48 research outputs found

    Landscape planning for Ukrainian rural communities: challenges, outputs, prospects

    Get PDF
    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 territories’ 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 communities’ 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

    Full text link
    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

    Full text link
    1959 von R. PREBISCH im Rahmen globaler WirtschaftsraumerΓΆrterungen – IndustrielΓ€nder hier, ”EntwicklungslΓ€nder” dort – 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 Maßnahmen 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 – Monostrukturen, Unterentwicklung, fehlende industrielle Endfertigung, geringe Anbindung – sowohl der relativen wie der wirklichen peripheren RΓ€ume ΓΌberwunden bzw. bis zu einem bestimmten Grad ΓΌberwunden werden

    β€œNEW” GEOGRAPHY IN UKRAINIAN REALITY: MISSION AND DEVELOPMENT TRENDS

    Get PDF
    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 β€œnew geography” and β€œUkrainian reality” 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 moreβ€”β€œre-discovering of the world.” It is natural that each country meets challenges in its own ways. Therefore, by using the combination of the words β€œnew geography” and β€œUkrainian realities,” 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 β€œnew geography” are provided

    Die ΓΆkologische Situation in der Ukraine und GrundsΓ€tze einer ΓΆkologischen Landesentwicklungspolitik

    Full text link
    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!

    Get PDF
    In 2020, State Institution β€œRomodanov Neurosurgery Institute of NAMS of Ukraine” 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 (1951–1964), A.P. Romodanov (1964–1993), Yu.P. Zozulia (1993–2013), E.G. Pedachenko (since February 2013).Today, the Institute’s 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 β€œRomodanov Neurosurgery Institute of NAMS of Ukraine” 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‘ΠΈΠ½Ρ‚Π΅Π· Ρ‚Π° класифікація ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΈΡ… Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–ΠΉ Ρ€ΡƒΡ…Ρƒ Π²Π°Π½Ρ‚Π°ΠΆΡƒ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ

    Get PDF
    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 devicesΠŸΡ€ΠΎΠ΄ΠΎΠ»ΠΆΠ΅Π½ΠΎ исслСдования возмоТностСй гСомСтричСского модСлирования нСхаотичСских пСриодичСских Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΉ двиТСния Π³Ρ€ΡƒΠ·Π° ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ ΠΈ Π΅Π΅ разновидностСй. Π’ Π»ΠΈΡ‚Π΅Ρ€Π°Ρ‚ΡƒΡ€Π΅ ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΎΠΉ (swinging spring) Π½Π°Π·Ρ‹Π²Π°ΡŽΡ‚ Ρ€Π°Π·Π½ΠΎΠ²ΠΈΠ΄Π½ΠΎΡΡ‚ΡŒ матСматичСского маятника, состоящСго ΠΈΠ· Ρ‚ΠΎΡ‡Π΅Ρ‡Π½ΠΎΠ³ΠΎ Π³Ρ€ΡƒΠ·Π°, присоСдинСнного ΠΊ нСвСсомой ΠΏΡ€ΡƒΠΆΠΈΠ½Π΅. Π’Ρ‚ΠΎΡ€ΠΎΠΉ ΠΊΠΎΠ½Π΅Ρ† ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ фиксируСтся Π½Π΅ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎ. Π Π°ΡΡΠΌΠ°Ρ‚Ρ€ΠΈΠ²Π°ΡŽΡ‚ΡΡ маятниковыС колСбания ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ Π² Π²Π΅Ρ€Ρ‚ΠΈΠΊΠ°Π»ΡŒΠ½ΠΎΠΉ плоскости ΠΏΡ€ΠΈ условии сохранСния прямолинСйности Π΅Π΅ оси. Искомая траСктория Π³Ρ€ΡƒΠ·Π° ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ модСлируСтся с использованиСм ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ Π›Π°Π³Ρ€Π°Π½ΠΆΠ° Π²Ρ‚ΠΎΡ€ΠΎΠ³ΠΎ Ρ€ΠΎΠ΄Π°.ΠΠΊΡ‚ΡƒΠ°Π»ΡŒΠ½ΠΎΡΡ‚ΡŒ Ρ‚Π΅ΠΌΡ‹ опрСдСляСтся Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΠΎΡΡ‚ΡŒΡŽ исслСдования условий отмСТСвания ΠΎΡ‚ Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½Ρ‹Ρ… ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ элСмСнтов мСханичСских конструкций, Π² состав ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Ρ… входят ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹, Π° ΠΈΠΌΠ΅Π½Π½ΠΎ опрСдСлСния Ρ€Π°Ρ†ΠΈΠΎΠ½Π°Π»ΡŒΠ½Ρ‹Ρ… Π·Π½Π°Ρ‡Π΅Π½ΠΈΠΉ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ² для обСспСчСния пСриодичСских Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΉ ΠΈΡ… ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ. ΠšΠ°Ρ‡Π°ΡŽΡ‰ΠΈΠ΅ΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚ΡŒ ΠΊΠ°ΠΊ мСханичСскиС ΠΈΠ»Π»ΡŽΡΡ‚Ρ€Π°Ρ†ΠΈΠΈ ΠΏΡ€ΠΈ исслСдовании слоТных тСхнологичСских процСссов динамичСских систСм, ΠΊΠΎΠ³Π΄Π° Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎ связанныС ΠΊΠΎΠ»Π΅Π±Π°Ρ‚Π΅Π»ΡŒΠ½Ρ‹Π΅ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ‚Ρ‹ систСмы ΠΎΠ±ΠΌΠ΅Π½ΠΈΠ²Π°ΡŽΡ‚ΡΡ энСргиСй ΠΌΠ΅ΠΆΠ΄Ρƒ собой.ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Π½Ρ‹Π΅ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ ΠΏΡ€ΠΈΠΎΠ±Ρ‰ΠΈΡ‚ΡŒ ΠΊ ΠΏΠ΅Ρ€Π΅Ρ‡Π½ΡŽ числовых ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ² ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ Π΅Ρ‰Π΅ ΠΈ пСриодичСскиС ΠΊΡ€ΠΈΠ²Ρ‹Π΅ ΠΊΠ°ΠΊ "ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ‹" Π² графичСской Ρ„ΠΎΡ€ΠΌΠ΅. Π’. Π΅. ΠΎΠΏΡ€Π΅Π΄Π΅Π»ΠΈΡ‚ΡŒ числовыС значСния ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ², ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Π΅ Π±Ρ‹ обСспСчили сущСствованиС Π·Π°Π²Π΅Π΄ΠΎΠΌΠΎ Π·Π°Π΄Π°Π½Π½ΠΎΠΉ Ρ„ΠΎΡ€ΠΌΡ‹ пСриодичСской Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ двиТСния Π³Ρ€ΡƒΠ·Π° ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹. РассмотрСн ΠΏΡ€ΠΈΠΌΠ΅Ρ€ вычислСния массы Π³Ρ€ΡƒΠ·Π° ΠΏΠΎ извСстным ТСсткости ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹, Π΅Π΅ Π΄Π»ΠΈΠ½Π΅ Π±Π΅Π· Π½Π°Π³Ρ€ΡƒΠ·ΠΊΠΈ, Π½Π°Ρ‡Π°Π»ΡŒΠ½Ρ‹ΠΌ условиям ΠΈΠ½ΠΈΡ†ΠΈΠ°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ, Π° Ρ‚Π°ΠΊΠΆΠ΅ (Π²Π½ΠΈΠΌΠ°Π½ΠΈΠ΅) Ρ„ΠΎΡ€ΠΌΠ΅ пСриодичСской Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ этого Π³Ρ€ΡƒΠ·Π°. ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Ρ‹ пСриодичСскиС Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ двиТСния Π³Ρ€ΡƒΠ·Π° для ΠΌΠΎΠ΄ΠΈΡ„ΠΈΠΊΠ°Ρ†ΠΈΠΉ ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹,, Ρ‚Π°ΠΊΠΈΡ… ΠΊΠ°ΠΊ подвСшСнной ΠΊ ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎΠΉ Ρ‚Π΅Π»Π΅ΠΆΠΊΠ΅, ось ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠΉ совпадаСт с матСматичСским маятником. А Ρ‚Π°ΠΊΠΆΠ΅ Π΄Π²ΡƒΡ… ΠΊΠ°Ρ‡Π°ΡŽΡ‰ΠΈΡ…ΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½ с ΠΎΠ±Ρ‰ΠΈΠΌ ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½Ρ‹ΠΌ Π³Ρ€ΡƒΠ·ΠΎΠΌ ΠΈ с Ρ€Π°Π·Π½Ρ‹ΠΌΠΈ Ρ‚ΠΎΡ‡ΠΊΠ°ΠΌΠΈ крСплСния.ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Π½Ρ‹Π΅ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΏΡ€ΠΎΠΈΠ»Π»ΡŽΡΡ‚Ρ€ΠΈΡ€ΠΎΠ²Π°Π½Ρ‹ ΠΊΠΎΠΌΠΏΡŒΡŽΡ‚Π΅Ρ€Π½Ρ‹ΠΌΠΈ анимациями ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ ΡΠΎΠΎΡ‚Π²Π΅Ρ‚ΡΡ‚Π²ΡƒΡŽΡ‰ΠΈΡ… ΠΊΠ°Ρ‡Π°ΡŽΡ‰ΠΈΡ…ΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½ ΠΈ ΠΈΡ… разновидностСй.Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚ΡŒ ΠΊΠ°ΠΊ ΠΏΠ°Ρ€Π°Π΄ΠΈΠ³ΠΌΡƒ для изучСния Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½Ρ‹Ρ… связанных систСм, Π° Ρ‚Π°ΠΊΠΆΠ΅ ΠΏΡ€ΠΈ расчСтах Π²Π°Ρ€ΠΈΠ°Π½Ρ‚ΠΎΠ² мСханичСских устройств, Π³Π΄Π΅ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ Π²Π»ΠΈΡΡŽΡ‚ Π½Π° ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠ΅ ΠΈΡ… элСмСнтов. А Ρ‚Π°ΠΊΠΆΠ΅ Π² случаях, ΠΊΠΎΠ³Π΄Π° Π² тСхнологиях использования мСханичСских устройств Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΠΎ ΠΎΡ‚ΠΌΠ΅ΠΆΠ΅Π²Π°Ρ‚ΡŒΡΡ ΠΎΡ‚ Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½Ρ‹Ρ… ΠΏΠ΅Ρ€Π΅ΠΌΠ΅Ρ‰Π΅Π½ΠΈΠΉ Π³Ρ€ΡƒΠ·ΠΎΠ² ΠΈ ΠΎΠ±Π΅ΡΠΏΠ΅Ρ‡ΠΈΡ‚ΡŒ пСриодичСскиС Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ ΠΈΡ… Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡΠŸΡ€ΠΎΠ΄ΠΎΠ²ΠΆΠ΅Π½ΠΎ дослідТСння моТливостСй Π³Π΅ΠΎΠΌΠ΅Ρ‚Ρ€ΠΈΡ‡Π½ΠΎΠ³ΠΎ модСлювання Π½Π΅Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΈΡ… Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–ΠΉ Ρ€ΡƒΡ…Ρƒ Π²Π°Π½Ρ‚Π°ΠΆΡƒ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Ρ‚Π° Ρ—Ρ— Ρ€Ρ–Π·Π½ΠΎΠ²ΠΈΠ΄Ρ–Π². Π’ Π»Ρ–Ρ‚Π΅Ρ€Π°Ρ‚ΡƒΡ€Ρ– Ρ…ΠΈΡ‚Π½ΠΎΡŽ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΎΡŽ (swinging spring) Π½Π°Π·ΠΈΠ²Π°ΡŽΡ‚ΡŒ Ρ€Ρ–Π·Π½ΠΎΠ²ΠΈΠ΄ ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΎΠ³ΠΎ маятника, який ΡΠΊΠ»Π°Π΄Π°Ρ”Ρ‚ΡŒΡΡ Π· Ρ‚ΠΎΡ‡ΠΊΠΎΠ²ΠΎΠ³ΠΎ Π²Π°Π½Ρ‚Π°ΠΆΡƒ, ΠΏΡ€ΠΈΡ”Π΄Π½Π°Π½ΠΎΠ³ΠΎ Π΄ΠΎ Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ. Π”Ρ€ΡƒΠ³ΠΈΠΉ ΠΊΡ–Π½Π΅Ρ†ΡŒ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Ρ„Ρ–ΠΊΡΡƒΡ”Ρ‚ΡŒΡΡ Π½Π΅Ρ€ΡƒΡ…ΠΎΠΌΠΎ. Π ΠΎΠ·Π³Π»ΡΠ΄Π°ΡŽΡ‚ΡŒΡΡ маятникові коливання ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Ρƒ Π²Π΅Ρ€Ρ‚ΠΈΠΊΠ°Π»ΡŒΠ½Ρ–ΠΉ ΠΏΠ»ΠΎΡ‰ΠΈΠ½Ρ– Π·Π° ΡƒΠΌΠΎΠ²ΠΈ збСрСТСння прямолінійності Ρ—Ρ— осі. Π¨ΡƒΠΊΠ°Π½Π° траєкторія Π²Π°Π½Ρ‚Π°ΠΆΡƒ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ ΠΌΠΎΠ΄Π΅Π»ΡŽΡ”Ρ‚ΡŒΡΡ Π· використанням Ρ€Ρ–Π²Π½ΡΠ½ΡŒ Π›Π°Π³Ρ€Π°Π½ΠΆΠ° Π΄Ρ€ΡƒΠ³ΠΎΠ³ΠΎ Ρ€ΠΎΠ΄Ρƒ.ΠΠΊΡ‚ΡƒΠ°Π»ΡŒΠ½Ρ–ΡΡ‚ΡŒ Ρ‚Π΅ΠΌΠΈ Π²ΠΈΠ·Π½Π°Ρ‡Π°Ρ”Ρ‚ΡŒΡΡ Π½Π΅ΠΎΠ±Ρ…Ρ–Π΄Π½Ρ–ΡΡ‚ΡŽ дослідТСння ΡƒΠΌΠΎΠ² відмСТування Π²Ρ–Π΄ Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½ΠΈΡ… коливань Π΅Π»Π΅ΠΌΠ΅Π½Ρ‚Ρ–Π² ΠΌΠ΅Ρ…Π°Π½Ρ–Ρ‡Π½ΠΈΡ… конструкцій, Π΄ΠΎ складу яких Π²Ρ…ΠΎΠ΄ΡΡ‚ΡŒ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ, Π° самС визначСння Ρ€Π°Ρ†Ρ–ΠΎΠ½Π°Π»ΡŒΠ½ΠΈΡ… Π·Π½Π°Ρ‡Π΅Π½ΡŒ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ–Π² для забСзпСчСння ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΈΡ… Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–ΠΉ Ρ—Ρ… коливань. Π₯ΠΈΡ‚Π½Ρ– ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ ΠΌΠΎΠΆΠ½Π° використати як ΠΌΠ΅Ρ…Π°Π½Ρ–Ρ‡Π½Ρ– Ρ–Π»ΡŽΡΡ‚Ρ€Π°Ρ†Ρ–Ρ— ΠΏΡ€ΠΈ дослідТСнні складних Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³Ρ–Ρ‡Π½ΠΈΡ… процСсів Π΄ΠΈΠ½Π°ΠΌΡ–Ρ‡Π½ΠΈΡ… систСм, ΠΊΠΎΠ»ΠΈ Π½Π΅Π»Ρ–Π½Ρ–ΠΉΠ½ΠΎ Π·Π²'язані ΠΊΠΎΠ»ΠΈΠ²Π°Π»ΡŒΠ½Ρ– ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ‚ΠΈ систСми ΠΎΠ±ΠΌΡ–Π½ΡŽΡŽΡ‚ΡŒΡΡ Π΅Π½Π΅Ρ€Π³Ρ–Ρ”ΡŽ ΠΌΡ–ΠΆ собою.ΠžΠ΄Π΅Ρ€ΠΆΠ°Π½Ρ– Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ΡŒ Π΄ΠΎΠ»ΡƒΡ‡ΠΈΡ‚ΠΈ Π΄ΠΎ ΠΏΠ΅Ρ€Π΅Π»Ρ–ΠΊΡƒ числових ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ–Π² Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Ρ‰Π΅ ΠΉ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½Ρ– ΠΊΡ€ΠΈΠ²Ρ– як "ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΈ" Π² Π³Ρ€Π°Ρ„Ρ–Ρ‡Π½Ρ–ΠΉ Ρ„ΠΎΡ€ΠΌΡ–. Π’ΠΎΠ±Ρ‚ΠΎ Π²ΠΈΠ·Π½Π°Ρ‡ΠΈΡ‚ΠΈ числові значСння ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ–Π², які Π± Π·Π°Π±Π΅Π·ΠΏΠ΅Ρ‡ΠΈΠ»ΠΈ існування Π½Π°ΠΏΠ΅Ρ€Π΅Π΄ Π·Π°Π΄Π°Π½ΠΎΡ— Ρ„ΠΎΡ€ΠΌΠΈ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΎΡ— Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–Ρ— Ρ€ΡƒΡ…Ρƒ Π²Π°Π½Ρ‚Π°ΠΆΡƒ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ. Розглянуто ΠΏΡ€ΠΈΠΊΠ»Π°Π΄ обчислСння маси Π²Π°Π½Ρ‚Π°ΠΆΡƒ Π·Π° Π²Ρ–Π΄ΠΎΠΌΠΈΠΌΠΈ ΠΆΠΎΡ€ΡΡ‚ΠΊΡ–ΡΡ‚ΡŽ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ, Ρ—Ρ— довТиною Π±Π΅Π· навантаТСння, ΠΏΠΎΡ‡Π°Ρ‚ΠΊΠΎΠ²ΠΈΠΌΠΈ ΡƒΠΌΠΎΠ²Π°ΠΌΠΈ Ρ–Π½Ρ–Ρ†Ρ–Π°Π»Ρ–Π·Π°Ρ†Ρ–Ρ— коливань, Π° Ρ‚Π°ΠΊΠΎΠΆ (ΡƒΠ²Π°Π³Π°) Ρ„ΠΎΡ€ΠΌΠΎΡŽ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΎΡ— Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–Ρ— Ρ†ΡŒΠΎΠ³ΠΎ Π²Π°Π½Ρ‚Π°ΠΆΡƒ. ΠžΠ΄Π΅Ρ€ΠΆΠ°Π½ΠΎ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½Ρ– Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–Ρ— Ρ€ΡƒΡ…Ρƒ Π²Π°Π½Ρ‚Π°ΠΆΡƒ для ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠ°Ρ†Ρ–ΠΉ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ - Ρ‚Π°ΠΊΠΈΡ… як ΠΏΡ–Π΄Π²Ρ–ΡˆΠ΅Π½ΠΎΡ— Π΄ΠΎ Ρ€ΡƒΡ…ΠΎΠΌΠΎΠ³ΠΎ Π²Ρ–Π·ΠΊΠ° Ρ– Π²Ρ–ΡΡŒ якої Π·Π±Ρ–Π³Π°Ρ”Ρ‚ΡŒΡΡ Π· ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΈΠΌ маятником. А Ρ‚Π°ΠΊΠΎΠΆ Π΄Π²ΠΎΡ… Ρ…ΠΈΡ‚Π½ΠΈΡ… ΠΏΡ€ΡƒΠΆΠΈΠ½ Π·Ρ– ΡΠΏΡ–Π»ΡŒΠ½ΠΈΠΌ Ρ€ΡƒΡ…ΠΎΠΌΠΈΠΌ Π²Π°Π½Ρ‚Π°ΠΆΠ΅ΠΌ Ρ– Π· Ρ€Ρ–Π·Π½ΠΈΠΌΠΈ Ρ‚ΠΎΡ‡ΠΊΠ°ΠΌΠΈ кріплСння.ΠžΠ΄Π΅Ρ€ΠΆΠ°Π½Ρ– Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ ΠΏΡ€ΠΎΡ–Π»ΡŽΡΡ‚Ρ€ΠΎΠ²Π°Π½ΠΎ ΠΊΠΎΠΌΠΏ'ΡŽΡ‚Π΅Ρ€Π½ΠΈΠΌΠΈ анімаціями коливань Π²Ρ–Π΄ΠΏΠΎΠ²Ρ–Π΄Π½ΠΈΡ… Ρ…ΠΈΡ‚Π½ΠΈΡ… ΠΏΡ€ΡƒΠΆΠΈΠ½ Ρ‚Π° Ρ—Ρ… Ρ€Ρ–Π·Π½ΠΎΠ²ΠΈΠ΄Ρ–Π².Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ ΠΌΠΎΠΆΠ½Π° використати як ΠΏΠ°Ρ€Π°Π΄ΠΈΠ³ΠΌΡƒ для вивчСння Π½Π΅Π»Ρ–Π½Ρ–ΠΉΠ½ΠΈΡ… Π·Π²'язаних систСм, Π° Ρ‚Π°ΠΊΠΎΠΆ ΠΏΡ€ΠΈ Ρ€ΠΎΠ·Ρ€Π°Ρ…ΡƒΠ½ΠΊΠ°Ρ… Π²Π°Ρ€Ρ–Π°Π½Ρ‚Ρ–Π² ΠΌΠ΅Ρ…Π°Π½Ρ–Ρ‡Π½ΠΈΡ… пристроїв, Π΄Π΅ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Π²ΠΏΠ»ΠΈΠ²Π°ΡŽΡ‚ΡŒ Π½Π° коливання Ρ—Ρ… Π΅Π»Π΅ΠΌΠ΅Π½Ρ‚Ρ–Π². А Ρ‚Π°ΠΊΠΎΠΆ Ρƒ Π²ΠΈΠΏΠ°Π΄ΠΊΠ°Ρ…, ΠΊΠΎΠ»ΠΈ Π² тСхнологіях використання ΠΌΠ΅Ρ…Π°Π½Ρ–Ρ‡Π½ΠΈΡ… пристроїв Π½Π΅ΠΎΠ±Ρ…Ρ–Π΄Π½ΠΎ відмСТуватися Π²Ρ–Π΄ Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΏΠ΅Ρ€Π΅ΠΌΡ–Ρ‰Π΅Π½ΡŒ Π²Π°Π½Ρ‚Π°ΠΆΡ–Π² Ρ– Π·Π°Π±Π΅Π·ΠΏΠ΅Ρ‡ΠΈΡ‚ΠΈ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½Ρ– Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–Ρ— Ρ—Ρ… Ρ€ΡƒΡ…

    Π‘ΠΈΠ½Ρ‚Π΅Π· Ρ‚Π° класифікація ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΈΡ… Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–ΠΉ Ρ€ΡƒΡ…Ρƒ Π²Π°Π½Ρ‚Π°ΠΆΡƒ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ

    Get PDF
    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 devicesΠŸΡ€ΠΎΠ΄ΠΎΠ»ΠΆΠ΅Π½ΠΎ исслСдования возмоТностСй гСомСтричСского модСлирования нСхаотичСских пСриодичСских Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΉ двиТСния Π³Ρ€ΡƒΠ·Π° ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ ΠΈ Π΅Π΅ разновидностСй. Π’ Π»ΠΈΡ‚Π΅Ρ€Π°Ρ‚ΡƒΡ€Π΅ ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΎΠΉ (swinging spring) Π½Π°Π·Ρ‹Π²Π°ΡŽΡ‚ Ρ€Π°Π·Π½ΠΎΠ²ΠΈΠ΄Π½ΠΎΡΡ‚ΡŒ матСматичСского маятника, состоящСго ΠΈΠ· Ρ‚ΠΎΡ‡Π΅Ρ‡Π½ΠΎΠ³ΠΎ Π³Ρ€ΡƒΠ·Π°, присоСдинСнного ΠΊ нСвСсомой ΠΏΡ€ΡƒΠΆΠΈΠ½Π΅. Π’Ρ‚ΠΎΡ€ΠΎΠΉ ΠΊΠΎΠ½Π΅Ρ† ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ фиксируСтся Π½Π΅ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎ. Π Π°ΡΡΠΌΠ°Ρ‚Ρ€ΠΈΠ²Π°ΡŽΡ‚ΡΡ маятниковыС колСбания ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ Π² Π²Π΅Ρ€Ρ‚ΠΈΠΊΠ°Π»ΡŒΠ½ΠΎΠΉ плоскости ΠΏΡ€ΠΈ условии сохранСния прямолинСйности Π΅Π΅ оси. Искомая траСктория Π³Ρ€ΡƒΠ·Π° ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ модСлируСтся с использованиСм ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ Π›Π°Π³Ρ€Π°Π½ΠΆΠ° Π²Ρ‚ΠΎΡ€ΠΎΠ³ΠΎ Ρ€ΠΎΠ΄Π°.ΠΠΊΡ‚ΡƒΠ°Π»ΡŒΠ½ΠΎΡΡ‚ΡŒ Ρ‚Π΅ΠΌΡ‹ опрСдСляСтся Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΠΎΡΡ‚ΡŒΡŽ исслСдования условий отмСТСвания ΠΎΡ‚ Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½Ρ‹Ρ… ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ элСмСнтов мСханичСских конструкций, Π² состав ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Ρ… входят ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹, Π° ΠΈΠΌΠ΅Π½Π½ΠΎ опрСдСлСния Ρ€Π°Ρ†ΠΈΠΎΠ½Π°Π»ΡŒΠ½Ρ‹Ρ… Π·Π½Π°Ρ‡Π΅Π½ΠΈΠΉ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ² для обСспСчСния пСриодичСских Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΉ ΠΈΡ… ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ. ΠšΠ°Ρ‡Π°ΡŽΡ‰ΠΈΠ΅ΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚ΡŒ ΠΊΠ°ΠΊ мСханичСскиС ΠΈΠ»Π»ΡŽΡΡ‚Ρ€Π°Ρ†ΠΈΠΈ ΠΏΡ€ΠΈ исслСдовании слоТных тСхнологичСских процСссов динамичСских систСм, ΠΊΠΎΠ³Π΄Π° Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎ связанныС ΠΊΠΎΠ»Π΅Π±Π°Ρ‚Π΅Π»ΡŒΠ½Ρ‹Π΅ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ‚Ρ‹ систСмы ΠΎΠ±ΠΌΠ΅Π½ΠΈΠ²Π°ΡŽΡ‚ΡΡ энСргиСй ΠΌΠ΅ΠΆΠ΄Ρƒ собой.ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Π½Ρ‹Π΅ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ ΠΏΡ€ΠΈΠΎΠ±Ρ‰ΠΈΡ‚ΡŒ ΠΊ ΠΏΠ΅Ρ€Π΅Ρ‡Π½ΡŽ числовых ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ² ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ Π΅Ρ‰Π΅ ΠΈ пСриодичСскиС ΠΊΡ€ΠΈΠ²Ρ‹Π΅ ΠΊΠ°ΠΊ "ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ‹" Π² графичСской Ρ„ΠΎΡ€ΠΌΠ΅. Π’. Π΅. ΠΎΠΏΡ€Π΅Π΄Π΅Π»ΠΈΡ‚ΡŒ числовыС значСния ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΎΠ², ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Π΅ Π±Ρ‹ обСспСчили сущСствованиС Π·Π°Π²Π΅Π΄ΠΎΠΌΠΎ Π·Π°Π΄Π°Π½Π½ΠΎΠΉ Ρ„ΠΎΡ€ΠΌΡ‹ пСриодичСской Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ двиТСния Π³Ρ€ΡƒΠ·Π° ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹. РассмотрСн ΠΏΡ€ΠΈΠΌΠ΅Ρ€ вычислСния массы Π³Ρ€ΡƒΠ·Π° ΠΏΠΎ извСстным ТСсткости ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹, Π΅Π΅ Π΄Π»ΠΈΠ½Π΅ Π±Π΅Π· Π½Π°Π³Ρ€ΡƒΠ·ΠΊΠΈ, Π½Π°Ρ‡Π°Π»ΡŒΠ½Ρ‹ΠΌ условиям ΠΈΠ½ΠΈΡ†ΠΈΠ°Π»ΠΈΠ·Π°Ρ†ΠΈΠΈ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ, Π° Ρ‚Π°ΠΊΠΆΠ΅ (Π²Π½ΠΈΠΌΠ°Π½ΠΈΠ΅) Ρ„ΠΎΡ€ΠΌΠ΅ пСриодичСской Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ этого Π³Ρ€ΡƒΠ·Π°. ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Ρ‹ пСриодичСскиС Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ двиТСния Π³Ρ€ΡƒΠ·Π° для ΠΌΠΎΠ΄ΠΈΡ„ΠΈΠΊΠ°Ρ†ΠΈΠΉ ΠΊΠ°Ρ‡Π°ΡŽΡ‰Π΅ΠΉΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹,, Ρ‚Π°ΠΊΠΈΡ… ΠΊΠ°ΠΊ подвСшСнной ΠΊ ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½ΠΎΠΉ Ρ‚Π΅Π»Π΅ΠΆΠΊΠ΅, ось ΠΊΠΎΡ‚ΠΎΡ€ΠΎΠΉ совпадаСт с матСматичСским маятником. А Ρ‚Π°ΠΊΠΆΠ΅ Π΄Π²ΡƒΡ… ΠΊΠ°Ρ‡Π°ΡŽΡ‰ΠΈΡ…ΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½ с ΠΎΠ±Ρ‰ΠΈΠΌ ΠΏΠΎΠ΄Π²ΠΈΠΆΠ½Ρ‹ΠΌ Π³Ρ€ΡƒΠ·ΠΎΠΌ ΠΈ с Ρ€Π°Π·Π½Ρ‹ΠΌΠΈ Ρ‚ΠΎΡ‡ΠΊΠ°ΠΌΠΈ крСплСния.ΠŸΠΎΠ»ΡƒΡ‡Π΅Π½Π½Ρ‹Π΅ Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΏΡ€ΠΎΠΈΠ»Π»ΡŽΡΡ‚Ρ€ΠΈΡ€ΠΎΠ²Π°Π½Ρ‹ ΠΊΠΎΠΌΠΏΡŒΡŽΡ‚Π΅Ρ€Π½Ρ‹ΠΌΠΈ анимациями ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ ΡΠΎΠΎΡ‚Π²Π΅Ρ‚ΡΡ‚Π²ΡƒΡŽΡ‰ΠΈΡ… ΠΊΠ°Ρ‡Π°ΡŽΡ‰ΠΈΡ…ΡΡ ΠΏΡ€ΡƒΠΆΠΈΠ½ ΠΈ ΠΈΡ… разновидностСй.Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚Ρ‹ ΠΌΠΎΠΆΠ½ΠΎ ΠΈΡΠΏΠΎΠ»ΡŒΠ·ΠΎΠ²Π°Ρ‚ΡŒ ΠΊΠ°ΠΊ ΠΏΠ°Ρ€Π°Π΄ΠΈΠ³ΠΌΡƒ для изучСния Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½Ρ‹Ρ… связанных систСм, Π° Ρ‚Π°ΠΊΠΆΠ΅ ΠΏΡ€ΠΈ расчСтах Π²Π°Ρ€ΠΈΠ°Π½Ρ‚ΠΎΠ² мСханичСских устройств, Π³Π΄Π΅ ΠΏΡ€ΡƒΠΆΠΈΠ½Ρ‹ Π²Π»ΠΈΡΡŽΡ‚ Π½Π° ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠ΅ ΠΈΡ… элСмСнтов. А Ρ‚Π°ΠΊΠΆΠ΅ Π² случаях, ΠΊΠΎΠ³Π΄Π° Π² тСхнологиях использования мСханичСских устройств Π½Π΅ΠΎΠ±Ρ…ΠΎΠ΄ΠΈΠΌΠΎ ΠΎΡ‚ΠΌΠ΅ΠΆΠ΅Π²Π°Ρ‚ΡŒΡΡ ΠΎΡ‚ Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½Ρ‹Ρ… ΠΏΠ΅Ρ€Π΅ΠΌΠ΅Ρ‰Π΅Π½ΠΈΠΉ Π³Ρ€ΡƒΠ·ΠΎΠ² ΠΈ ΠΎΠ±Π΅ΡΠΏΠ΅Ρ‡ΠΈΡ‚ΡŒ пСриодичСскиС Ρ‚Ρ€Π°Π΅ΠΊΡ‚ΠΎΡ€ΠΈΠΈ ΠΈΡ… Π΄Π²ΠΈΠΆΠ΅Π½ΠΈΡΠŸΡ€ΠΎΠ΄ΠΎΠ²ΠΆΠ΅Π½ΠΎ дослідТСння моТливостСй Π³Π΅ΠΎΠΌΠ΅Ρ‚Ρ€ΠΈΡ‡Π½ΠΎΠ³ΠΎ модСлювання Π½Π΅Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΈΡ… Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–ΠΉ Ρ€ΡƒΡ…Ρƒ Π²Π°Π½Ρ‚Π°ΠΆΡƒ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Ρ‚Π° Ρ—Ρ— Ρ€Ρ–Π·Π½ΠΎΠ²ΠΈΠ΄Ρ–Π². Π’ Π»Ρ–Ρ‚Π΅Ρ€Π°Ρ‚ΡƒΡ€Ρ– Ρ…ΠΈΡ‚Π½ΠΎΡŽ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΎΡŽ (swinging spring) Π½Π°Π·ΠΈΠ²Π°ΡŽΡ‚ΡŒ Ρ€Ρ–Π·Π½ΠΎΠ²ΠΈΠ΄ ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΎΠ³ΠΎ маятника, який ΡΠΊΠ»Π°Π΄Π°Ρ”Ρ‚ΡŒΡΡ Π· Ρ‚ΠΎΡ‡ΠΊΠΎΠ²ΠΎΠ³ΠΎ Π²Π°Π½Ρ‚Π°ΠΆΡƒ, ΠΏΡ€ΠΈΡ”Π΄Π½Π°Π½ΠΎΠ³ΠΎ Π΄ΠΎ Π½Π΅Π²Π°Π³ΠΎΠΌΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ. Π”Ρ€ΡƒΠ³ΠΈΠΉ ΠΊΡ–Π½Π΅Ρ†ΡŒ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Ρ„Ρ–ΠΊΡΡƒΡ”Ρ‚ΡŒΡΡ Π½Π΅Ρ€ΡƒΡ…ΠΎΠΌΠΎ. Π ΠΎΠ·Π³Π»ΡΠ΄Π°ΡŽΡ‚ΡŒΡΡ маятникові коливання ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Ρƒ Π²Π΅Ρ€Ρ‚ΠΈΠΊΠ°Π»ΡŒΠ½Ρ–ΠΉ ΠΏΠ»ΠΎΡ‰ΠΈΠ½Ρ– Π·Π° ΡƒΠΌΠΎΠ²ΠΈ збСрСТСння прямолінійності Ρ—Ρ— осі. Π¨ΡƒΠΊΠ°Π½Π° траєкторія Π²Π°Π½Ρ‚Π°ΠΆΡƒ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ ΠΌΠΎΠ΄Π΅Π»ΡŽΡ”Ρ‚ΡŒΡΡ Π· використанням Ρ€Ρ–Π²Π½ΡΠ½ΡŒ Π›Π°Π³Ρ€Π°Π½ΠΆΠ° Π΄Ρ€ΡƒΠ³ΠΎΠ³ΠΎ Ρ€ΠΎΠ΄Ρƒ.ΠΠΊΡ‚ΡƒΠ°Π»ΡŒΠ½Ρ–ΡΡ‚ΡŒ Ρ‚Π΅ΠΌΠΈ Π²ΠΈΠ·Π½Π°Ρ‡Π°Ρ”Ρ‚ΡŒΡΡ Π½Π΅ΠΎΠ±Ρ…Ρ–Π΄Π½Ρ–ΡΡ‚ΡŽ дослідТСння ΡƒΠΌΠΎΠ² відмСТування Π²Ρ–Π΄ Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½ΠΈΡ… коливань Π΅Π»Π΅ΠΌΠ΅Π½Ρ‚Ρ–Π² ΠΌΠ΅Ρ…Π°Π½Ρ–Ρ‡Π½ΠΈΡ… конструкцій, Π΄ΠΎ складу яких Π²Ρ…ΠΎΠ΄ΡΡ‚ΡŒ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ, Π° самС визначСння Ρ€Π°Ρ†Ρ–ΠΎΠ½Π°Π»ΡŒΠ½ΠΈΡ… Π·Π½Π°Ρ‡Π΅Π½ΡŒ ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ–Π² для забСзпСчСння ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΈΡ… Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–ΠΉ Ρ—Ρ… коливань. Π₯ΠΈΡ‚Π½Ρ– ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ ΠΌΠΎΠΆΠ½Π° використати як ΠΌΠ΅Ρ…Π°Π½Ρ–Ρ‡Π½Ρ– Ρ–Π»ΡŽΡΡ‚Ρ€Π°Ρ†Ρ–Ρ— ΠΏΡ€ΠΈ дослідТСнні складних Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³Ρ–Ρ‡Π½ΠΈΡ… процСсів Π΄ΠΈΠ½Π°ΠΌΡ–Ρ‡Π½ΠΈΡ… систСм, ΠΊΠΎΠ»ΠΈ Π½Π΅Π»Ρ–Π½Ρ–ΠΉΠ½ΠΎ Π·Π²'язані ΠΊΠΎΠ»ΠΈΠ²Π°Π»ΡŒΠ½Ρ– ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ‚ΠΈ систСми ΠΎΠ±ΠΌΡ–Π½ΡŽΡŽΡ‚ΡŒΡΡ Π΅Π½Π΅Ρ€Π³Ρ–Ρ”ΡŽ ΠΌΡ–ΠΆ собою.ΠžΠ΄Π΅Ρ€ΠΆΠ°Π½Ρ– Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ Π΄ΠΎΠ·Π²ΠΎΠ»ΡΡŽΡ‚ΡŒ Π΄ΠΎΠ»ΡƒΡ‡ΠΈΡ‚ΠΈ Π΄ΠΎ ΠΏΠ΅Ρ€Π΅Π»Ρ–ΠΊΡƒ числових ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ–Π² Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Ρ‰Π΅ ΠΉ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½Ρ– ΠΊΡ€ΠΈΠ²Ρ– як "ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€ΠΈ" Π² Π³Ρ€Π°Ρ„Ρ–Ρ‡Π½Ρ–ΠΉ Ρ„ΠΎΡ€ΠΌΡ–. Π’ΠΎΠ±Ρ‚ΠΎ Π²ΠΈΠ·Π½Π°Ρ‡ΠΈΡ‚ΠΈ числові значСння ΠΏΠ°Ρ€Π°ΠΌΠ΅Ρ‚Ρ€Ρ–Π², які Π± Π·Π°Π±Π΅Π·ΠΏΠ΅Ρ‡ΠΈΠ»ΠΈ існування Π½Π°ΠΏΠ΅Ρ€Π΅Π΄ Π·Π°Π΄Π°Π½ΠΎΡ— Ρ„ΠΎΡ€ΠΌΠΈ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΎΡ— Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–Ρ— Ρ€ΡƒΡ…Ρƒ Π²Π°Π½Ρ‚Π°ΠΆΡƒ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ. Розглянуто ΠΏΡ€ΠΈΠΊΠ»Π°Π΄ обчислСння маси Π²Π°Π½Ρ‚Π°ΠΆΡƒ Π·Π° Π²Ρ–Π΄ΠΎΠΌΠΈΠΌΠΈ ΠΆΠΎΡ€ΡΡ‚ΠΊΡ–ΡΡ‚ΡŽ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ, Ρ—Ρ— довТиною Π±Π΅Π· навантаТСння, ΠΏΠΎΡ‡Π°Ρ‚ΠΊΠΎΠ²ΠΈΠΌΠΈ ΡƒΠΌΠΎΠ²Π°ΠΌΠΈ Ρ–Π½Ρ–Ρ†Ρ–Π°Π»Ρ–Π·Π°Ρ†Ρ–Ρ— коливань, Π° Ρ‚Π°ΠΊΠΎΠΆ (ΡƒΠ²Π°Π³Π°) Ρ„ΠΎΡ€ΠΌΠΎΡŽ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½ΠΎΡ— Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–Ρ— Ρ†ΡŒΠΎΠ³ΠΎ Π²Π°Π½Ρ‚Π°ΠΆΡƒ. ΠžΠ΄Π΅Ρ€ΠΆΠ°Π½ΠΎ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½Ρ– Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–Ρ— Ρ€ΡƒΡ…Ρƒ Π²Π°Π½Ρ‚Π°ΠΆΡƒ для ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠ°Ρ†Ρ–ΠΉ Ρ…ΠΈΡ‚Π½ΠΎΡ— ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ - Ρ‚Π°ΠΊΠΈΡ… як ΠΏΡ–Π΄Π²Ρ–ΡˆΠ΅Π½ΠΎΡ— Π΄ΠΎ Ρ€ΡƒΡ…ΠΎΠΌΠΎΠ³ΠΎ Π²Ρ–Π·ΠΊΠ° Ρ– Π²Ρ–ΡΡŒ якої Π·Π±Ρ–Π³Π°Ρ”Ρ‚ΡŒΡΡ Π· ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΈΠΌ маятником. А Ρ‚Π°ΠΊΠΎΠΆ Π΄Π²ΠΎΡ… Ρ…ΠΈΡ‚Π½ΠΈΡ… ΠΏΡ€ΡƒΠΆΠΈΠ½ Π·Ρ– ΡΠΏΡ–Π»ΡŒΠ½ΠΈΠΌ Ρ€ΡƒΡ…ΠΎΠΌΠΈΠΌ Π²Π°Π½Ρ‚Π°ΠΆΠ΅ΠΌ Ρ– Π· Ρ€Ρ–Π·Π½ΠΈΠΌΠΈ Ρ‚ΠΎΡ‡ΠΊΠ°ΠΌΠΈ кріплСння.ΠžΠ΄Π΅Ρ€ΠΆΠ°Π½Ρ– Ρ€Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ ΠΏΡ€ΠΎΡ–Π»ΡŽΡΡ‚Ρ€ΠΎΠ²Π°Π½ΠΎ ΠΊΠΎΠΌΠΏ'ΡŽΡ‚Π΅Ρ€Π½ΠΈΠΌΠΈ анімаціями коливань Π²Ρ–Π΄ΠΏΠΎΠ²Ρ–Π΄Π½ΠΈΡ… Ρ…ΠΈΡ‚Π½ΠΈΡ… ΠΏΡ€ΡƒΠΆΠΈΠ½ Ρ‚Π° Ρ—Ρ… Ρ€Ρ–Π·Π½ΠΎΠ²ΠΈΠ΄Ρ–Π².Π Π΅Π·ΡƒΠ»ΡŒΡ‚Π°Ρ‚ΠΈ ΠΌΠΎΠΆΠ½Π° використати як ΠΏΠ°Ρ€Π°Π΄ΠΈΠ³ΠΌΡƒ для вивчСння Π½Π΅Π»Ρ–Π½Ρ–ΠΉΠ½ΠΈΡ… Π·Π²'язаних систСм, Π° Ρ‚Π°ΠΊΠΎΠΆ ΠΏΡ€ΠΈ Ρ€ΠΎΠ·Ρ€Π°Ρ…ΡƒΠ½ΠΊΠ°Ρ… Π²Π°Ρ€Ρ–Π°Π½Ρ‚Ρ–Π² ΠΌΠ΅Ρ…Π°Π½Ρ–Ρ‡Π½ΠΈΡ… пристроїв, Π΄Π΅ ΠΏΡ€ΡƒΠΆΠΈΠ½ΠΈ Π²ΠΏΠ»ΠΈΠ²Π°ΡŽΡ‚ΡŒ Π½Π° коливання Ρ—Ρ… Π΅Π»Π΅ΠΌΠ΅Π½Ρ‚Ρ–Π². А Ρ‚Π°ΠΊΠΎΠΆ Ρƒ Π²ΠΈΠΏΠ°Π΄ΠΊΠ°Ρ…, ΠΊΠΎΠ»ΠΈ Π² тСхнологіях використання ΠΌΠ΅Ρ…Π°Π½Ρ–Ρ‡Π½ΠΈΡ… пристроїв Π½Π΅ΠΎΠ±Ρ…Ρ–Π΄Π½ΠΎ відмСТуватися Π²Ρ–Π΄ Ρ…Π°ΠΎΡ‚ΠΈΡ‡Π½ΠΈΡ… ΠΏΠ΅Ρ€Π΅ΠΌΡ–Ρ‰Π΅Π½ΡŒ Π²Π°Π½Ρ‚Π°ΠΆΡ–Π² Ρ– Π·Π°Π±Π΅Π·ΠΏΠ΅Ρ‡ΠΈΡ‚ΠΈ ΠΏΠ΅Ρ€Ρ–ΠΎΠ΄ΠΈΡ‡Π½Ρ– Ρ‚Ρ€Π°Ρ”ΠΊΡ‚ΠΎΡ€Ρ–Ρ— Ρ—Ρ… Ρ€ΡƒΡ…

    Phenological shifts of abiotic events, producers and consumers across a continent

    Get PDF
    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
    corecore