Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

Category theory based solution for the building block replacement problem in materials design

An important objective in materials design is to develop a systematic methodology for replacing unavailable or expensive material building blocks by simpler and abundant ones, while maintaining or improving the functionality of the material. The mathematical field of category theory provides a formal specification language which lies at the heart of such a methodology. In this paper, we apply material ologs, category-theoretic descriptions of hierarchical materials, to rigorously define a process by which material building blocks can be replaced by others while maintaining large-scale properties, to the extent possible. We demonstrate the implementation of this approach by using algebraic techniques to predict concrete conditions needed for building block replacement. As an example, we specify structure–function relationships in two systems: a laminated composite and a structure–function analogue, a fruit salad. In both systems we illustrate how ologs provide us with a mathematical tool that allows us to replace one building block with others to achieve approximately the same functionality, and how to use them to model and design seemingly distinct physical systems with a consistent mathematical framework

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

Computing covariant vectors, Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study

Covariant vectors, Lyapunov vectors, or Oseledets vectors are increasingly being used for a variety of model analyses in areas such as partial differential equations, nonautonomous differentiable dynamical systems, and random dynamical systems. These vectors identify spatially varying directions of specific asymptotic growth rates and obey equivariance principles. In recent years new computational methods for approximating Oseledets vectors have been developed, motivated by increasing model complexity and greater demands for accuracy. In this numerical study we introduce two new approaches based on singular value decomposition and exponential dichotomies and comparatively review and improve two recent popular approaches of Ginelli et al. (2007) and Wolfe and Samelson (2007). We compare the performance of the four approaches via three case studies with very different dynamics in terms of symmetry, spectral separation, and dimension. We also investigate which methods perform well with limited data

Penerapan sistem pakar berbasis web dengan metode forward chaining untuk mengidentifikasi penyakit pada ayam

Komoditas ayam di indonesia mempunyai prospek pasar yang sangat baik karena didukung oleh karakteristik produk yang dapat diterima oleh semua lapisan masyarakat, karena harga daging ayam yang relatif lebih murah (dibandingkan dengan daging sapi maupun kambing) dengan akses yang mudah diperoleh karena sudah menyebar di seluruh wilayah tanah air. Berternak ayam menjadi salah satu pilihan dalam memulai usaha, terutama berternak ayam ras petelur karena sangat potensial dikembangkan untuk diambil telur dan dagingnya dengan produksi utama adalah telur.Akan tetapi tentu akan ada banyak masalah yang harus dihadapi terutama maslah penyakit. Maka dari itu dibutuhkan sebuah alternatif yang dapat membantu dalam mengetahui berbagai penyakit ayam, yaitu sistem pakar berbasis web dengan metode Forward Chaining, yaitu metode yang bekerja dengan mengumpulkan fakta-fakta yang ada menuju kepada Sistem pakar ini nantinya akan dibuat dengan menggunakan bahasa pemrograman PHP dan juga MySQL sebagai databasenya. Sehingga aplikasi sistem pakar nanti akan berbentuk sebuah website

RELEVANCE ANALYSIS OF CIVIL ENGINEERING COMPETENCY ACCORDING TO THE CONSTRUCTION INDUSTRY NEEDS IN VOCATIONAL HIGH SCHOOL

Vocational High School (VHS) graduates as new workers are expected to be able to enter the workforce immediately after completing their education with the skills they have. But in reality, many graduates from vocational students do not work according to their field of expertise. This study aims to reveal competencies according to standards and needed by the construction industry and how much relevance is the level of competence in the curriculum and implemented in schools. The study was conducted in 15 construction industries with the characteristics of the respondents, namely directors, project and site managers, estimators, senior engineers and drafters, and architects. This type of research is quantitative descriptive research. The instrument, which consisted of 37 competency items, was validated using Exploratory Factor Analysis (EFA) techniques and the reliability was based on the Average Variance Extracted and Construct Reliability (CR) values. Overall, the competency instrument has met the Goodness of Fit (GoF) of construct validity and reliability. The results of the study reveal the level of relevance of civil engineering competencies based on three aspects, namely basic knowledge, work skills, and personal, obtaining results of 80.856% with relevant categories. These results are a reflection of the percentage of the construction service industry's needs for the competencies mastered by civil engineering graduates. This can be interpreted that the curriculum used in schools has taken into account the needs of the industry

Local Stability of Dynamical Processes in Random Media

A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical processes corresponding to infinite--dimensional dynamical systems. The method is illustrated by several examples, by the random diffusion equation, random wave equation, and random Schrodinger equation. The evolution equation for the density matrix of a quasiopen statistical system subjest to the action of random surrounding is considered. The stationary solutions to this equation are found to be unstable against arbitrary small finite random perturbations. The notion of random structural stability is introduced.Comment: 2 files, 34 pages, late

Chronicles of nature calendar, a long-term and large-scale multitaxon database on phenology

We present an extensive, large-scale, long-term and multitaxon database on phenological and climatic variation, involving 506,186 observation dates acquired in 471 localities in Russian Federation, Ukraine, Uzbekistan, Belarus and Kyrgyzstan. The data cover the period 1890–2018, with 96% of the data being from 1960 onwards. The database is rich in plants, birds and climatic events, but also includes insects, amphibians, reptiles and fungi. The database includes multiple events per species, such as the onset days of leaf unfolding and leaf fall for plants, and the days for first spring and last autumn occurrences for birds. The data were acquired using standardized methods by permanent staff of national parks and nature reserves (87% of the data) and members of a phenological observation network (13% of the data). The database is valuable for exploring how species respond in their phenology to climate change. Large-scale analyses of spatial variation in phenological response can help to better predict the consequences of species and community responses to climate change.publishedVersio

Erot spatiaalisissa ja ajallisissa reaktionormeissa kevään ja syksyn fenologisille tapahtumille

For species to stay temporally tuned to their environment, they use cues such as the accumulation of degree-days. The relationships between the timing of a phenological event in a population and its environmental cue can be described by a population-level reaction norm. Variation in reaction norms along environmental gradients may either intensify the envi- ronmental effects on timing (cogradient variation) or attenu- ate the effects (countergradient variation). To resolve spatial and seasonal variation in species’ response, we use a unique dataset of 91 taxa and 178 phenological events observed across a network of 472 monitoring sites, spread across the nations of the former Soviet Union. We show that compared to local rates of advancement of phenological events with the advancement of temperature-related cues (i.e., variation within site over years), spatial variation in reaction normsPeer reviewe