Resonance in the Cart-Pendulum System—An Asymptotic Approach

The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-parametric pendulum attached with a damped system. Using Lagrange’s equations in terms of generalized coordinates, the fundamental equations of motion (EOM) are derived. The method of multiple scales (MMS) is applied to obtain the approximate solutions of these equations up to the second order of approximation. Resonance cases are classified, in which the primary external and internal resonance are investigated simultaneously to establish both the solvability conditions and the modulation equations. In the context of the stability conditions of these solutions, the equilibrium points are obtained and graphically displayed to derive the probable steady-state solutions near the resonances. The temporal histories of the attained results, the amplitude, and the phases of the dynamical system are depicted in graphs to describe the motion of the system at any instance. The stability and instability zones of the system are explored, and it is discovered that the system’s performance is stable for a significant number of its variables.

Resilience

This chapter extends the concept of resilience past its popular use and abuse to consider the deeper set of concepts that shape understandings of stability and instability in ecological relationships. Here, bundles of supporting concepts, each carrying implicit values, threaten to turn a multitude of useful ideas into a mess of conflicting frameworks. While resilience is a concept that developed out of the empirical grounds of ecology, it becomes, for sustainability science, a ‘term of art’ that expands to encompass the qualitative discourses of the humanistic sciences.

Oikography: Ethnographies of House-ing in Critical Times

Houses are at once built shelters; collections of relations, affects, and moralities; and nodes within neighborhoods, communities, and larger political-economic and environmental regimes. This Colloquy proposes oikography as an ethnographic approach that deconstructs technocratic assumptions about the house and traces the plasticity of dwelling across multiple space-times, with a focus on the action of house-ing. Inspired by critical perspectives emanating from the diasporic, post-plantation house, we explore the reciprocal process of people making houses and houses making people amid ongoing calamity. The processes of house-ing reveal houses as unpredictable human-nonhuman entities, modulated by tensions between stability and instability, borders and fluxes, stillness and movement. Oikography is thus attuned to multirelational efforts at creating provisional dwellings, grounds from which the past is gauged and future horizons crafted. Resumo As casas são ao mesmo tempo abrigos construídos, coleções de relações, afetos e moralidades, e nodos dentro de bairros, comunidades e regimes político-econômicos e ambientais. Esta coletânea propõe a oikografia como uma abordagem etnográfica que desmonta pressupostos tecnocráticos sobre a casa e traça a plasticidade da moradia através de múltiplos espaços e temporalidades, com foco nas ações de house-ing. Inspirados por perspectivas críticas que emanam do viver diaspórico e pós-plantação, exploramos o processo recíproco de pessoas fazendo casas e casas fazendo pessoas em meio a calamidades recorrentes. Os processos de house-ing mostram as casas como entidades humano-não humanas imprevisíveis, moduladas por tensões entre estabilidade e instabilidade, limites e fluxos, repouso e movimento. A oikografia está assim em sintonia com os esforços multi-relacionais de criação de vivendas provisórias, bases a partir das quais o passado é aferido e horizontes futuros são traçados. Resumen Las casas son a la vez refugios construidos, complejos de relaciones, afectos y moralidades, nodos dentro de barrios, comunidades, regímenes político-económicos y medioambientales. Este dossier propone a la oikografía como un enfoque etnográfico que deconstruye los supuestos tecnocráticos sobre la casa y rastrea su plasticidad a través de tiempos y espacios, focalizando las acciones de house-ing. Inspirados en las perspectivas críticas que emanan del vivir diaspórico y de la post-plantación, exploramos el proceso recíproco de personas que hacen casas y de casas que hacen personas en medio a las calamidades del mundo contemporáneo. Los procesos de house-ing muestran a las casas como entidades humanas-no humanas impredecibles, moduladas por tensiones entre estabilidad e inestabilidad, fronteras y flujos, quietud y movimiento. La oikografía está, por lo tanto, en sintonía con los esfuerzos multirrelacionales para crear hogares provisorios, terrenos desde los que se observa el pasado y se elaboran horizontes de futuro.

Analysis of the Strong and Weak Monotonic External Stability of the Resonance in a Perturbed Dynamical System

A perturbed dynamical system involving two ordinary differential equations is under review. Whereupon, the differential equation for determining the fast phase contains the ratio of the two frequencies. When these frequencies coincide for a long time, a resonance is implemented in this system. The aim of this paper is to obtain the conditions of monotonic external stability and instability of this resonance. The sufficient conditions for the external stability and instability of the resonance defined in this paper assume that the signs of the analyzed derivatives remain unchanged in the non-resonant section of the change in the independent variable. This paper gives a new classification of the phenomenon of external stability of resonance, which includes weak, linear, and strong stability. It should be noted that the conditions of monotonic external stability and instability of the resonance presented in this paper can be used in various scientific and technological problems, in which resonances are observed. Particularly, the concluding part of the paper considers the application of the results obtained within the framework of the problem of the perturbed motion of a rigid body relative to a fixed point.

Stability and Instability of Traveling Wave Solutions to Nonlinear Wave Equations

In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition that allows us to prove the global nonlinear asymptotic stability of the plane wave. The proof of global stability requires us to analyze the geometry of the interaction between the background plane wave and the perturbation. When this condition is not met, we are able to prove linear instability assuming an additional genericity condition. The linear instability is shown using a geometric optics ansatz.

On maintaining the stability of the equilibrium of nonlinear oscillators under conservative perturbations

The problem of Yu.N. Bibikov on maintaining the stability of the equilibrium position of two interconnected nonlinear oscillators under the action of small, in a certain sense, conservative perturbing forces is considered. With different methods of reducing the system to the Hamiltonian form, some features are revealed for the case when the perturbing forces of the interaction of two oscillators are potential. The conditions for preserving the stability and instability of the equilibrium of two oscillators for the case of sufficiently small disturbing forces are obtained. The problem of maintaining the stability of the equilibrium under conservative perturbations is also considered in the more general situation of an arbitrary number of oscillators with power potentials with rational exponents, which leads to the case of a generalized homogeneous potential of an unperturbed system. The example given shows the applicability of the proposed approach in the case when the order of smallness of the perturbing forces coincides with the order of smallness of the unperturbed Hamiltonian.

REFLECTION OF TWO LAWS OF SPELLING IN THE SPEECH OF UKRAINIAN RESPONDENTS OF THE DIASPORA: NORMS AND DEVIATIONS

The article is devoted to the oral speech of Ukrainian diaspora’s youth (America, Canada, Italy, the Czech Republic, Poland, Germany, Moldova, the Transnistrian Moldavian Republic) at the synchronous level, in particular the pronunciation features of the Ukrainian language. Based on the poll the normativeness and historical organicity are proved. Also, pronunciation problems and orthoepic deviations are indicated; the percentage of mastery of orthoepy of sound combinations was determined, in particular, the pronunciation of hushing sounds before sibilants and vice versa in a wide local and social representation of foreign countries. Our research aims to try to determine the percentage of orthoepy, to identify, analyze and describe typical pronunciation mistakes, in particular the pronunciation of hushing sounds before sibilants and vice versa in a wide local and social representation abroad. Our task is to analyze the speech of Ukrainian respondents in the diaspora, to indicate the stability and instability of a particular norm; to trace the reflection of the pronunciation of these sound combinations in old written notes, and compare with the speech of Ukrainian respondents in Ukraine. The object of the research is Ukrainian speech of the diaspora of different spheres and age groups. The subject of the research is the mastery of orthoepic norms of the modern Ukrainian language, in particular the orthoepy of sound combinations (hushing sounds before sibilants; sibilants before hushing sounds). The results of a poll are the actual material of the study. It is 100 recordings lasting 300 minutes (5 hours). The poll was attended by 100 people of Ukrainian origin who lives abroad: 10 residents of the United States, 10 residents of Canada, 30 residents of Europe - Poland (2), Germany (3), Italy (5), the Czech Republic (10), Moldova (10) and 50 students of Taras Shevchenko University (Tiraspol, Transnistria). The informants live there for 10 years. They should read aloud and record the words for the analysis of the pronunciation of sibilants before hushing sounds (in the prefixes роз-, без-, з-; in the middle of the word). Thus, the fixation of hushing sounds instead of sibilants is a common phenomenon and can be traced in many monuments of different periods, but the real rate of pronunciation sibilants before hushing sounds by foreign respondents is 26%, by all informants (Ukrainian and foreign together) is 35 %; pronunciation of sibilants before hushing sounds residents of foreign origin of Ukrainian origin is 14% and by all informants in general also 14%. Undoubtedly, we consider these norms to be weak, and if we take into account the gender factor, they are mostly observed by women, both in Ukraine and abroad. In the speech of most men, we trace the pronunciation of the pronunciation [чц '] as [ц'], [шс '] as [с':]. We see the prospect of further research in the study of orthoepic speech deviations of modern youth of the Ukrainian diaspora, in particular in the pronunciation of other sound combinations.

General stability and exponential growth of nonlinear variable coefficient wave equation with logarithmic source and memory term

This paper is concerned with the asymptotic stability and instability of solutions to a variable coefficient logarithmic wave equation with nonlinear damping and memory term. This model describes wave travelling through nonhomogeneous viscoelastic materials. By choosing appropriate multiplier and using weighted energy method, we prove the exponential decay of the energy. Besides, we also obtain the instability at the infinity of the solutions in the presence of the nonlinear damping.