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Mechanics

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The snooty Harvard Dons called Daniel Waterhouse a doctor of cranks.

Mechanics

Expanded from Wikipedia

Mechanics (Latin mechanicus, from the Greek mechanikos, "one skilled in machines") is a variety of specialised sciences pertaining to the functions and routine operations of machines, machine-like devices or objects. When preceded by a qualifier, mechanics refers to the study of empirically mechanical functions of a stated quantity or property. One who assembles and maintains mechanical devices is termed a 'mechanic'.

Disciplines of Mechanics

•Acoustic theory

Acoustic theory is the field relating to mathematical description of sound waves. It is derived from fluid dynamics. The propagation of sound waves in air can be modeled by an equation of motion and an equation of continuity. With some simplifications, they can be given as follows: \rho_0 \frac{\partial}{\partial t} \mathbf{v}(\mathbf{x}, t) + \nabla p(\mathbf{x}, t) = 0 \frac{\partial}{\partial t} p(\mathbf{x}, t) + \rho_0 c^2 \nabla \cdot \mathbf{v}(\mathbf{x}, t) = 0 where p(\mathbf{x}, t) is the acoustic pressure and \mathbf{v}(\mathbf{x}, t) is the acoustic fluid velocity vector, \mathbf{x} is the vector of spatial coordinates x,y,z, t is the time, ρ0 is the static density of air and c is the speed of sound in air.

•Biomechanics

Biomechanics is the study of the mechanics and other physical aspects of living organisms and their parts. Biomechanics studies the forces that act on limbs, the aerodynamics of bird and insect flight, the hydrodynamics of swimming in fish and locomotion in general across all forms of life, from individual cells to whole organisms.

Tensional integrity of biological forms: new research into the strength of biologically formed structures shows a remarkable similarity to the principle of tensegrity. The tensegrity concept states that structures formed with a combination of prestressed and tensioned parts have an overall integrity greater than that found in the sum of their parts. The degree of increased strengh of tensegrity structures depends on the efficacy of their design to of their parts to function, both with each other and within their particular environment.

Biology, mechanics, orthosis, physics, physiology interact in Biomechanics.

•Continuum mechanics

Continuum mechanics is a branch of physics that deals with solids and fluids (i.e., liquids and gases). Continuum mechanics makes the assumption that these materials are continuous: the fact that matter is made of atoms is ignored. Therefore, physical quantities, such as space, time, energy, and momentum can be handled in the infinitesimal limit. Differential equations are thus the mathematical tool of choice for continuum mechanics. These differential equations are often derived from fundamental physical laws, such as conservation of mass or conservation of momentum.

The physical laws of solids and fluids should not depend on the coordinate system of the differential equations. Continuum mechanics thus uses tensors, which are mathematical objects that are independent of coordinate system. These tensors can be expressed in coordinate systems, for computational convenience. See tensor analysis for more information.

There are two main branches of continuum mechanics: * Elasticity, which deals with the physics of solids. * Fluid dynamics, which deals with the physics of fluids.

The boundary between these two branches is blurry, because elasticity handles materials with viscosity.

•Fluid mechanics

Fluid dynamics (also called fluid mechanics) is the study of fluids, that is liquids and gases. The solution of a fluid dynamic problem normally involves calculating for various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time.

•Lie group symmetries

n mathematics, a Lie group (pronounced "lee", named after Sophus Lie) is an analytic real or complex manifold that is also a group such that the group operations multiplication and inversion are analytic maps. Lie groups are important in mathematical analysis, physics and geometry because they serve to describe the symmetry of analytical structures. They were introduced by Sophus Lie in 1870 in order to study symmetries of differential equations.

While the Euclidean space Rn is a real Lie group (with ordinary vector addition as the group operation), more typical examples are groups of invertible matrices (under matrix multiplication), for instance the group SO(3) of all rotations in 3-dimensional space.

In mathematics, the orthogonal group of degree n over a field F (written as O(n,F)) is the group of n-by-n orthogonal matrices with entries from F, with the group operation that of matrix multiplication. This is a subgroup of the general linear group GL(n,F).

•Mechatronics

Mechatronics is the synergistic combination of mechanical engineering ("mecha" for mechanisms) , electronic engineering ("tronics" from electronics ), and software engineering. The purpose of this interdisciplinary engineering field is the study of automata from an engineering perspective and serves the purposes of controlling advanced hybrid-systems such as production systems, synergy-drives, planetary-rovers, automotive subsystems such as anti-block system, gyroscopic spin-assist and every day equipment such as autofocus cameras, video, hard disks, cd-players, washing machines, lego-matics etc.

It is centred on mechanics, electronics and computing which, combined, make possible the generation of simpler, more economical, reliable and versatile systems. The word "mechatronics" was first coined by a senior engineer of a Japanese company, Yaskawa[1], in 1969.

•Newtonian physics & Classical Mechanics

Classical mechanics is the physics of forces, acting upon bodies. It is often referred to as "Newtonian mechanics" after Newton and his laws of motion. Classical mechanics is subdivided into statics (which deals with objects in equilibrium) and dynamics (which deals with objects in motion).

Classical mechanics produces very accurate results within the domain of everyday experience. It is superseded by relativistic mechanics for systems moving at large velocities near the speed of light, quantum mechanics for systems at small distance scales, and relativistic quantum field theory for systems with both properties. Nevertheless, classical mechanics is still very useful, because (i) it is much simpler and easier to apply than these other theories, and (ii) it has a very large range of approximate validity. Classical mechanics can be used to describe the motion of human-sized objects (such as tops and baseballs), many astronomical objects (such as planets and galaxies), and even certain microscopic objects (such as organic molecules).

Although classical mechanics is roughly compatible with other "classical" theories such as classical electrodynamics and thermodynamics, there are inconsistencies that were discovered in the late 19th century that can only be resolved by more modern physics. In particular, classical nonrelativistic electrodynamics predicts that the speed of light is a constant relative to an aether medium, a prediction that is difficult to reconcile with classical mechanics and which led to the development of special relativity. When combined with classical thermodynamics, classical mechanics leads to the Gibbs paradox in which entropy is not a well-defined quantity and to the ultraviolet catastrophe in which a blackbody is predicted to emit infinite amounts of energy. The effort at resolving these problems led to the development of quantum mechanics.

•Quantum Mechanics

Quantum mechanics describes the instantaneous state of a system with a wave function that encodes the probability distribution of all measurable properties, or observables . Possible observables for a system include energy, position, momentum , and angular momentum . Quantum mechanics does not assign definite values to the observables, instead making predictions about their probability distributions. The wavelike properties of matter are explained by the interference of wave functions.

Wave functions can change as time progresses. For example, a particle moving in empty space may be described by a wave function that is a wave packet centered around some mean position . As time progresses, the center of the wave packet changes, so that the particle becomes more likely to be located at a different position. The time evolution of wave functions is described by the Schrödinger equation.

Some wave functions describe probability distributions that are constant in time. Many systems that would be treated dynamically in classical mechanics are described by such static wave functions. For example, an electron in an unexcited atom is pictured classically as a particle circling the atomic nucleus , whereas in quantum mechanics it is described by a static, spherically symmetric probability cloud surrounding the nucleus.

When a measurement is performed on an observable of the system, the wavefunction turns into one of a set of wavefunctions that are called eigenstates of the observable. This process is known as wavefunction collapse. The relative probabilities of collapsing into each of the possible eigenstates is described by the instantaneous wavefunction just before the collapse. Consider the above example of a particle moving in empty space. If we measure the particle's position, we will obtain a random value x. In general, it is impossible for us to predict with certainty the value of x which we will obtain, although it is probable that we will obtain one that is near the center of the wave packet, where the amplitude of the wave function is large. After the measurement has been performed, the wavefunction of the particle collapses into one that is sharply concentrated around the observed position x.

During the process of wavefunction collapse, the wavefunction does not obey the Schrödinger equation. The Schrödinger equation is deterministic in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a measurement, the eigenstate to which the wavefunction collapses is probabilistic, not deterministic. The probabilistic nature of quantum mechanics thus stems from the act of measurement.

One of the consequences of wavefunction collapse is that certain pairs of observables, such as position and momentum, can never be simultaneously ascertained to arbitrary precision. This effect is known as Heisenberg's uncertainty principle.

•Strength of materials

Strength of materials is the scientific area of applied mechanics for the study of the strength of engineerig materials and their mechanical behaviour in general (such as stress, deformation, strain and stress-strain relations). Strength is considered in terms of compressive strength, tensile strength, and shear strength, namely the limit states of compressive stress, tensile stress and shear stress respectively.

Materials Science seems to be the US version of this field of study. It includes those parts of chemistry, physics, geology, and even biology that deal with the physical properties of materials. It is usually considered an applied science, in which the properties under study have some industrial purpose.

Materials science encompasses all classes of materials, the study of each of which may be considered a separate field: metals and metallurgy, ceramics, semiconductors and other electronic materials, polymers, and Biomaterials. Metallurgy and ceramics have long and separate histories as engineering disciplines, but because the science that underlies these disciplines applies to all classes of materials, materials science is recognized as a distinct discipline.

Materials science is related to materials engineering, which tends to focus on processing techniques (casting, rolling, welding, ion implantation, crystal growth, thin-film deposition, sintering, glassblowing, etc.), analytical techniques ( electron microscopy, x-ray diffraction, calorimetry, nuclear microscopy (HEFIB) etc.), materials design, and cost/benefit tradeoffs in industrial production of materials.

•Statistical mechanics

Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of Mechanics, which is concerned with the motion of particles or objects when subjected to a force. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in every day life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum). In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules.

•Theory of relativity

E=MC2 Albert Einstein's theory of relativity is a set of two theories in physics: special relativity and general relativity. The core idea of both theories is that two observers who move relative to each other will often measure different 'time' and 'space' intervals for the same events, but the content of physical law will be the same for both.

Special relativity, developed in 1905, only considers observers in inertial reference frames which are in uniform motion with respect to each other. The theory postulates that the speed of light in vacuum will be the same for these observers. This leads to redefinitions of such fundamental notions as time, distance, mass, energy and momentum with wide ranging consequences. Moving objects appear heavier and compressed in the direction they are moving, while moving clocks appear to run slower. Light has momentum. The speed of light emerges as an upper limit for the speed of matter and information. Mass and energy are seen as equivalent. Two events judged to be simultaneous by one observer may be seen as non-simultaneous by other observers which are in motion with respect to the first one. The theory does not account for gravitational effects. The mathematical basis of special relativity is provided by the Lorentz transformation.

General relativity was published by Einstein in 1916 (submitted November 25 1915). It uses the mathematics of differential geometry and tensors in order to describe gravity. The laws of general relativity are the same for all observers, even if they are accelerated with respect to each other. General relativity is a geometrical theory which postulates that the presence of mass and energy "curves" space, and this curvature affects the path of free particles (and even the path of light), an effect we interpret as a gravitational force. The theory can be used to build models of the evolution of the universe and is hence a crucial tool in cosmology.