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    Wyświetlanie 1-14 z 14
    Tytuł:
    A structural optimisation viewpoint on growth phenomena
    Autorzy:
    Barthold, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/201312.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    computational mechanics
    structural optimisation
    sensitivity analysis
    configurational mechanics
    growth
    Opis:
    Evolutionary solid bodies undergoing changes of mass, of properties, and of shapes are considered in models of growth and adaptation and similarily in structural optimisation. A fundamental separation of different growth phenomena and a subsequent parametrisation using independent design variables for the amount of substance as well as for molar mass and molar volume facilitates an efficient formulation of the design space. Thus, the effects of design variations, i.e. change of amount of substance, on the variations of the structural response, i.e. the deformation in physical space, can be clearly described. Overall, a novel treatment of growth processes based on an evolution of the amount of substance is outlined. The parallelism of variations in physical and design space are highlighted and compared with the multiplicative decomposition of the deformation gradient into a growth and an elastic part incorporating an incompatible intermediate configuration. This drawback is overcome by a compatible manifold based on material points modelling the amount of substance outside of any geometrical space.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 2; 247-252
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Static axial crush performance of unfilled and elastomer-filled composite tubes
    Autorzy:
    Ochelski, S.
    Bogusz, P.
    Kiczko, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/200998.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    mechanical properties
    absorbed energy
    polymer composites
    elastomers
    experimental mechanics
    Opis:
    The paper presents the results of the experimental static axial crush performance of unfilled and filled composite tubes. Composites are widely used as materials for energy absorbing structures because of their low density and a very high absorbed energy in relation to the mass ratio. Foamed materials are used in order to additionally increase their efficiency, because of stabilizing the progressive crush. It was proved by many authors that various foamed materials positively influence the energy absorption. In this work authors took effort to evaluate a very different material as a filler of common composite elements . elastomers. Elastomers are materials characterised by very high crush strains and viscoelastic properties. The tube shaped specimens made of epoxy composite, reinforced with carbon or glass fabrics were filled with elastomers of 40; 60; 70 and 90. ShA hardnesses. The influence of the elastomer hardness and the filling degree on the energy absorption factor (EA) was evaluated. The degree of filling the specimens with elastomers is determined by a different size of the elastomer perforation. Elastomers have a negative impact on the energy absorbed by the composite tubes.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 1; 37-43
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Static axial crush performance of unfilled and foamed-filled composite tubes
    Autorzy:
    Ochelski, S.
    Bogusz, P.
    Kiczko, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/201001.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    mechanical properties
    absorbed energy
    polymer composites
    foamed materials
    experimental mechanics
    Opis:
    The use and the combination of new, high efficient materials for crashworthiness is of great interest nowadays. Foamed materials are commonly used to increase efficiency of composite materials. Based on the results obtained by Brachos and Douglas, it can be concluded that the sum of the energy absorption capabilities of the foamed filling and unfilled composite tubes is smaller than the energy absorbed by the tubes filled with the same filling. The paper presents the results of the experimental investigations into the influence of filling the tubes with different materials on the impact energy absorption capability. The tube shaped specimens made of epoxy composite, reinforced with carbon or glass fabrics were filled with foamed aluminium or foamed poly(vinyl chloride). It was proved that the foamed materials increase the energy absorption and the absorbed energy of the tubes filled with foams is greater than the sum of the energy absorbed by the composite tube without filling and the foamed material itself investigated separately, when the wall thickness is more than 2 mm. The investigations of the filled tubes with the thickness of walls equal to 1 mm showed lower absorbed energy values because the crushing force had decreased during the crush. The investigations were executed to show what are the effects of filling composite energy absorbing elements in the shape of tubes with foamed materials. Additionally, influence of tube wall thickness and crush mechanism were studied.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 1; 31-35
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Computational modelling of concrete behaviour under static and dynamic conditions
    Autorzy:
    Marzec, I.
    Tejchman, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/202016.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    concrete
    damage mechanics
    dynamic loading
    elasto-plasticity
    non-local theory
    viscosity
    Opis:
    The paper presents results of FE simulations of the concrete behaviour under quasi-static and dynamic loading. For quasi-static cyclic analyses, an enhanced coupled elasto-plastic-damage constitutive model has been used. To take the effect of the loading velocity into account, viscous and inertial terms have been also included. To ensure the mesh-independence and to properly reproduce strain localization in the entire range of strain rates, a constitutive formulation has been enhanced by a characteristic length of micro-structure by means of a non-local theory. Numerical results have been compared with some corresponding laboratory tests.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 1; 85-96
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Heat effects measurements in process of dynamic crash of polymer composites
    Autorzy:
    Ochelski, S.
    Bogusz, P.
    Kiczko, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/201006.pdf
    Data publikacji:
    2012
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    mechanical properties
    heat effect
    absorbed energy
    polymer composites
    experimental mechanics
    dynamic investigations
    Opis:
    In the work, the attempt to determine the influence of loading rate on temperature of the surface of the crushed composite energy absorbing elements was undertaken. The specimens made of epoxy composites reinforced with glass fabrics and carbon fabrics of the structures [(0/90)T ]n were subjected to dynamic investigations. Thermovision investigations were conducted during energy absorbing tests. A thermovision camera enables the measurement of the temperature on the whole surface of the specimen visible in the camera lens while the measurement with the use of thermocouple is only local and has great heat inertia. During the investigations, the increase of specimen temperature related to impact velocity occurs. The temperature increase is caused by friction between the particles of the crushed specimen and by friction between the specimen and the support of the strength machine. At high loading rates, the increase of temperature on the surface of the specimens was significantly greater than the softening temperature of the epoxy resin E-53.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2012, 60, 1; 25-30
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Pyramidal ceramic armor ability to defeat projectile threat by changing its trajectory
    Autorzy:
    Stanislawek, S.
    Morka, A.
    Niezgoda, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/202070.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    computational mechanics
    ballistic protection
    composite armor
    ceramics
    mechanika obliczeniowa
    ochrona balistyczna
    kompozytowy pancerz
    ceramika
    Opis:
    This paper presents a numerical study of a multilayer composite panel impacted by an AP (Armor Piercing) 14.5×114 mm B32 projectile. The composite consists of alternating layers of hard ceramic and a ductile aluminum alloy. While the alloy layer consists of typical plate, ceramics confront projectiles in the form of ceramic pyramids. The studied models are compared with a reference structure, which is a standard double layer panel. The problem has been solved with the usage of modeling and simulation methods as well as a finite elements method implemented in LS-DYNA software. Space discretization for each option was built with three dimensional elements ensuring satisfying accuracy of the calculations. For material behavior simulation, specific models including the influence of the strain rate and temperature changes were considered. A steel projectile and aluminum plate material were described by the Johnson-Cook model and a ceramic target by the Johnson-Holmquist model. The obtained results indicate that examined structures can be utilized as a lightweight ballistic armor in certain conditions. However, panels consisting of sets of ceramic prisms are a little easier to penetrate. Despite this fact, a ceramic layer is much less susceptible to overall destruction, making it more applicable for the armor usage. What is most important in this study is that significant projectile trajectory deviation is detected, depending on the impact point. Such an effect may be utilized in solutions, where a target is situated relatively far from an armor.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2015, 63, 4; 843-849
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Modelling of hydro-thermo-chemo-mechanical phenomena in building materials
    Autorzy:
    Gawin, D.
    Koniorczyk, M.
    Pesavento, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/202013.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    building materials
    chemical degradation
    hydro-thermal processes
    mechanics of multi-phase porous media
    numerical solution
    Opis:
    IssueJournal/Yearbook Volume Issue Page Issues Volume 61 (2013) Issue 1 (Mar 2013) , pp. 5-286 Volume 60 (2012) Issue 4 (Dec 2012) , pp. 673-859 Issue 3 (Sep 2012) , pp. 371-667 Issue 2 (Jun 2012) , pp. 185-368 Issue 1 (Mar 2012) , pp. 3-178 Volume 59 (2011) Issue 4 (Dec 2011) , pp. 371-579 Issue 3 (Sep 2011) , pp. 247-366 Issue 2 (Jun 2011) , pp. 125-243 Issue 1 (Mar 2011) , pp. 3-115 Volume 58 (2010) Issue 4 (Dec 2010) , pp. 463-716 Issue 3 (Sep 2010) , pp. 347-458 Issue 2 (Jun 2010) , pp. 217-342 Issue 1 (Mar 2010) , pp. 3-207 Volume 57 (2009) Issue 4 (Dec 2009) , pp. 297-398 Issue 3 (Sep 2009) , pp. 195-292 Issue 2 (Jun 2009) , pp. 123-188 Issue 1 (Mar 2009) , pp. 3-116 Most Downloaded Articles Joint reactions in rigid or flexible body mechanisms with redundant constraints by Wojtyra, M. and Frączek, J. Modified current differencing transconductance amplifier – new versatile active element by Malcher, A. Particle swarm optimization of artificial-neural-network-based on-line trained speed controller for battery electric vehicle by Ufnalski, B. and Grzesiak , L.M. Laser modification of the materials surface layer – a review paper by Kusinski, J./ Kac, S./ Kopia, A./ Radziszewska, A./ Rozmus-Górnikowska, M./ Major, B./ Major, L./ Marczak, J. and Lisiecki, A. Gas sensors based on nanostructures of semiconductors ZnO and TiO2 by Pustelny, T./ Procek, M./ Maciak, E./ Stolarczyk, A./ Drewniak, S./ Urbańczyk, M./ Setkiewicz, M./ Gut, K. and Opilski, Z. View Top 20 Most Downloaded Articles Previous Article Next Article Go to table of contents Download full text pdf (PDF, 1 MB) Modelling of hydro-thermo-chemo-mechanical phenomena in building materials D. Gawin1 / M. Koniorczyk1 / F. Pesavento2 1Department of Building Physics and Building Materials, Lodz University of Technology, 6 Politechniki Ave., 90-924 Lodz, Poland 2Department of Civil, Architectural and Environmental Engineering, University of Padova, Via Marzolo 9, 35131 Padova, Italy Citation Information: Bulletin of the Polish Academy of Sciences: Technical Sciences. Volume 61, Issue 1, Pages 51–63, ISSN (Print) 0239-7528, DOI: 10.2478/bpasts-2013-0004, May 2013 Publication History: Published Online: 2013-05-01 Abstract A general approach to modelling chemical degradation processes in building materials, due to combined action of variable hydrothermal, chemical and mechanical loads, is presented. Mechanics of multiphase porous media and damage mechanics are applied for this purpose, and kinetics of degradation processes is described with evolution equations based on thermodynamics of chemical reactions. The mass-, energy - and momentum balances, as well as the evolution equations, constitutive and physical relations are briefly summarized. Then, the model governing equations are numerically solved with the finite element method. Three examples of the model application for analyzing degradation processes of building materials are presented and discussed. The first one deals with capillary suction of the salt solution by two different building materials, the second one with the salt crystallization during drying of a brick wall, and the third one concerns calcium leaching from a concrete wall due to the chemical attack of pure water under pressure gradient at two different temperatures.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 1; 51-63
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Investigations on an influence of the material properties on vibrations of active rocker-bogie suspension
    Autorzy:
    Sokół, Krzysztof
    Pierzgalski, Maciej
    Powiązania:
    https://bibliotekanauki.pl/articles/2173528.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    frequency analysis
    suspension
    rover
    mobile platform
    computational mechanics
    analiza częstotliwości
    zawieszenie
    łazik
    platforma mobilna
    mechanika obliczeniowa
    Opis:
    Unmanned vehicles are often used in everyday life, mostly by rescue teams or scientists exploring new terrains. In those constructions, the suspension has constant dimensions, which leads to many disadvantages and limits the application area. The solution to these problems can be creating a six-wheeled mobile platform that can dynamically change the wheelbase in relation to the area of action or terrain inclination angle. The active change in location of the center of gravity gives a possibility to access sloppy obstacles not available with classical suspensions. The main scope of this study is to investigate the influence of material properties on vibration frequency at different lengths of suspension members. The obtained results will allow finding the optimum material for producing a prototype unit.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2022, 70, 1; e138239, 1--7
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Physical interpretation of the Cosserat mechanics for a collection of atoms
    Autorzy:
    Sikoń, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/201587.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Cosserat theory polar atom
    mechanical quantum number
    statistical mechanics
    condensed matter
    atom
    mechanika kwantowa
    mechanika statystyczna
    materia skondensowana
    teoria ośrodka Cosseratów
    Opis:
    In this work, the Cosserat medium is analyzes as a set of atoms. These atoms are under the action of a mechanical load. The statistical analysis is preceded by a description of a single atom using classical mechanics and quantum mechanics. The behavior of the atoms in the field generated by mechanical change of the interatomic distance is shown as a phenomenon which can explain the Cosserat mechanics in a continuum.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 2; 333-338
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fabrication and characterization of composite materials based on porous ceramic preform infiltrated by elastomer
    Autorzy:
    Chabera, P.
    Boczkowska, A.
    Witek, A.
    Oziębło, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/202111.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    ceramic matrix composites
    ceramic
    mechanical properties
    damage mechanics
    scanning electron microscopy
    kompozyty z matrycą ceramiczną
    ceramika
    właściwości mechaniczne
    mechanika szkód
    skaningowa mikroskopia elektronowa
    Opis:
    The paper presents the experimental results of fabrication and characterization of ceramic- elastomer composites. They were obtained using pressure infiltration of porous ceramics by elastomer As a result the composites in which two phases are interpenetrating three-dimensionally and topologically throughout the microstructure were obtained. In order to enhance mechanical properties of preforms a high isostatic pressure method was utilized. The obtained ceramic preforms with porosity gradient within the range of 20-40% as well as composites were characterized by X-ray tomography. The effect of volume fraction of pores on residual porosity of composites was examined. These results are in accordance with SEM images which show the microstructure of composites without any delaminations and voids. Such composites exhibit a high initial strength with the ability to sustain large deformations due to combining the ceramic stiffness and rubbery elasticity of elastomer. Static compression tests for the obtained composites were carried out and the energy dissipated during compression was calculated as the area under the stress-strain curve. The dynamic behavior of the composite was investigated using the split Hopkinson pressure bar technique. It was found that ceramic-elastomer composites effectively dissipate the energy. Moreover, a ballistic test was carried out using armor piercing bullets.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2015, 63, 1; 193-199
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Proposal of the hybrid solution to determining the selected fracture parameters for SEN(B) specimens dominated by plane strain
    Autorzy:
    Graba, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/201318.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fracture mechanics
    fracture parameters
    limit load
    finite element method
    single edge notched specimen
    mechanika złamania
    parametry złamania
    obciążenie graniczne
    metoda elementów skończonych
    pojedyncza krawędź skrawająca
    Opis:
    In the paper, new hybrid (numerical-analytical) methods to calculate the J-integral, the CTOD, and the load line displacement are presented. The proposed solutions are based on FEM calculations which were done for SEN(B) specimens dominated by plane strain condition. The paper includes the verification of the existing limit load solution for SEN(B) specimen with proposal of the new analytical formulae, which were used for building hybrid equations for determining three selected fracture mechanics parameters.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 4; 523-532
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Quantum magnetostriction effect resulting from the asymmetric structure of matter measured with EPR spectrometer
    Autorzy:
    Sikoń, Marek
    Bidzinska, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/2204518.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    atomic arm of action
    non-paired electron/nucleon
    polar rotation
    Cosserat mechanics
    EPR
    electron paramagnetic resonance
    elektron niesparowany
    nukleon niesparowany
    atomowe ramię działania
    obrót biegunowy
    mechanika Cosserata
    elektronowy rezonans paramagnetyczny
    Opis:
    This paper explains the rotation and displacement as well as the couple and force stress in material with unpaired electrons/nucleons subjected to a magnetic field. This phenomenon is described in terms of quantum mechanics for nanoparticle and quantum statistical mechanics for loose nanomaterial. Quantitative calculations are carried out based on experimental data collected under the magnetic field of an EPR spectrometer from a set of nanocrystallites of hydrated copper sulfate.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 1; art. no. e144575
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mechanics of infinitesimal gyroscopes on helicoid-catenoid deformation family of minimal surfaces
    Autorzy:
    Kovalchuk, Vasyl
    Gołubowska, Barbara
    Mladenov, Ivaïlo M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2128134.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    action-angle analysis
    mechanics of infinitesimal gyroscopes
    geodesic equations of motion
    geodetic equations of motion
    helicoid-catenoid deformation family of minimal surfaces
    elliptic integrals
    elliptic functions
    analiza kąta działania
    mechanika nieskończenie małych żyroskopów
    równanie ruchu geodezyjne
    całki eliptyczne
    funkcje eliptyczne
    rodzina deformacji helikoidów minimalnych powierzchni
    rodzina deformacji katenoidów minimalnych powierzchni
    Opis:
    In this paper we explore the mechanics of infinitesimal gyroscopes (test bodies with internal degrees of freedom) moving on an arbitrary member of the helicoid-catenoid family of minimal surfaces. As the configurational spaces within this family are far from being trivial manifolds, the problem of finding the geodesic and geodetic motions presents a real challenge. We have succeeded in finding the solutions to those motions in an explicit parametric form. It is shown that in both cases the solutions can be expressed through the elliptic integrals and elliptic functions, but in the geodetic case some appropriately chosen compatibility conditions for glueing together different branches of the solution are needed. Additionally, an action-angle analysis of the corresponding Hamilton-Jacobi equations is performed for external potentials that are well-suited to the geometry of the problem under consideration. As a result, five different sets of conditions between the three action variables and the total energy of the infinitesimal gyroscopes are obtained.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 2; e136727, 1--10
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mechanics of infinitesimal gyroscopes on helicoid-catenoid deformation family of minimal surfaces
    Autorzy:
    Kovalchuk, Vasyl
    Gołubowska, Barbara
    Mladenov, Ivaïlo M.
    Powiązania:
    https://bibliotekanauki.pl/articles/2173588.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    action-angle analysis
    mechanics of infinitesimal gyroscopes
    geodesic equations of motion
    geodetic equations of motion
    helicoid-catenoid deformation family of minimal surfaces
    elliptic integrals
    elliptic functions
    analiza kąta działania
    mechanika nieskończenie małych żyroskopów
    równanie ruchu geodezyjne
    całki eliptyczne
    funkcje eliptyczne
    rodzina deformacji helikoidów minimalnych powierzchni
    rodzina deformacji katenoidów minimalnych powierzchni
    Opis:
    In this paper we explore the mechanics of infinitesimal gyroscopes (test bodies with internal degrees of freedom) moving on an arbitrary member of the helicoid-catenoid family of minimal surfaces. As the configurational spaces within this family are far from being trivial manifolds, the problem of finding the geodesic and geodetic motions presents a real challenge. We have succeeded in finding the solutions to those motions in an explicit parametric form. It is shown that in both cases the solutions can be expressed through the elliptic integrals and elliptic functions, but in the geodetic case some appropriately chosen compatibility conditions for glueing together different branches of the solution are needed. Additionally, an action-angle analysis of the corresponding Hamilton-Jacobi equations is performed for external potentials that are well-suited to the geometry of the problem under consideration. As a result, five different sets of conditions between the three action variables and the total energy of the infinitesimal gyroscopes are obtained.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 2; art. no. e136727
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-14 z 14

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