Concepts Of Classical Mechanics Research Articles

On cat–human interaction from the viewpoint of physics: An equation of motion

This paper provides an enjoyable example through which several concepts of classical mechanics can be understood. We introduce an equation that models the motion of a cat in the presence of a person. The cat is considered as a point particle moving in a potential induced by the person. We demonstrate that this approach to the problem reproduces characteristic behaviors of these curious animals. For instance, the fact that cats do not typically come when they are called, or that they remain longer on the lap of their favorite person; even “zoomies” are reproduced (cats randomly run back and forth across the house). We use this model problem to explore topics of current research such as stochastic equations and periodically driven systems. The pedagogical value of this work and its potential use in teaching are discussed.

The General Gauss Principle of Least Constraint

Abstract This paper develops a general form of Gauss’s Principle of Least Constraint, which deals with the manner in which Nature appears to orchestrate the motion of constrained mechanical systems. The theory of constrained motion has been at the heart of classical mechanics since the days of Lagrange, and it is used in various areas of science and engineering like analytical dynamics, quantum mechanics, statistical physics, and nonequilibrium thermodynamics. The new principle permits the constraints on any mechanical system to be inconsistent and shows that Nature handles these inconsistent constraints in the least squares sense. This broadening of Gauss’s original principle leads to two forms of the General Gauss Principle obtained in this paper. They explain why the motion that Nature generates is robust with respect to inaccuracies with which constraints are often specified in modeling naturally occurring and engineered systems since their specification in dynamical systems are often only approximate, and many physical systems may not exactly satisfy them at every instant of time. An important byproduct of the new principle is a refinement of the notion of what constitutes a virtual displacement, a foundational concept in all classical mechanics.

FOUNDATIONS OF CLASSICAL PHYSICS AND CHRISTIAN THEOLOGY

The article discusses the twists and turns of the history of formulation of the inertia principle of classical mechanics and their dependence on the theological concepts of their time. The points of view on the movement and inertia of Aristotle, the authors of late scholasticism, Galileo, Descartes and Newton are subject to discussion. The fundamental concepts of classical mechanics are also compared with the tradition of Protestant theology.

THE USE OF CONCEPT MAPS MADE WITH CMAPTOOLS IN THE CLASSICAL MECHANICS TEACHING IN MEXICAN PROFESSIONAL EDUCATION

This paper presents the results of a scientific pedagogical research, which goal was to reveal,how the using of the concept maps made with CmapTools, helps in the teaching of classical mechanics inMexican professional education. In particular, the results obtained from the study carried out in NationalPolytechnic Institute of Mexico, are presented. Authors found, that metallurgical engineering students moresuccessful learn the basic concepts of classical mechanics by creating conceptual maps with CMapTools.The way in which such conceptual maps must be carried out, implies preparation by the teacher of goodcontent quality evaluated with a semantic evaluation rubric. According to the study carried out, thisinnovative teaching technology improved understanding of classical mechanics, affects positively thesignificant learning of the basic concepts of classical mechanics and increased students ́ motivation to studythese aspects of mechanics.

Coulomb Interaction between Electrons and a New Concept of Atom

It is shown that the approximation of a strong Coulomb interaction between electrons results in a new model of the atom with a spatial quantization of electrons accompanied by their quantization in energy. This model implies that electrons rotate in circular orbits centered outside the atomic nucleus and only orbit axes pass through it. The Coulomb interaction between electrons leads to a spherically symmetric distribution of their orbits on the surfaces of equipotential spheres of a spherically symmetric electrostatic field of the nucleus. The distribution is similar to “inscribing” electron orbits into faces of regular nucleus-centered polyhedra so each polyhedron corresponds to a certain electron state (s, p, d, f), and a certain set of polyhedra corresponds to a certain period of the Mendeleev Table. It is shown that a spherically symmetric distribution of electron orbits gives rise to the formation of electron pairs in which electron orbits with a common axis are located symmetrically with respect to the nucleus and the orbital magnetic moments of the electrons are oppositely directed. The physical meaning of the electron spin concept becomes clear. The spin turns out to be related to the orbital magnetic moment of an electron and reflects the fact that two electrons of a pair rotate in opposite directions relative to their common axis. So the spin is one of characteristics of the electron state in the atom associated with electron rotation in the orbit centered outside the nucleus. The atomic model gives an insight into the periodicity of changes in the atomic properties with increasing nuclear charge and the reasons for an electron double energy quantization associated with different states and periods. The model shows that the atomic structure and properties can be explained by using concepts of classical mechanics and classical electrodynamics which regard the electron as a particle.

Quantum mechanical work

Regarded as one of the most fundamental concepts of classical mechanics and thermodynamics, work has received well-grounded definitions within the quantum framework since the 1970s, having being successfully applied to many contexts. Recent developments on the concept have taken place in the emergent field of quantum thermodynamics, where work is frequently characterized as a stochastic variable. Notwithstanding this remarkable progress, it is still debatable whether some sensible notion of work can be posed for a strictly quantum instance involving a few-particle system prepared in a pure state and abandoned to its closed autonomous dynamics. By treating work as a quantum mechanical observable with a well defined classical limit, here we show that this scenario can be satisfactorily materialized. We prove, by explicit examples, that one can indeed assign eigensystems to work operators. This paves the way for frameworks involving quantum superposition and nonlocal steering of work. We also show that two-point measurement protocols can be inappropriate to describe work (and other two-time physical quantities), especially in the semiclassical regime. However subtle it may be, our quantum mechanical notion of work is experimentally testable and requires an updating of our intuition regarding the concept of two-time elements of reality. In this context, we derive a work-energy uncertainty relation, and we illustrate how energy conservation emerges as an element of physical reality.

Kepler's law for optical beams.

It is well known that optics and classical mechanics are intimately related. One of the most important concepts in classical mechanics is that of a particle in a central potential that leads to the Newtonian description of the planetary dynamics. Within this, a relevant result is Kepler's second law that is related to the conservation of orbital angular momentum, one of the fundamental laws in physics. In this paper, we demonstrate that it is possible to find the conditions that allow us to state Kepler's second law for optical beams with orbital angular momentum by analyzing the streamlines of their energy flow. We find that the optical Kepler's law is satisfied only for cylindrical symmetric beams in contrast to the classical mechanics situation that is satisfied for the other conic geometries, namely, parabolic, elliptical and hyperbolic. We propose a novel approach to confirm our analytic results: we observe the propagation of the Arago's spot created by a beam with orbital angular momentum as a local "light-tracer" instead of looking at the propagation of the whole beam. The observed patterns fully agree with the prediction of our formalism.

Developing Educational YouTube Videos as a Tool to Learn and Teach Physics

Introductory physics courses can be a challenge for some college students, especially those that have not taken Advanced Placement (AP) physics courses in high school. Even some classical mechanics concepts, such as energy, power, or the laws of Newton, can be non-intuitive and hard to grasp. When it comes to evaluating the learning outcome of our students, some of the aspects we evaluate are their abilities to solve numerical problems. By solving problems the students show how well they understood the concepts and the problem-solving methods. But students can practice enough and learn how to solve related numerical exercises without a deep understanding of the physical concepts. When asked more conceptual questions, some students struggle and lack confidence.

Using concept maps to understand mechanical physics concepts in high school students

The work presents a didactic proposal on the use of concept maps, for the understanding of mechanical physics. A didactic intervention based on Ausubel’s theory was applied with the following activities: design, implementation and application of workshops based on real physical situations, where the elaboration of concept maps is the central axis, under the quantitative paradigm of interpretative level and action research method. The informants were 43 tenth grade students from a public educational institution located in the Department of Norte de Santander, Colombia. The results obtained showed that the use of concept maps as a didactic intervention favoured the significant learning of classical mechanics concepts. It was evident that the participating students achieved reflective analysis about the resolution of problems about the concepts of mechanics.

Linearization-based methods for the calibration of bonded-particle models

In the work at hand, two methods for the calibration of the elastic material parameters of bonded-particle models (BPMs) are proposed. These methods are based on concepts of classical mechanics and enable a faster calibration compared to the conventional trial and error strategy. Moreover, they can be used to counter-check the consistency of the BPM. In the first method, the mathematical model is linearized and solved in a classical matrix-vector formulation similar to a finite element scheme. Further linearization in the second approach enables the direct calculation of the elastic stiffness tensor, reducing computational costs massively. To analyze the capabilities and limitations of both methods, they have been applied in three different case studies. Obtained results have shown that the new strategy allows us to significantly reduce the calculation time.

Dynamics of localized continuum inside a charged particle

This article explains how a charged body can retain its integrity despite electrostatic repulsion within itself. The study requires derivation of the field equations governing the velocity of any arbitrary element within the system. These relations are obtained from two Lagrangian principles based on obvious and least disruptive modifications of known concepts in classical mechanics. The two Lagrangians lead to a relativistic energy-momentum equation describing the motion and Maxwell’s equations quantifying the electromagnetic fields, respectively. The energy-momentum relation shows that rigid body motions creating stationary fields in a rotating frame is a viable solution for the velocity inside the continuum. It also yields a combined potential which remains constant throughout the rotating particle. This constancy coupled with Maxwell’s equations and boundary conditions for proper interfacial continuity provides the charge distribution and geometric shape required for continued coherence of the domain. The paper presents specific simulations for slender annuli steadily rotating about the axis of symmetry where the charge density and the axial width are plotted as radial functions. Curiously, when the analysis is extended to systems with different axes of rotation and symmetry, the proportionalities between energy and frequency as well as momentum and wave-number can be established. Such results are very similar to Planck’s and de Broglie’s laws, even though derived from classical principles. Thus, the presented theory might have deeper implications like, for example, in mathematical computation of fine structure constant.

Mechanical instabilities of aorta drive blood stem cell production: a live study.

During embryogenesis of all vertebrates, haematopoietic stem/progenitor cells (HSPCs) extrude from the aorta by a complex process named endothelial-to-haematopoietic transition (EHT). HSPCs will then colonize haematopoietic organs allowing haematopoiesis throughout adult life. The mechanism underlying EHT including the role of each aortic endothelial cell (EC) within the global aorta dynamics remains unknown. In the present study, we show for the first time that EHT involves the remodelling of individual cells within a collective migration of ECs which is tightly orchestrated, resulting in HSPCs extrusion in the sub-aortic space without compromising aorta integrity. By performing a cross-disciplinary study which combines high-resolution 4D imaging and theoretical analysis based on the concepts of classical mechanics, we propose that this complex developmental process is dependent on mechanical instabilities of the aorta preparing and facilitating the extrusion of HSPCs.

Mechanical misconceptions: Have we lost the “mechanics” in “sports biomechanics”?

Biomechanics principally stems from two disciplines, mechanics and biology. However, both the application and language of the mechanical constructs are not always adhered to when applied to biological systems, which can lead to errors and misunderstandings within the scientific literature. Here we address three topics that seem to be common points of confusion and misconception, with a specific focus on sports biomechanics applications: (1) joint reaction forces as they pertain to loads actually experienced by biological joints; (2) the partitioning of scalar quantities into directional components; and (3) weight and gravity alteration. For each topic, we discuss how mechanical concepts have been commonly misapplied in peer-reviewed publications, the consequences of those misapplications, and how biomechanics, exercise science, and other related disciplines can collectively benefit by more carefully adhering to and applying concepts of classical mechanics.

Investigating Students’ Physico-mathematical Difficulties in Classical Mechanics and Designing an Instructional Model

The study investigated students’ physico-mathematical difficulties in classical mechanics and designed an instructional model. The three objectives that guided the study were namely: to identify physico-mathematical difficulties students have in classical mechanics, to explore the existing instructional models and design a suitable instructional model to address physico-mathematical difficulties in classical mechanics and to verify and evaluate the effectiveness of the designed instructional model. The study was undertaken with a purposive sample of 140 students and 10 instructors learning and teaching classical mechanics respectively from the Copperbelt University and Mukuba University on the Copperbelt Province of Zambia. A descriptive mixed method survey design approach was used. A pilot study was conducted, instruments adjusted and survey implemented, instructional model designed and evaluated for its effectiveness. Four achievement tests comprising physico-mathematical concepts, the questionnaire, interviews and focus group discussions were used to collect data. The Microsoft Excel package was used to generate tables and percentages. Qualitative data from interview and focus group discussions were analysed qualitatively by the MAXQDA (Max Qualitative Data Analysis) software. The results of the study revealed that students had physico-mathematical difficulties in classical mechanics bordering on the students’ inabilities to use vectors, graphs, functions and mathematization in classical mechanics. Furthermore, it was found that the strategy of teaching mathematical concepts before introducing concepts in classical mechanics was used at the two institutions. However, these physico-mathematical difficulties still persisted. Therefore, the study recommended that instructors in classical mechanics should have necessary background information about students before teaching them. Information includes the prior knowledge of students. The study also recommended that instructors use suitable learning methods or materials that would engage students or make abstract physico-mathematical concepts more observable.

Viscosity Modeling of Ionic Liquids Using the Friction Theory and a Simple Cubic Equation of State

In the present work, the well-known friction theory (FT) based on friction concepts of classical mechanics and the van der Waals theory of fluids has been modified to accurately represent the dynamic viscosity of pure ionic liquids in a rather simplified manner. Unlike previous FT applications to pure ionic liquids, the dilute gas limit for viscosity was excluded from the present model since it is negligible for ionic liquids which exhibit extremely low vapor pressures; the friction term thus prevailed for viscosity calculations. The latter was expressed in terms of new temperature-dependent friction coefficients whereas the repulsive and attractive pressure terms were in turn estimated from two simple cubic equations of state (Soave or Peng–Robinson) rather than using sophisticated multiparameter equations of state such as SAFT- or CPA-based expressions previously used by other authors. The resulting model was successfully validated during the representation of experimental dynamic viscosities of three f...

Lagrangian for RLC circuits using analogy with the classical mechanics concepts

We study and formulate the Lagrangian for the LC, RC, RL, and RLC circuits by using the analogy concept with the mechanical problem in classical mechanics formulations. We found that the Lagrangian for the LC and RLC circuits are governed by two terms i. e. kinetic energy-like and potential energy-like terms. The Lagrangian for the RC circuit is only a contribution from the potential energy-like term and the Lagrangian for the RL circuit is only from the kinetic energy-like term.

Beyond velocity and acceleration: jerk, snap and higher derivatives

The higher derivatives of motion are rarely discussed in the teaching of classical mechanics of rigid bodies; nevertheless, we experience the effect not only of acceleration, but also of jerk and snap. In this paper we will discuss the third and higher order derivatives of displacement with respect to time, using the trampolines and theme park roller coasters to illustrate this concept. We will also discuss the effects on the human body of different types of acceleration, jerk, snap and higher derivatives, and how they can be used in physics education to further enhance the learning and thus the understanding of classical mechanics concepts.

O ESQUEMA DE MOVIMENTO COMO ORGANIZADOR DA AÇÃO EM MECÂNICA CLÁSSICA E RELATIVÍSTICA

O presente trabalho relata a utilização do conceito de esquema como uma das referências para análise do processo de significação do tempo relativo. Ele se coloca dentro de uma perspectiva atual que discute a inclusão de temas de Física Moderna no ensino médio, investigando as condições para que tal inclusão possa ocorrer. Para tanto, foi produzida uma sequência didática apoiada na transição entre os conceitos-chave da Mecânica Clássica e a Teoria da Relatividade, onde um dos pontos centrais era a discussão sobre a influência do referencial no estudo dos movimentos. As atividades de pesquisa duraram 16 horas-aulas em uma escola de terceira série do ensino médio e foram bastante diversificadas. Analisamos, neste trabalho, episódios de interação verbal e atividades escritas dos estudantes ligados ao conceito de referencial e a influência sobre a noção de tempo relativo. Foram identificados diferentes conteúdos epistêmicos nos esquemas de movimento e de tempo dos estudantes. Concluímos nossa pesquisa com a indicação de que pode ocorrer uma assimilação recíproca entre os esquemas de tempo e de movimento.

Force analysis as a support to computer-aided tolerancing of planar linkages

The paper proposes a method for tolerance analysis on planar structures and mechanisms. As for generic assemblies, deviations on a functional requirement involving different parts are calculated from tolerance specifications on individual part dimensions. For a linkage the requirement is usually the position or orientation of a given element (link, joint) with respect to a fixed frame, and the solution of the problem has some additional difficulties such as the correct treatment of joint clearances. The paper points out that, for underconstrained or exactly constrained linkages, tolerance analysis can be treated by analogy with a force analysis problem. The static analogy is first introduced and justified from well-known concepts of classical mechanics, and then translated into a calculation procedure that is able to evaluate the propagation of deviations from different types of dimensions (lengths of links, diameters of pins and holes at joints), as well as from linear and angular actuators. Problems of high complexity are shown to be easily solvable by the proposed method by means of available software tools for the structural analysis of planar frames and trusses.

Mechanics of the brain: perspectives, challenges, and opportunities.

The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today’s open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.