China
Africa
Explore chapters and articles related to this topic
Mechanics and Texture Analysis
Published in Gregory S. Chirikjian, Alexander B. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis, 2021
Gregory S. Chirikjian, Alexander B. Kyatkin
Classical mechanics is the study of the interplay between forces acting on matter and the resulting motion of matter. Quantitative results are based on four essential balances of quantities in any system composed of matter: (1) balancing the mass entering and leaving the system; (2) balancing the change in momentum of the system with applied force; (3) balancing the change in angular momentum with applied moments of force; and (4) balancing the total energy in the system with the net contributions from external sources. The laws of conservation of mass, momentum, angular momentum, and energy follow from these balances in the absence of external influences.
Energy, Environment, and Renewable Energy
Published in Radian Belu, Fundamentals and Source Characteristics of Renewable Energy Systems, 2019
Current is measured in amperes (A), voltage in volts (V), and resistance in ohms (Ω). When the V and I are expressed in volts and amperes, P is expressed in watts. From Equation (1.4), electrical energy in joule is power in watts multiplied by time in seconds. More often electrical energy is expressed in kilowatt-hours (kWh) by dividing energy in joules by a conversion factor 3.6 106 J/kWh. Energy can be transferred between systems in a variety of ways, such as the transmission of electromagnetic energy via photons, physical collisions which transfer kinetic energy, and the conductive transfer of thermal energy. Energy is strictly conserved and is also locally conserved wherever it can be defined. Classical mechanics distinguishes between kinetic energy, which is determined by an object’s movement through space, and potential energy, which is a function of the position of an object within a field. Kinetic energy associated with moving objects defined for an object of mass, m, moving at velocity v, as: () E=12mv2
Conceptual basis of classical mechanics
Published in Bijan Kumar Bagchi, Advanced Classical Mechanics, 2017
Classical mechanics is the study of physical laws that control the motion of material objects which are under the action of a force or system of forces. It provides the basis for the growth of modern science. It has applications that cover areas such as physics, chemistry, applied mathematics, biology and engineering sciences. In particular, it seeks to address and explain the dynamics of particles and rigid bodies, general classes of interactive systems, rotating Earth problems, motion of charged objects, planetary motions around the Sun and modeling of biological systems. Classical mechanics has an extraordinarily rich history that began about the time of Galileo (1564–1642) although its basic foundations were laid later by Newton (1642–1727) in his famous treatise, the Principia. He enumerated a set of three axioms which became the cornerstone in explaining most of the qualitative features of classical mechanics. In this chapter we discuss these laws and provide a multi-layered perspective on them.
Thermal gaussian wave packets
Published in Molecular Physics, 2021
The Gaussian distribution of Equation (5) was used in Ref. [11] to derive an expression for the mean square displacement (MSD) of a free particle within the framework of Bohmian quantum dynamics. That expression is given in Equation (85) of Ref. [11] and is consistent with results from classical mechanics. Notwithstanding this consistency, two remarks arise from the results obtained in the present work. First, given that the width used in that expression (and in Equation (5)) is finite, the temperature T used in Equation (5) must be reinterpreted: from Equation (19) one follows that Equation (6) should read where T is the temperature of the particle in thermal equilibrium with its environment. Secondly, Equation (85) of Ref. [11] was derived under the assumption that the initial values of the Bohmian trajectories have the same Gaussian probability distribution of Equation (5), i.e. a localised distribution around some average value. Yet, as shown in the present work, a single Gaussian distribution is not representative of a thermal state of the free particle. A different quantum mechanical expression for the MSD of a free particle is derived in ref. [22] on the basis of the thermal wave packet from Equation (8).
Numerical solution of Maxwell equations to study photothermal signals on a dielectric monolayer
Published in Journal of Modern Optics, 2019
Marco A. Molina-González, Arnulfo Castellanos-Moreno, Adalberto Corella-Madueño
A particle acted by a potential V(), described by classical mechanics, can have an analogy in geometrical optics by changing V() for the square of the refractive index. This formal relation has been used to study a problem in mechanics to translate the solution to an interesting system in optics (1–7). One of this is a spherical metallic particle inside a dielectric media, such that the particle is heated first by a laser. The refractive index is modified in each point (), such that the new system can be described by adding a new perturbative term to the dielectric function. This is proportional to 1/r, where r is the distance from the hot point to (). The analogy with classical mechanics is a particle whose motion occurs in a plane, the Kepler problem. Therefore, it is possible to think in a dielectric monolayer with a hot point that can be produced by some external mean, so that the photothermal detection can be studied.
Adiabatic and nonadiabatic dynamics in classical mechanics for coupled fast and slow modes: sudden transition caused by the fast mode against the slaving principle
Published in Molecular Physics, 2018
Let us turn to classical mechanics. One of the physically important aspects in the study on hierarchical dynamics is to comprehend how the slow modes emerge from the Hamiltonian systems. As for the molecular nonadiabatic dynamics, fast-and-slow is simply due to the difference of masses (heavy nuclei and light electrons). However, the mechanical origins of the birth of very slow modes can be found even in two-dimensional Hamiltonian (conservative) systems, which are mainly due to breakdown of the adiabatic invariance [21] and chaotic dynamics [20]. The theory of stagnant motion deeply studied by Aizawa [22] and the studies based on the Nekholoshev theorem [20,23] are among the most typical works as such. These theories explain both how slow modes are generated and how the relevant dynamical states take very long time to escape from complicated phase-space structures [20]. Similarly, motions confined in a thin quasi-separatrix exhibit a sudden transition of state in intermittent manner often with a very long time-scale [24,25]. However, those mechanisms seem to heavily depend on the two-dimensional chaotic dynamics [20]. A physical interpretation about the slow relaxation in liquid-water dynamics [7] has been given by Shudo et al. [26], based on the theories of Hamilton dynamics. It is not yet clear though whether such intricate geometrical structures in low-dimensional phase-space can dominate the global dynamics in a large-dimensional dynamics such as molecular clusters and proteins.