΎΠ·Π³Π»ΡΠ½ΡΡΠΎ ΠΏΡΠΈΠΊΠ»Π°Π΄ ΠΎΠ±ΡΠΈΡΠ»Π΅Π½Π½Ρ ΠΌΠ°ΡΠΈ Π²Π°Π½ΡΠ°ΠΆΡ Π·Π° Π²ΡΠ΄ΠΎΠΌΠΈΠΌΠΈ ΠΆΠΎΡΡΡΠΊΡΡΡΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ, ΡΡ Π΄ΠΎΠ²ΠΆΠΈΠ½ΠΎΡ Π±Π΅Π· Π½Π°Π²Π°Π½ΡΠ°ΠΆΠ΅Π½Π½Ρ, ΠΏΠΎΡΠ°ΡΠΊΠΎΠ²ΠΈΠΌΠΈ ΡΠΌΠΎΠ²Π°ΠΌΠΈ ΡΠ½ΡΡΡΠ°Π»ΡΠ·Π°ΡΡΡ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ, Π° ΡΠ°ΠΊΠΎΠΆ (ΡΠ²Π°Π³Π°) ΡΠΎΡΠΌΠΎΡ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΎΡ ΡΡΠ°ΡΠΊΡΠΎΡΡΡ ΡΡΠΎΠ³ΠΎ Π²Π°Π½ΡΠ°ΠΆΡ. ΠΠ΄Π΅ΡΠΆΠ°Π½ΠΎ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½Ρ ΡΡΠ°ΡΠΊΡΠΎΡΡΡ ΡΡΡ
Ρ Π²Π°Π½ΡΠ°ΠΆΡ Π΄Π»Ρ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠ°ΡΡΠΉ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ - ΡΠ°ΠΊΠΈΡ
ΡΠΊ ΠΏΡΠ΄Π²ΡΡΠ΅Π½ΠΎΡ Π΄ΠΎ ΡΡΡ
ΠΎΠΌΠΎΠ³ΠΎ Π²ΡΠ·ΠΊΠ° Ρ Π²ΡΡΡ ΡΠΊΠΎΡ Π·Π±ΡΠ³Π°ΡΡΡΡΡ Π· ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ½ΠΈΠΌ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠΎΠΌ. Π ΡΠ°ΠΊΠΎΠΆ Π΄Π²ΠΎΡ
Ρ
ΠΈΡΠ½ΠΈΡ
ΠΏΡΡΠΆΠΈΠ½ Π·Ρ ΡΠΏΡΠ»ΡΠ½ΠΈΠΌ ΡΡΡ
ΠΎΠΌΠΈΠΌ Π²Π°Π½ΡΠ°ΠΆΠ΅ΠΌ Ρ Π· ΡΡΠ·Π½ΠΈΠΌΠΈ ΡΠΎΡΠΊΠ°ΠΌΠΈ ΠΊΡΡΠΏΠ»Π΅Π½Π½Ρ.ΠΠ΄Π΅ΡΠΆΠ°Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΏΡΠΎΡΠ»ΡΡΡΡΠΎΠ²Π°Π½ΠΎ ΠΊΠΎΠΌΠΏ'ΡΡΠ΅ΡΠ½ΠΈΠΌΠΈ Π°Π½ΡΠΌΠ°ΡΡΡΠΌΠΈ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΠΈΡ
Ρ
ΠΈΡΠ½ΠΈΡ
ΠΏΡΡΠΆΠΈΠ½ ΡΠ° ΡΡ
ΡΡΠ·Π½ΠΎΠ²ΠΈΠ΄ΡΠ².Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΌΠΎΠΆΠ½Π° Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°ΡΠΈ ΡΠΊ ΠΏΠ°ΡΠ°Π΄ΠΈΠ³ΠΌΡ Π΄Π»Ρ Π²ΠΈΠ²ΡΠ΅Π½Π½Ρ Π½Π΅Π»ΡΠ½ΡΠΉΠ½ΠΈΡ
Π·Π²'ΡΠ·Π°Π½ΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ, Π° ΡΠ°ΠΊΠΎΠΆ ΠΏΡΠΈ ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΠ°Ρ
Π²Π°ΡΡΠ°Π½ΡΡΠ² ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΈΡ
ΠΏΡΠΈΡΡΡΠΎΡΠ², Π΄Π΅ ΠΏΡΡΠΆΠΈΠ½ΠΈ Π²ΠΏΠ»ΠΈΠ²Π°ΡΡΡ Π½Π° ΠΊΠΎΠ»ΠΈΠ²Π°Π½Π½Ρ ΡΡ
Π΅Π»Π΅ΠΌΠ΅Π½ΡΡΠ². Π ΡΠ°ΠΊΠΎΠΆ Ρ Π²ΠΈΠΏΠ°Π΄ΠΊΠ°Ρ
, ΠΊΠΎΠ»ΠΈ Π² ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΡΡΡ
Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΈΡ
ΠΏΡΠΈΡΡΡΠΎΡΠ² Π½Π΅ΠΎΠ±Ρ
ΡΠ΄Π½ΠΎ Π²ΡΠ΄ΠΌΠ΅ΠΆΡΠ²Π°ΡΠΈΡΡ Π²ΡΠ΄ Ρ
Π°ΠΎΡΠΈΡΠ½ΠΈΡ
ΠΏΠ΅ΡΠ΅ΠΌΡΡΠ΅Π½Ρ Π²Π°Π½ΡΠ°ΠΆΡΠ² Ρ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠΈΡΠΈ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½Ρ ΡΡΠ°ΡΠΊΡΠΎΡΡΡ ΡΡ
ΡΡΡ
Π‘ΠΈΠ½ΡΠ΅Π· ΡΠ° ΠΊΠ»Π°ΡΠΈΡΡΠΊΠ°ΡΡΡ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΈΡ ΡΡΠ°ΡΠΊΡΠΎΡΡΠΉ ΡΡΡ Ρ Π²Π°Π½ΡΠ°ΠΆΡ Ρ ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ
The study of possibilities of geometric modeling of non-chaotic periodic paths of motion of a load of a swinging spring and its variants has been continued. In literature, a swinging spring is considered as a kind of mathematical pendulum which consists of a point load attached to a massless spring. The second end of the spring is fixed motionless. Pendular oscillations of the spring in a vertical plane are considered in conditions of maintaining straightness of its axis. The searched path of the spring load was modeled using Lagrange second-degree equations.Urgency of the topic is determined by the need to study conditions of dissociation from chaotic oscillations of elements of mechanical structures including springs, namely definition of rational parameter values to provide periodic paths of their oscillations. Swinging springs can be used as mechanical illustrations in the study of complex technological processes of dynamic systems when nonlinearly coupled oscillatory components of the system exchange energy with each other.The obtained results make it possible to add periodic curves as Β«parametersΒ» in a graphic form to the list of numerical parameters of the swinging spring. That is, to determine numerical values of the parameters that would ensure existence of a predetermined form of the periodic path of motion of the spring load. An example of calculation of the load mass was considered based on the known stiffness of the spring, its length without load, initial conditions of initialization of oscillations as well as (attention!) the form of periodic path of this load. Periodic paths of the load motion for the swinging spring modifications (such as suspension to the movable carriage whose axis coincides with the mathematical pendulum) and two swinging springs with a common moving load and with different mounting points were obtained.The obtained results are illustrated by computer animation of oscillations of corresponding swinging springs and their varieties.The results can be used as a paradigm for studying nonlinear coupled systems as well as for calculation of variants of mechanical devices where springs influence oscillation of their elements and in cases when it is necessary to separate from chaotic motions of loads and provide periodic paths of their motion in technologies using mechanical devicesΠΡΠΎΠ΄ΠΎΠ»ΠΆΠ΅Π½ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠ΅ΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π΅Ρ
Π°ΠΎΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΉ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ Π³ΡΡΠ·Π° ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ ΠΈ Π΅Π΅ ΡΠ°Π·Π½ΠΎΠ²ΠΈΠ΄Π½ΠΎΡΡΠ΅ΠΉ. Π Π»ΠΈΡΠ΅ΡΠ°ΡΡΡΠ΅ ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½ΠΎΠΉ (swinging spring) Π½Π°Π·ΡΠ²Π°ΡΡ ΡΠ°Π·Π½ΠΎΠ²ΠΈΠ΄Π½ΠΎΡΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ°, ΡΠΎΡΡΠΎΡΡΠ΅Π³ΠΎ ΠΈΠ· ΡΠΎΡΠ΅ΡΠ½ΠΎΠ³ΠΎ Π³ΡΡΠ·Π°, ΠΏΡΠΈΡΠΎΠ΅Π΄ΠΈΠ½Π΅Π½Π½ΠΎΠ³ΠΎ ΠΊ Π½Π΅Π²Π΅ΡΠΎΠΌΠΎΠΉ ΠΏΡΡΠΆΠΈΠ½Π΅. ΠΡΠΎΡΠΎΠΉ ΠΊΠΎΠ½Π΅Ρ ΠΏΡΡΠΆΠΈΠ½Ρ ΡΠΈΠΊΡΠΈΡΡΠ΅ΡΡΡ Π½Π΅ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎ. Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠΎΠ²ΡΠ΅ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΡ ΠΏΡΡΠΆΠΈΠ½Ρ Π² Π²Π΅ΡΡΠΈΠΊΠ°Π»ΡΠ½ΠΎΠΉ ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠΈ ΠΏΡΠΈ ΡΡΠ»ΠΎΠ²ΠΈΠΈ ΡΠΎΡ
ΡΠ°Π½Π΅Π½ΠΈΡ ΠΏΡΡΠΌΠΎΠ»ΠΈΠ½Π΅ΠΉΠ½ΠΎΡΡΠΈ Π΅Π΅ ΠΎΡΠΈ. ΠΡΠΊΠΎΠΌΠ°Ρ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΡ Π³ΡΡΠ·Π° ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΡΠ΅ΡΡΡ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ°Π³ΡΠ°Π½ΠΆΠ° Π²ΡΠΎΡΠΎΠ³ΠΎ ΡΠΎΠ΄Π°.ΠΠΊΡΡΠ°Π»ΡΠ½ΠΎΡΡΡ ΡΠ΅ΠΌΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΡΡΡ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΠΎΡΠΌΠ΅ΠΆΠ΅Π²Π°Π½ΠΈΡ ΠΎΡ Ρ
Π°ΠΎΡΠΈΡΠ½ΡΡ
ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ² ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ, Π² ΡΠΎΡΡΠ°Π² ΠΊΠΎΡΠΎΡΡΡ
Π²Ρ
ΠΎΠ΄ΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ, Π° ΠΈΠΌΠ΅Π½Π½ΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ°ΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² Π΄Π»Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΉ ΠΈΡ
ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ. ΠΠ°ΡΠ°ΡΡΠΈΠ΅ΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ ΠΊΠ°ΠΊ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈΠ»Π»ΡΡΡΡΠ°ΡΠΈΠΈ ΠΏΡΠΈ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ»ΠΎΠΆΠ½ΡΡ
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ, ΠΊΠΎΠ³Π΄Π° Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎ ΡΠ²ΡΠ·Π°Π½Π½ΡΠ΅ ΠΊΠΎΠ»Π΅Π±Π°ΡΠ΅Π»ΡΠ½ΡΠ΅ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΠΎΠ±ΠΌΠ΅Π½ΠΈΠ²Π°ΡΡΡΡ ΡΠ½Π΅ΡΠ³ΠΈΠ΅ΠΉ ΠΌΠ΅ΠΆΠ΄Ρ ΡΠΎΠ±ΠΎΠΉ.ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ ΠΏΡΠΈΠΎΠ±ΡΠΈΡΡ ΠΊ ΠΏΠ΅ΡΠ΅ΡΠ½Ρ ΡΠΈΡΠ»ΠΎΠ²ΡΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ Π΅ΡΠ΅ ΠΈ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΊΡΠΈΠ²ΡΠ΅ ΠΊΠ°ΠΊ "ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡ" Π² Π³ΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠΎΡΠΌΠ΅. Π’. Π΅. ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΡΡ ΡΠΈΡΠ»ΠΎΠ²ΡΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ², ΠΊΠΎΡΠΎΡΡΠ΅ Π±Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΠ»ΠΈ ΡΡΡΠ΅ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΠ΅ Π·Π°Π²Π΅Π΄ΠΎΠΌΠΎ Π·Π°Π΄Π°Π½Π½ΠΎΠΉ ΡΠΎΡΠΌΡ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΈ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ Π³ΡΡΠ·Π° ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ. Π Π°ΡΡΠΌΠΎΡΡΠ΅Π½ ΠΏΡΠΈΠΌΠ΅Ρ Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΡ ΠΌΠ°ΡΡΡ Π³ΡΡΠ·Π° ΠΏΠΎ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΠΌ ΠΆΠ΅ΡΡΠΊΠΎΡΡΠΈ ΠΏΡΡΠΆΠΈΠ½Ρ, Π΅Π΅ Π΄Π»ΠΈΠ½Π΅ Π±Π΅Π· Π½Π°Π³ΡΡΠ·ΠΊΠΈ, Π½Π°ΡΠ°Π»ΡΠ½ΡΠΌ ΡΡΠ»ΠΎΠ²ΠΈΡΠΌ ΠΈΠ½ΠΈΡΠΈΠ°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ, Π° ΡΠ°ΠΊΠΆΠ΅ (Π²Π½ΠΈΠΌΠ°Π½ΠΈΠ΅) ΡΠΎΡΠΌΠ΅ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΈ ΡΡΠΎΠ³ΠΎ Π³ΡΡΠ·Π°. ΠΠΎΠ»ΡΡΠ΅Π½Ρ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΈ Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡ Π³ΡΡΠ·Π° Π΄Π»Ρ ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΠΉ ΠΊΠ°ΡΠ°ΡΡΠ΅ΠΉΡΡ ΠΏΡΡΠΆΠΈΠ½Ρ,, ΡΠ°ΠΊΠΈΡ
ΠΊΠ°ΠΊ ΠΏΠΎΠ΄Π²Π΅ΡΠ΅Π½Π½ΠΎΠΉ ΠΊ ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎΠΉ ΡΠ΅Π»Π΅ΠΆΠΊΠ΅, ΠΎΡΡ ΠΊΠΎΡΠΎΡΠΎΠΉ ΡΠΎΠ²ΠΏΠ°Π΄Π°Π΅Ρ Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠΌ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠΎΠΌ. Π ΡΠ°ΠΊΠΆΠ΅ Π΄Π²ΡΡ
ΠΊΠ°ΡΠ°ΡΡΠΈΡ
ΡΡ ΠΏΡΡΠΆΠΈΠ½ Ρ ΠΎΠ±ΡΠΈΠΌ ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΡΠΌ Π³ΡΡΠ·ΠΎΠΌ ΠΈ Ρ ΡΠ°Π·Π½ΡΠΌΠΈ ΡΠΎΡΠΊΠ°ΠΌΠΈ ΠΊΡΠ΅ΠΏΠ»Π΅Π½ΠΈΡ.ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΡΠΎΠΈΠ»Π»ΡΡΡΡΠΈΡΠΎΠ²Π°Π½Ρ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΡΠΌΠΈ Π°Π½ΠΈΠΌΠ°ΡΠΈΡΠΌΠΈ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡΠΈΡ
ΠΊΠ°ΡΠ°ΡΡΠΈΡ
ΡΡ ΠΏΡΡΠΆΠΈΠ½ ΠΈ ΠΈΡ
ΡΠ°Π·Π½ΠΎΠ²ΠΈΠ΄Π½ΠΎΡΡΠ΅ΠΉ.Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡ ΠΊΠ°ΠΊ ΠΏΠ°ΡΠ°Π΄ΠΈΠ³ΠΌΡ Π΄Π»Ρ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ
ΡΠ²ΡΠ·Π°Π½Π½ΡΡ
ΡΠΈΡΡΠ΅ΠΌ, Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠΈ ΡΠ°ΡΡΠ΅ΡΠ°Ρ
Π²Π°ΡΠΈΠ°Π½ΡΠΎΠ² ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΡΡΠΎΠΉΡΡΠ², Π³Π΄Π΅ ΠΏΡΡΠΆΠΈΠ½Ρ Π²Π»ΠΈΡΡΡ Π½Π° ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠ΅ ΠΈΡ
ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ². Π ΡΠ°ΠΊΠΆΠ΅ Π² ΡΠ»ΡΡΠ°ΡΡ
, ΠΊΠΎΠ³Π΄Π° Π² ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΡΡ
ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΡΡΠΎΠΉΡΡΠ² Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎ ΠΎΡΠΌΠ΅ΠΆΠ΅Π²Π°ΡΡΡΡ ΠΎΡ Ρ
Π°ΠΎΡΠΈΡΠ½ΡΡ
ΠΏΠ΅ΡΠ΅ΠΌΠ΅ΡΠ΅Π½ΠΈΠΉ Π³ΡΡΠ·ΠΎΠ² ΠΈ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΡΡ ΠΏΠ΅ΡΠΈΠΎΠ΄ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΡΠ°Π΅ΠΊΡΠΎΡΠΈΠΈ ΠΈΡ
Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡΠΡΠΎΠ΄ΠΎΠ²ΠΆΠ΅Π½ΠΎ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΠΌΠΎΠΆΠ»ΠΈΠ²ΠΎΡΡΠ΅ΠΉ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΡΠ²Π°Π½Π½Ρ Π½Π΅Ρ
Π°ΠΎΡΠΈΡΠ½ΠΈΡ
ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΈΡ
ΡΡΠ°ΡΠΊΡΠΎΡΡΠΉ ΡΡΡ
Ρ Π²Π°Π½ΡΠ°ΠΆΡ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΡΠ° ΡΡ ΡΡΠ·Π½ΠΎΠ²ΠΈΠ΄ΡΠ². Π Π»ΡΡΠ΅ΡΠ°ΡΡΡΡ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΎΡ (swinging spring) Π½Π°Π·ΠΈΠ²Π°ΡΡΡ ΡΡΠ·Π½ΠΎΠ²ΠΈΠ΄ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ½ΠΎΠ³ΠΎ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠ°, ΡΠΊΠΈΠΉ ΡΠΊΠ»Π°Π΄Π°ΡΡΡΡΡ Π· ΡΠΎΡΠΊΠΎΠ²ΠΎΠ³ΠΎ Π²Π°Π½ΡΠ°ΠΆΡ, ΠΏΡΠΈΡΠ΄Π½Π°Π½ΠΎΠ³ΠΎ Π΄ΠΎ Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ. ΠΡΡΠ³ΠΈΠΉ ΠΊΡΠ½Π΅ΡΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΡΡΠΊΡΡΡΡΡΡΡ Π½Π΅ΡΡΡ
ΠΎΠΌΠΎ. Π ΠΎΠ·Π³Π»ΡΠ΄Π°ΡΡΡΡΡ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠΎΠ²Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Π½Ρ ΠΏΡΡΠΆΠΈΠ½ΠΈ Ρ Π²Π΅ΡΡΠΈΠΊΠ°Π»ΡΠ½ΡΠΉ ΠΏΠ»ΠΎΡΠΈΠ½Ρ Π·Π° ΡΠΌΠΎΠ²ΠΈ Π·Π±Π΅ΡΠ΅ΠΆΠ΅Π½Π½Ρ ΠΏΡΡΠΌΠΎΠ»ΡΠ½ΡΠΉΠ½ΠΎΡΡΡ ΡΡ ΠΎΡΡ. Π¨ΡΠΊΠ°Π½Π° ΡΡΠ°ΡΠΊΡΠΎΡΡΡ Π²Π°Π½ΡΠ°ΠΆΡ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΠΌΠΎΠ΄Π΅Π»ΡΡΡΡΡΡ Π· Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½ΡΠΌ ΡΡΠ²Π½ΡΠ½Ρ ΠΠ°Π³ΡΠ°Π½ΠΆΠ° Π΄ΡΡΠ³ΠΎΠ³ΠΎ ΡΠΎΠ΄Ρ.ΠΠΊΡΡΠ°Π»ΡΠ½ΡΡΡΡ ΡΠ΅ΠΌΠΈ Π²ΠΈΠ·Π½Π°ΡΠ°ΡΡΡΡΡ Π½Π΅ΠΎΠ±Ρ
ΡΠ΄Π½ΡΡΡΡ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΡΠΌΠΎΠ² Π²ΡΠ΄ΠΌΠ΅ΠΆΡΠ²Π°Π½Π½Ρ Π²ΡΠ΄ Ρ
Π°ΠΎΡΠΈΡΠ½ΠΈΡ
ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ Π΅Π»Π΅ΠΌΠ΅Π½ΡΡΠ² ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΈΡ
ΠΊΠΎΠ½ΡΡΡΡΠΊΡΡΠΉ, Π΄ΠΎ ΡΠΊΠ»Π°Π΄Ρ ΡΠΊΠΈΡ
Π²Ρ
ΠΎΠ΄ΡΡΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ, Π° ΡΠ°ΠΌΠ΅ Π²ΠΈΠ·Π½Π°ΡΠ΅Π½Π½Ρ ΡΠ°ΡΡΠΎΠ½Π°Π»ΡΠ½ΠΈΡ
Π·Π½Π°ΡΠ΅Π½Ρ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ² Π΄Π»Ρ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠ΅Π½Π½Ρ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΈΡ
ΡΡΠ°ΡΠΊΡΠΎΡΡΠΉ ΡΡ
ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ. Π₯ΠΈΡΠ½Ρ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΠΌΠΎΠΆΠ½Π° Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°ΡΠΈ ΡΠΊ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½Ρ ΡΠ»ΡΡΡΡΠ°ΡΡΡ ΠΏΡΠΈ Π΄ΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½Π½Ρ ΡΠΊΠ»Π°Π΄Π½ΠΈΡ
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΡΡΠ½ΠΈΡ
ΠΏΡΠΎΡΠ΅ΡΡΠ² Π΄ΠΈΠ½Π°ΠΌΡΡΠ½ΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ, ΠΊΠΎΠ»ΠΈ Π½Π΅Π»ΡΠ½ΡΠΉΠ½ΠΎ Π·Π²'ΡΠ·Π°Π½Ρ ΠΊΠΎΠ»ΠΈΠ²Π°Π»ΡΠ½Ρ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠΈ ΡΠΈΡΡΠ΅ΠΌΠΈ ΠΎΠ±ΠΌΡΠ½ΡΡΡΡΡΡ Π΅Π½Π΅ΡΠ³ΡΡΡ ΠΌΡΠΆ ΡΠΎΠ±ΠΎΡ.ΠΠ΄Π΅ΡΠΆΠ°Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡΡΡ Π΄ΠΎΠ»ΡΡΠΈΡΠΈ Π΄ΠΎ ΠΏΠ΅ΡΠ΅Π»ΡΠΊΡ ΡΠΈΡΠ»ΠΎΠ²ΠΈΡ
ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ² Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ ΡΠ΅ ΠΉ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½Ρ ΠΊΡΠΈΠ²Ρ ΡΠΊ "ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΈ" Π² Π³ΡΠ°ΡΡΡΠ½ΡΠΉ ΡΠΎΡΠΌΡ. Π’ΠΎΠ±ΡΠΎ Π²ΠΈΠ·Π½Π°ΡΠΈΡΠΈ ΡΠΈΡΠ»ΠΎΠ²Ρ Π·Π½Π°ΡΠ΅Π½Π½Ρ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΡΠ², ΡΠΊΡ Π± Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠΈΠ»ΠΈ ΡΡΠ½ΡΠ²Π°Π½Π½Ρ Π½Π°ΠΏΠ΅ΡΠ΅Π΄ Π·Π°Π΄Π°Π½ΠΎΡ ΡΠΎΡΠΌΠΈ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΎΡ ΡΡΠ°ΡΠΊΡΠΎΡΡΡ ΡΡΡ
Ρ Π²Π°Π½ΡΠ°ΠΆΡ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ. Π ΠΎΠ·Π³Π»ΡΠ½ΡΡΠΎ ΠΏΡΠΈΠΊΠ»Π°Π΄ ΠΎΠ±ΡΠΈΡΠ»Π΅Π½Π½Ρ ΠΌΠ°ΡΠΈ Π²Π°Π½ΡΠ°ΠΆΡ Π·Π° Π²ΡΠ΄ΠΎΠΌΠΈΠΌΠΈ ΠΆΠΎΡΡΡΠΊΡΡΡΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ, ΡΡ Π΄ΠΎΠ²ΠΆΠΈΠ½ΠΎΡ Π±Π΅Π· Π½Π°Π²Π°Π½ΡΠ°ΠΆΠ΅Π½Π½Ρ, ΠΏΠΎΡΠ°ΡΠΊΠΎΠ²ΠΈΠΌΠΈ ΡΠΌΠΎΠ²Π°ΠΌΠΈ ΡΠ½ΡΡΡΠ°Π»ΡΠ·Π°ΡΡΡ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ, Π° ΡΠ°ΠΊΠΎΠΆ (ΡΠ²Π°Π³Π°) ΡΠΎΡΠΌΠΎΡ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½ΠΎΡ ΡΡΠ°ΡΠΊΡΠΎΡΡΡ ΡΡΠΎΠ³ΠΎ Π²Π°Π½ΡΠ°ΠΆΡ. ΠΠ΄Π΅ΡΠΆΠ°Π½ΠΎ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½Ρ ΡΡΠ°ΡΠΊΡΠΎΡΡΡ ΡΡΡ
Ρ Π²Π°Π½ΡΠ°ΠΆΡ Π΄Π»Ρ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠ°ΡΡΠΉ Ρ
ΠΈΡΠ½ΠΎΡ ΠΏΡΡΠΆΠΈΠ½ΠΈ - ΡΠ°ΠΊΠΈΡ
ΡΠΊ ΠΏΡΠ΄Π²ΡΡΠ΅Π½ΠΎΡ Π΄ΠΎ ΡΡΡ
ΠΎΠΌΠΎΠ³ΠΎ Π²ΡΠ·ΠΊΠ° Ρ Π²ΡΡΡ ΡΠΊΠΎΡ Π·Π±ΡΠ³Π°ΡΡΡΡΡ Π· ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ½ΠΈΠΌ ΠΌΠ°ΡΡΠ½ΠΈΠΊΠΎΠΌ. Π ΡΠ°ΠΊΠΎΠΆ Π΄Π²ΠΎΡ
Ρ
ΠΈΡΠ½ΠΈΡ
ΠΏΡΡΠΆΠΈΠ½ Π·Ρ ΡΠΏΡΠ»ΡΠ½ΠΈΠΌ ΡΡΡ
ΠΎΠΌΠΈΠΌ Π²Π°Π½ΡΠ°ΠΆΠ΅ΠΌ Ρ Π· ΡΡΠ·Π½ΠΈΠΌΠΈ ΡΠΎΡΠΊΠ°ΠΌΠΈ ΠΊΡΡΠΏΠ»Π΅Π½Π½Ρ.ΠΠ΄Π΅ΡΠΆΠ°Π½Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΏΡΠΎΡΠ»ΡΡΡΡΠΎΠ²Π°Π½ΠΎ ΠΊΠΎΠΌΠΏ'ΡΡΠ΅ΡΠ½ΠΈΠΌΠΈ Π°Π½ΡΠΌΠ°ΡΡΡΠΌΠΈ ΠΊΠΎΠ»ΠΈΠ²Π°Π½Ρ Π²ΡΠ΄ΠΏΠΎΠ²ΡΠ΄Π½ΠΈΡ
Ρ
ΠΈΡΠ½ΠΈΡ
ΠΏΡΡΠΆΠΈΠ½ ΡΠ° ΡΡ
ΡΡΠ·Π½ΠΎΠ²ΠΈΠ΄ΡΠ².Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΈ ΠΌΠΎΠΆΠ½Π° Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°ΡΠΈ ΡΠΊ ΠΏΠ°ΡΠ°Π΄ΠΈΠ³ΠΌΡ Π΄Π»Ρ Π²ΠΈΠ²ΡΠ΅Π½Π½Ρ Π½Π΅Π»ΡΠ½ΡΠΉΠ½ΠΈΡ
Π·Π²'ΡΠ·Π°Π½ΠΈΡ
ΡΠΈΡΡΠ΅ΠΌ, Π° ΡΠ°ΠΊΠΎΠΆ ΠΏΡΠΈ ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΠ°Ρ
Π²Π°ΡΡΠ°Π½ΡΡΠ² ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΈΡ
ΠΏΡΠΈΡΡΡΠΎΡΠ², Π΄Π΅ ΠΏΡΡΠΆΠΈΠ½ΠΈ Π²ΠΏΠ»ΠΈΠ²Π°ΡΡΡ Π½Π° ΠΊΠΎΠ»ΠΈΠ²Π°Π½Π½Ρ ΡΡ
Π΅Π»Π΅ΠΌΠ΅Π½ΡΡΠ². Π ΡΠ°ΠΊΠΎΠΆ Ρ Π²ΠΈΠΏΠ°Π΄ΠΊΠ°Ρ
, ΠΊΠΎΠ»ΠΈ Π² ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΡΡΡ
Π²ΠΈΠΊΠΎΡΠΈΡΡΠ°Π½Π½Ρ ΠΌΠ΅Ρ
Π°Π½ΡΡΠ½ΠΈΡ
ΠΏΡΠΈΡΡΡΠΎΡΠ² Π½Π΅ΠΎΠ±Ρ
ΡΠ΄Π½ΠΎ Π²ΡΠ΄ΠΌΠ΅ΠΆΡΠ²Π°ΡΠΈΡΡ Π²ΡΠ΄ Ρ
Π°ΠΎΡΠΈΡΠ½ΠΈΡ
ΠΏΠ΅ΡΠ΅ΠΌΡΡΠ΅Π½Ρ Π²Π°Π½ΡΠ°ΠΆΡΠ² Ρ Π·Π°Π±Π΅Π·ΠΏΠ΅ΡΠΈΡΠΈ ΠΏΠ΅ΡΡΠΎΠ΄ΠΈΡΠ½Ρ ΡΡΠ°ΡΠΊΡΠΎΡΡΡ ΡΡ
ΡΡΡ
Phenological shifts of abiotic events, producers and consumers across a continent
Ongoing climate change can shift organism phenology in ways that vary depending on species, habitats and climate factors studied. To probe for large-scale patterns in associated phenological change, we use 70,709 observations from six decades of systematic monitoring across the former Union of Soviet Socialist Republics. Among 110 phenological events related to plants, birds, insects, amphibians and fungi, we find a mosaic of change, defying simple predictions of earlier springs, later autumns and stronger changes at higher latitudes and elevations. Site mean temperature emerged as a strong predictor of local phenology, but the magnitude and direction of change varied with trophic level and the relative timing of an event. Beyond temperature-associated variation, we uncover high variation among both sites and years, with some sites being characterized by disproportionately long seasons and others by short ones. Our findings emphasize concerns regarding ecosystem integrity and highlight the difficulty of predicting climate change outcomes. The authors use systematic monitoring across the former USSR to investigate phenological changes across taxa. The long-term mean temperature of a site emerged as a strong predictor of phenological change, with further imprints of trophic level, event timing, site, year and biotic interactions.Peer reviewe