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Search results for: SHALLOW WATER EQUATIONS
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Dynamic inequalities and equations of Volterra type on time scales
PublicationPraca dotyczy całkowo-różniczkowych równań dynamicznych typu Volterry z warunkami początkowymi. Stosując twierdzenie Banacha o punkcie stałym pokazano istnienie jedynego rozwiązania liniowego równania dynamicznego. Stosując metodę iteracji monotonicznych pokazano istnienie rozwiązań ekstremalnych dla problemów nieliniowych. Badano też nierówności dynamiczne. Praca zawiera również uwagi dotyczące zagadnień różniczkowych i różnicowych.
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Search for the fundamental solution to the vector acoustic wave equations
PublicationCzasowo-przestrzenna funkcja Greena pola swobodnego jest dobrze znanym rozwiązaniem podsta-wowym skalarnego niejednorodnego równania falowego. Wyraża ona odpowiedź ośrodka płynnego na punktowe zaburzenie o symetrii sferycznej. Odpowiedź ośrodka na zaburzenie wektorowe nie jest tak oczywista. Artykuł przedstawia oryginalne podejście do problemu, polegające na systematycznej, szcze-gółowej weryfikacji hipotetycznych rozwiązań skalarnych...
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Boundary vlue problems for difference equations with causal operators
PublicationPraca dotyczy problemów brzegowych dla równań różnicowych.Podano warunki dostateczne na istnienie ekstremalnych rozwiązań stosując metodę iteracji monotonicznych.
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First-order differential equations with nonlocal boundary conditions
PublicationWe study a first-order boundary value problem subject to some boundary conditions given by Riemann-Stieltjes integrals. Using a monotone iterative method, we formulate sufficient conditions which guarantee the existence of extremal or quasi-solutions in the corresponding region bounded by upper and lower solutions of our problems. The case when a unique solution exists is also investigated. Some examples are given to illustrate...
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Antiperiodic boundary value problems for functional differential equations
PublicationRównania różniczkowo funkcyjne z antyokresowymi warunkami brzegowymi są przedmiotem rozważań tej pracy. Podane zostały warunki dostateczne na istnienie jedynego rozwiązania, które jest granicą dwóch monotonicznych ciągów. Szybkość tej zbieżności jest również określona. Metoda dowodzenia oparta jest na metodzie kwasilinearyzacji. Otrzymano również pewne wyniki dotyczące problemów liniowych.
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Existence of solutions of differential equations with nonlinearmultipoint boundary conditions.
PublicationSformułowano warunki dostateczne na istnienie rozwiązań (jedynego lubekstremalnych) dla równań różniczkowych z warunkami jak wyżej przyzastosowaniu metody iteracji monotonicznych. O prawej stronie zagadnienia i nieliniowym warunku brzegowym zakładano między innymi, że spełniają jednostronny warunek Lipschitza.
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Periodic boundary value problems for functional differential equations
PublicationPrzedmiotem badań były równania różniczkowo-funkcyjne dość ogólnej postaci z warunkami brzegowymi typu okresowego. Podano warunki dostateczne na istnienie jedynego rozwiązania (zerowego) odpowiedniego zagadnienia liniowego z okresowymi warunkami brzegowymi. Te wyniki zostały wykorzystane aby pokazać, że odpowiednio skonstruowane ciągi monotoniczne są jednostajnie zbieżne do jedynego, w pewnym segmencie, rozwiązania zagadnienia...
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Boundary value problems for systems of functional differential equations
PublicationPraca dotyczy przybliżonych rozwiązań zagadnienia brzegowego dla funkcyjnych równań różniczkowych 2-go rzędu. Podano numeryczne algorytmy na wyznaczenie tego rozwiązania i warunki dostateczne, przy których metoda jest zgodna i zbieżna. Podano też konstrukcję metody dowolnego rzędu.
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Dressing chain equations associated with difference soliton systems
PublicationAnalogicznie do teorii równań różniczkowych solitonowych, wprowadzamy proce-durę ubierania pary Laxa. Stosujemy metodę dla budowy nowych rozwiązań napodstawie znanych. Wprowadza się uogólnione wielomiany Bella. Tworzy sięschemat dla ogólnych par Laxa w postaci wielomianów od pewnego automorfizmupierscieni. Podany został przykład równań Hiroty i Nahma.
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Nonlocal problems for functional partial differential equations of firstorder
PublicationRozważa się istnienie uogólnionych rozwiązań nielokalnych problemów dla quasiliniowych i nieliniowych równań różniczkowo-funkcyjnych cząstkowych pierwszego rzędu. Dowody twierdzeń bazują na metodzie bicharakterystyk i metodzie kolejnych przybliżeń.
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Numerical conditioning of delta-domain Lyapunov and Riccati equations
PublicationW pracy rozważono problem uwarunkowania dyskretno czasowych równań Lapunowa oraz równań Riccatiego - to znaczy problem wrażliwości rozwiązań takich równań na odchyłki ich parametrów od nominalnych wartości. Zdefiniowano odpowiedni "różniczkowy" wskaźnik uwarunkowania oraz podano efektywną metodę szacowania jego wartości. Udowodniono teoretycznie - a także przekonująco zilustrowano na drodze numerycznej - twierdzenie głoszące, iż...
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Quasilinearization methods for nonlinear parabolic equations with functional dependence
PublicationRozważamy problem Cauchy`ego dla nieliniowych równań parabolicznych z zależnością funkcyjną. Dowodzimy twierdzeń o szybkiej zbieżności ciągów kolejnych przybliżeń określonych w metodzie quasilinearyzacji w dwóch przypadkach: (i) argumentem funkcyjnym jest funkcja niewiadoma, (ii) zależność funkcyjna dotyczy również pochodnej funkcji niewiadomej.
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Quadrtic convergence of monotone iterations of differential-algebraic equations
PublicationZastosowano tu metodę quazilinearyzacji do równań różniczkowo-algebraicznych z warunkiem początkowym. Pokazano, że odpowiednie iteracje monotoniczne są zbieżne do jedynego rozwiązania.
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Darboux covariant equations of von Neumann type and their generalization.
PublicationOpisano nową klasę uogólnionych równań von Neumanna całkowalnych przez transformację Darboux. Uogólnienie zawiera jako przypadki szczególne nieliniowe równanie von Neumanna, r. Nahma, kratę Tody i inne.
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Second order differential equations with Dirichlet boundary conditions
PublicationZastosowano metodę kwazilinearyzacji aby wyznaczyć rozwiązanie przybliżone zagadnienia brzegowego dla równań różniczkowych rzędu drugiego. Pokazano kwadratową (lub prawie kwadratową) zbieżność tego rozwiązania do rozwiazania dokładnego.
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Implicit difference methods for parabolic functional differential equations.
PublicationPraca dotyczy przybliżania rozwiązań quasiliniowych parabolicznych równań różniczkowo-funkcyjnych za pomocą schematów różnicowych, uwikłanych ze względu na zmienną czasową. Wykonano pełną analizę zbieżności metod i pokazano na przykładzie, że nowe metody są istotnie lepsze od schematów jawnych. Dowód stabilności oparty jest na metodzie porównawczej z nieliniowymi oszacowaniami typu Perrona. Otrzymane wyniki można zastosować do...
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Differential equations with a singular matrix and convergence of approximate solutions
PublicationZastosowano metodę kwazilinearyzacji dla równań różniczkowych z macierzą osobliwą aby pokazać, że odpowiednie ciągi rozwiązań przybliżonych są kwadratowo zbieżne do rozwiązania naszego problemu.Metodę tę zastosowano do układów takich równań różniczkowych.
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Cavitation-Based Processes for Water and Wastewater Treatment
PublicationCavitation based on advanced oxidation processes (Cav-AOPs) is interesting alternatives for already implemented wastewater treatment technologies. Destructive and strongly undesirable phenomena in the industry, i.e., cavitation, revealed to be useful in a positive manner as a source of energy for chemical reactions. During the implosion of cavitation bubbles, focused energy and resulting high temperature and pressure allows to...
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Dissociation energies of protonated water clusters
PublicationRelative abundances of positively ionized water clusters formed in a low-pressure electrical discharge as function of reduced electric field were obtained by using drift cell and quadrupole mass spectrometer. It was noticed that some clusters say with n = 4 were more abundant than others, at comparable drift conditions. Dissociation energies have been derived from equilibrium conditions for relative clusters abundances. The Hartree-Fock...
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The influence of water and mineral oil on volumetric losses in a hydraulic motor
PublicationIn this paper volumetric losses in hydraulic motor supplied with water and mineral oil (two liquids having significantly different viscosity and lubricating properties) are described and comparison. The experimental tests were conducted using an innovative hydraulic satellite motor, that is dedicated to work with different liquid, including water. The sources of leaks in this motor are characterized and described also. On this...
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Quality Model for Integrated Security Monitoring and Control in Water Distribution Systems
PublicationThis article addresses the problem of drinking water distribution system (DWDS) security in the terms of water quality which in the era of terrorist threat is of high importance to the public. The contribution of this paper is the development of the so called security module to extend a multi-species water quality model. This gives an insight to the situation in DWDS not only under normal operational conditions but also in case...
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Correlated Particle Motion and THz Spectral Response of Supercritical Water
PublicationMolecular dynamics simulations of supercritical water reveal distinctly different distance-dependent modulations of dipolar response and correlations in particle motion compared to ambient conditions. The strongly perturbed H-bond network of water at supercritical conditions allows for considerable translationaland rotational freedom of individual molecules. These changes give rise to substantially different infrared spectra and...
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SESSILE DROPLET CONTACT ANGLE OF WATER-Al2O3, WATER-TiO2 AND WATER-Cu NANOFLUIDS
PublicationThe goal of the present work was the experimental determination of the contact angle of droplets of three nanofluids on various substrates. Of particular interest was effect of nanoparticle concentration on droplet contact angle.
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AUGMENTATION OF THE CRITICAL HEAT FLUX IN WATER-Al2O3, WATER-TiO2 AND WATER-Cu NANOFLUIDS
PublicationThe main aim of the proposed study is therefore recognition of the phenomena accompanying nucleate boiling crisis of selected nanofluids during boiling on horizontal tubes of various outside diameters. Of particular interest is impact of contact angle and tube diameter on the value of critical heat flux. The results obtained should give more light on the nature of nucleate boiling crisis and will serve as a basis for future theoretical...
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RESEARCH ON HYDRODYNAMIC PEEK JOURNAL BEARINGS LUBRICATED WITH WATER AND OIL
PublicationThe main purpose of the research was to determine the possibilities and experimentally test the benefits of replacing conventional oil lubrication with ecological water lubrication. Tests were carried out on a test rig for hydrodynamic radial bearings under conditions representative of the expected applications for the bearing in water turbines. Bearings made from the polymer material PEEK (polyether ether ketone) were tested under static...
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THIRD-ORDER EXPONENTIAL INTEGRATOR FOR LINEAR KLEIN–GORDON EQUATIONS WITH TIME AND SPACE-DEPENDANT MASS
PublicationAllowing for space- and time-dependance of mass in Klein–Gordon equations re- solves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their applicability to the domain of quantum cosmology, where the variation in mass may be accompanied by high oscillations....
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THIRD-ORDER EXPONENTIAL INTEGRATOR FOR LINEAR KLEIN–GORDON EQUATIONS WITH TIME AND SPACE-DEPENDANT MASS
PublicationAllowing for space- and time-dependance of mass in Klein–Gordon equations re- solves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their applicability to the domain of quantum cosmology, where the variation in mass may be accompanied by high oscillations....
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Recent Achievements in Constitutive Equations of Laminates and Functionally Graded Structures Formulated in the Resultant Nonlinear Shell Theory
PublicationThe development of constitutive equations formulated in the resultant nonlinear shell theory is presented. The specific features of the present shell theory are drilling rotation naturally included in the formulation and asymmetric measures of strains and stress resultants. The special attention in the chapter is given to recent achievements: progressive failure analysis of laminated shells and elastoplastic constitutive relation...
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The Influence of Water and Mineral Oil on Pressure Losses in Hydraulic Motor
PublicationIn this paper, pressure losses in hydraulic motor supplied with water and mineral oil (two liquids that have significantly different viscosity and lubricating properties) are described and compared. The experimental tests were conducted using a hydraulic satellite motor that is dedicated to working with different liquids, including water. The methodology of measuring the pressure drop in internal channels of this motor is also...
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Unusual structural properties of water within the hydration shell of hyperactive antifreeze protein
PublicationMany hypotheses can be encountered explaining the mechanism of action of antifreeze proteins. One widespread theory postulates that the similarity of structural properties of solvation water of antifreeze proteins to ice is crucial to the antifreeze activity of these agents. In order to investigate this problem, the structural properties of solvation water of the hyperactive antifreeze protein from Choristoneura fumiferana were...
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The role of heterotrophic plate count bacteria in bottled water quality assessment
PublicationThe ever-growing popularity of bottled water is the result of many factors. One of the most relevant is the widespread belief that bottled water is safer for drinking than tap water. In fact many literature sources describe the rapid growth of the amounts of microorganisms in bottled water samples following the bottling process. The main purpose of this article is to collect the information on the factors which may affect this...
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Assessment of the cell biovolume of phytoplankton widespread in coastal and inland water bodies
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Nodal models of Pressurized Water Reactor core for control purposes – A comparison study
PublicationThe paper focuses on the presentation and comparison of basic nodal and expanded multi-nodal models of the Pressurized Water Reactor (PWR) core, which includes neutron kinetics, heat transfer between fuel and coolant, and internal and external reactivity feedback processes. In the expanded multi-nodal model, the authors introduce a novel approach to the implementation of thermal power distribution phenomena into the multi-node...
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Very accurate time propagation of coupled Schrödinger equations for femto- and attosecond physics and chemistry, with C++ source code
PublicationIn this article, I present a very fast and high-precision (up to 33 decimal places) C++ implementation of the semi-global time propagation algorithm for a system of coupled Schrödinger equations with a time-dependent Hamiltonian. It can be used to describe time-dependent processes in molecular systems after excitation by femto- and attosecond laser pulses. It also works with an arbitrary user supplied Hamiltonian and can be used...
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Investigation of the thermal effects in water-lubricated journal bearings with axial grooves
PublicationWater-lubricated hydrodynamic journal bearings are frequently applied as stern tube bearings due to their advantages over other bearing types. They are environmentally friendly, can operate without sealings and in conditions of low friction losses. The most popular are bearings with open axial grooves, which require, for proper operation, forced axial flow of the lubricating water. Correctly designed and operated stern tube bearings...
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Modelling of a medium-term dynamics in a shallow tidal sea, based on combined physical and neural network methods
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Large red cyanobacterial mats (Spirulina subsalsa Oersted ex Gomont) in the shallow sublittoral of the southern Baltic
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Static Model of Steam/Water Cycle for Thermal and Economic Analysis
PublicationThe thermodynamic efficiency of typical conventional and nuclear power plants is insufficient. A large amount of the generated heat is removed to the environment and regarded as a waste. A solution which is commonly used to increase the efficiency and profitability of the existing and planned power plants refers to cogeneration of heat and power. To prepare sophisticated thermodynamic and economic analyses, a precise static model...
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Origin and fate of nanoparticles in marine water – Preliminary results
PublicationThe number, morphology and elemental composition of nanoparticles (<100 nm) in marine water was investigated using Variable Pressure Scanning Electron Microscopy (VP-SEM) and Energy-dispersive X-ray spectroscopy (EDS). Preliminary research conducted in the Baltic Sea showed that the number of nanoparticles in seawater varied from undetectable to 380 (x102) cm-3. Wind mixing and density barriers (thermocline) had a significant impact...
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THE INFLUENCE OF WATER-LAND RELATIONS ON THE LANDSCAPE AND ARCHITECTURE OF THE VISTULA DELTA (POLAND)
PublicationThe Vistula Delta is unique region of water domination. In this part of Europe, historic rural assumptions have been developing since the 12th century. Practically, it can be said that most of the systems were related to the coexistence of the human and the water element. Relations of water and land, developed specific types of villages such as a water-based village. Water landscape; polders, canals, dikes and rivers, hydro-technical...
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Modal Analysis of a Steel Radial Gate Exposed to Different Water Levels
PublicationWith the increase in water retention needs and planned river regulation, it might be important to investigate the dynamic resistance of vulnerable elements of hydroelectric power plants, including steel water locks. The most frequent dynamic loads affecting hydroengineering structures in Poland include vibrations caused by heavy road and railway traffic, piling works and mining tremors. More destructive dynamic loads, including...
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Reduction of Derivative pipeline effort in water turbine
PublicationThe paper presents an approach to evaluate and reduce the effort of the derivative pipeline in a water turbine of a hydrostatic power station in its vulnerable spots. Potential places of the biggest effort of the structure, as well as the coefficient of displacement and safety factor related to them were identified using FEM numerical method. Pipeline reinforcement was designed and made based on FEM analysis. Original technology...
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Drainage and capillary rise components in water balance of alluvial soils
PublicationPrzepływ wody przez dolny brzeg profilu glebowego stanowi ważny element wielu modeli pracy drenażu. Przeciekanie wody w głąb albo podsiąk kapilarny ku górze mierzone były metodą lizymetryczną w warunkach polowych podczas 4 lat (1972-1975). Podsiąk kapilarny wynosił 40-50% ogólnego zasilania w wodę w glebach typu Histosols, natomiast prawie zero w glebach typu Inceptisols. Pomierzone wartości pozwalaja na ocenę wymiany wody pomiedzy...
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Protection of surface water against contamination by wetland systems in Poland
PublicationOpisano systemy hydrofitowe stosowane do usuwania zanieczyszczeń z wód powierzchniowych zasilanych wodami opadowymi. Po wprowadzeniu systemów stwierdzono znaczną poprawę jakości wód analizowanych cieków.
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Properties of water in the region between a tubulin dimer and a single motor head of kinesin
PublicationA kinesin is a molecular motor that can perform movement on a microtubule track in a stepping-like manner. This motion is connected with processes of association and dissociation of kinesin and tubulin. Water is an important participant in these kinds of molecular interactions. This is why we have decided to investigate the dynamical and structural properties of water in the region between the kinesin catalytic domain and the tubulin...
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The impact of sediment, fresh and marine water on the concentration of chemical elements in water of the ice-covered lagoon
PublicationThe common use of chemical elements by man has been contributing to their extraction for centuries. As a consequence, they have been directly or indirectly introduced into the biogeochemical cycle. In the framework of many conventions, mining and processing of elements are currently subject to many restrictions. However, their large load that has already been deposited in the soil and bottom sediments can be remobilised and...
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Sustainable Development of Water Housing Using the Example of Poland: An Analysis of Scenarios
PublicationAt the turn of the 20th and 21st centuries, Polish cities began the process of returning to live by water. There is a growing interest in water reservoirs not only as places for recreation, but also as new areas suitable for living, at the very center of the city. Unfortunately, due to the lack of appropriate legal regulations, the dynamic development of floating homes (FHs) is starting to raise increasing concerns in Poland. Regardless...
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Verification of the criteria for evaluation of water and frost resistance of asphalt concrete
PublicationThe paper presents the results of field investigation - condition survey of existing pavements and the results of laboratory tests on water and frost resistance of samples cored from the these pavements. The purpose of testing was to verify the criteria for evaluation of the resistance of asphalt concrete to the action of water and frost by way of comparing the results of field and laboratory tests, followed by evaluation of their...
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Celebrating 50 years of SWIMs (Salt Water Intrusion Meetings)
PublicationThe Salt Water Intrusion Meetings, or SWIMs, are a series of meetings that focus on seawater intrusion in coastal aquifers and other salinisation processes. 2018 marks the 50th year of the SWIM and the 25th biennial meeting. The SWIM proceedings record half a century of research progress on site characterisation, geophysical and geochemical techniques, variable-density flow, modelling, and water management. The SWIM is positioning...
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Closed Form Constraint Equations Used to Express Frictionless Slip of Multibody Systems Attached to Finite Elements—Application to a Contact between a Double Pendulum and a Beam
PublicationThis paper focuses on the numerical modeling of the dynamics of mechanical systems. Robots that can inspect high-voltage lines inspired this research. Their control systems must anticipate potential grab positions appropriately. We intend to formulate equations dedicated to the numerical description of the robot/cable contact. The investigated problem is not straightforward, since parts of the modeled systems are numerically inhomogeneous....