Mechanics (Greek Greek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical ancient Greek literature and the New Testament of Μηχανική) is the branch of physics Physics is a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves concerned with the behavior of physical bodies In physics, a physical body or physical object is a collection of masses, taken to be one. For example, a cricket ball can be considered an object but the ball also consists of many particles (pieces of matter) when subjected to forces In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a or displacements A displacement is the shortest distance from the initial and final positions of a point P. Thus, it is the length of an imaginary straight path, typically distinct from the path actually travelled by P. A displacement vector represents the length and direction of that imaginary straight path, and the subsequent effects of the bodies on their environment. The discipline has its roots in several ancient civilizations (see History of classical mechanics The ancient Greek philosophers, and Aristotle in particular, were among the first to propose that there are abstract principles governing nature. Aristotle argued, in his paper On the Heavens, that every body has a "heaviness" and so tends to fall to its "natural place". From this he wrongly concluded that an object twice as and Timeline of classical mechanics Categories: Physics timelines | Mathematics timelines ). During the early modern period In history, the early modern era of modern history follows the late Middle Ages. Historians refer to the period beginning in AD 1453 and lasting to AD 1789. The events include the first European colonies, the rise of strong centralized governments, and the beginnings of recognizable nation states that are the direct antecedents of today's states, scientists such as Galileo Galileo Galilei was an Italian physicist, mathematician, astronomer and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the "father of modern observational astronomy,", Kepler Johannes Kepler was a German mathematician, astronomer and astrologer, and key figure in the 17th century scientific revolution. He is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican Astronomy. They also provided one of the, and especially Newton Sir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is considered by many scholars and members of the general public to be one of the most influential people in human history. His 1687 publication of the Philosophiæ Naturalis Principia Mathematica (usually called the, laid the foundation for what is now known as classical mechanics In the fields of physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain boundary under the action of a system of forces.

The system of study of mechanics is shown in the table below:

Branches of mechanics

Contents

Classical versus quantum

Classical mechanics In the fields of physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain boundary under the action of a system of forces
Newton's Second Law Newton's laws of motion are three physical laws that form the basis for classical mechanics. They have been expressed in several different ways over nearly three centuries, and can be summarised as follows:
History of classical mechanics The ancient Greek philosophers, and Aristotle in particular, were among the first to propose that there are abstract principles governing nature. Aristotle argued, in his paper On the Heavens, that every body has a "heaviness" and so tends to fall to its "natural place". From this he wrongly concluded that an object twice as · Timeline of classical mechanics Categories: Physics timelines | Mathematics timelines
Branches
Statics Statics is the branch of mechanics concerned with the analysis of loads on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity. When in static equilibrium, the system is either at rest, or its center of mass moves · Dynamics In classical mechanics, analytical dynamics, or more briefly dynamics, is concerned about the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies . The foundation of modern day dynamics is Newtonian mechanics and its reformulation as Lagrangian mechanics and Hamiltonian / Kinetics In physics and engineering, kinetics is a term for the branch of classical mechanics that is concerned with the relationship between the motion of bodies and its causes, namely forces and torques. Since the mid-20th century, the term "dynamics" has largely superseded "kinetics" in physics text books; the term "kinetics& · Kinematics Kinematics is the branch of classical mechanics that describes the motion of objects without consideration of the causes leading to the motion · Applied mechanics Applied mechanics is a branch of the physical sciences and the practical application of mechanics. Applied mechanics examines the response of bodies or systems of bodies to external forces. Some examples of mechanical systems include the flow of a liquid under pressure, the fracture of a solid from an applied force, or the vibration of an ear in · Celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on the orbits of artificial satellites. Lunar theory · Continuum mechanics Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuum. The French mathematician Augustin Louis Cauchy was the first to formulate such models in the 19th century, but research in the area continues today · Statistical mechanics Statistical mechanics is the application of probability theory (which contains mathematical tools for dealing with large populations) to study the thermodynamic behavior of systems of a large number of particles. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties
Formulations
Fundamental concepts
Space Space is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime. In mathematics one examines ' · Time Time is "a nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future." It is used to sequence events, to quantify the durations of events and the intervals between them, and to quantify and measure the motions of objects and other changes. Time is quantified in · Velocity In physics, velocity is the rate of change of position. It is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value of velocity is speed, a quantity that is measured in meters per second (m/s or ms−1) when using the SI (metric) system · Speed In kinematics, the instantaneous speed of an object is the magnitude of its instantaneous velocity (the rate of change of its position); it is thus the scalar equivalent of velocity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the · Mass In physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: Inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties · Acceleration In physics, and more specifically kinematics, acceleration is the change in velocity over time. Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up. However, as a vector quantity, acceleration is also the · Gravity Gravitation, or gravity, is one of the four fundamental interactions of nature , in which objects with mass attract one another. In everyday life, gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, thus accounting for · Force In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a · Impulse · Torque Torque, also called moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist / Moment / Couple · Momentum In classical mechanics, momentum is the product of the mass and velocity of an object (p = mv). In relativistic mechanics, this quantity is multiplied by the Lorentz factor. Momentum is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum. Linear momentum is a vector quantity, since it has a · Angular momentum In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system. The angular momentum L of a particle with respect to some point of origin is · Inertia Inertia is the resistance of any physical object to a change in its state of motion. It is represented numerically by an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to describe the motion of matter and how it is affected by applied forces. Inertia comes from the Latin word, " · Moment of inertia Moment of inertia, also called mass moment of inertia, rotational inertia, or the angular mass, is a measure of an object's resistance to changes in its rotation rate. It is the rotational analog of mass, the inertia of a rigid rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass · Reference frame A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer. It may also refer to both an observational reference frame and an attached · Energy In physics, energy is a quantity that can be assigned to any particle, object, or system of objects as a consequence of its physical state. Different forms of energy include kinetic, potential, thermal, gravitational, sound, elastic and electromagnetic energy. The forms of energy are often named after a related force. German physicist Hermann von · Kinetic energy The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude · Potential energy In physics, Potential energy is energy stored within a physical system as a result of the position or configuration of the different parts of that system. It has the potential to be converted into other forms of energy, such as kinetic energy, and to do work in the process. The SI unit of measure for energy and work is the joule (symbol J) · Mechanical work In physics, mechanical work is the amount of energy transferred by a force acting through a distance. Like energy, it is a scalar quantity, with SI units of joules. The term work was first coined in 1826 by the French mathematician Gaspard-Gustave Coriolis · Virtual work Virtual work on a system is the work resulting from either virtual forces acting through a real displacement or real forces acting through a virtual displacement. In this discussion, the term displacement may refer to a translation or a rotation, and the term force to a force or a moment. When the virtual quantities are independent variables, they · D'Alembert's principle
Core topics
Rigid body In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it. Even though such an object cannot physically exist due to relativity, objects can normally be · Rigid body dynamics In physics, rigid body dynamics is the study of the motion of rigid bodies. Unlike particles, which move only in three degrees of freedom , rigid bodies occupy space and have geometrical properties, such as a center of mass, moments of inertia, etc., that characterize motion in six degrees of freedom (translation in three directions plus rotation · Euler's equations (rigid body dynamics) · Motion In physics, motion is change of location or position of an object with respect to time. Change in motion is the result of an applied force. Motion is typically described in terms of velocity also seen as speed, acceleration, displacement, and time. An object's velocity cannot change unless it is acted upon by a force, as described by Newton's · Newton's laws of motion · Newton's law of universal gravitation · Equations of motion · Inertial frame of reference · Non-inertial reference frame · Rotating reference frame · Fictitious force · Linear motion · Mechanics of planar particle motion · Displacement (vector) · Relative velocity · Friction · Simple harmonic motion · Harmonic oscillator · Vibration · Damping · Damping ratio · Rotational motion · Circular motion · Uniform circular motion · Non-uniform circular motion · Centripetal force · Centrifugal force · Centrifugal force (rotating reference frame) · Reactive centrifugal force · Coriolis force · Pendulum · Rotational speed · Angular acceleration · Angular velocity · Angular frequency · Angular displacement
Scientists
Isaac Newton · Jeremiah Horrocks · Leonhard Euler · Jean le Rond d'Alembert · Alexis Clairaut · Joseph Louis Lagrange · Pierre-Simon Laplace · William Rowan Hamilton · Siméon-Denis Poisson
Quantum mechanics
Uncertainty principle
Introduction · Mathematical formulations
Background
Classical mechanics Old quantum theory Interference · Bra-ket notation Hamiltonian
Fundamental concepts
Quantum state · Wave function Superposition · Entanglement Complementarity · Duality · Uncertainty Measurement · Exclusion Decoherence · Ehrenfest theorem · Tunnelling
Experiments
Double-slit experiment Davisson–Germer experiment Stern–Gerlach experiment Bell's inequality experiment Popper's experiment Schrödinger's cat Elitzur–Vaidman bomb-tester Quantum eraser
Formulations
Schrödinger picture Heisenberg picture Interaction picture Matrix mechanics Sum over histories
Equations
Schrödinger equation Pauli equation Klein–Gordon equation Dirac equation Rydberg formula
Interpretations
de Broglie–Bohm · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variables · Many-worlds · Pondicherry · Quantum logic · Relational · Stochastic · Transactional · Objective collapse
Advanced topics
Quantum information science Scattering theory Quantum field theory Quantum chaos
Scientists
Bell • Bohm • Bohr • Born • Bose • de Broglie • Dirac • Ehrenfest • Everett • Feynman • Heisenberg • Jordan • Kramers • von Neumann • Pauli • Planck • Schrödinger • Sommerfeld • Wien • Wigner

The major division of the mechanics discipline separates classical mechanics from quantum mechanics.

Historically, classical mechanics came first, while quantum mechanics is a comparatively recent invention. Classical mechanics originated with Isaac Newton's Laws of motion in Principia Mathematica, while quantum mechanics didn't appear until 1900. Both are commonly held to constitute the most certain knowledge that exists about physical nature. Classical mechanics has especially often been viewed as a model for other so-called exact sciences. Essential in this respect is the relentless use of mathematics in theories, as well as the decisive role played by experiment in generating and testing them.

Quantum mechanics is of a wider scope, as it encompasses classical mechanics as a sub-discipline which applies under certain restricted circumstances. According to the correspondence principle, there is no contradiction or conflict between the two subjects, each simply pertains to specific situations. The correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of large quantum numbers. Quantum mechanics has superseded classical mechanics at the foundational level and is indispensable for the explanation and prediction of processes at molecular and (sub)atomic level. However, for macroscopic processes classical mechanics is able to solve problems which are unmanageably difficult in quantum mechanics and hence remains useful and well used.

Einsteinian versus Newtonian

Analogous to the quantum versus classical reformation, Einstein's general and special theories of relativity have expanded the scope of mechanics beyond the mechanics of Newton and Galileo, and made fundamental corrections to them, that become significant and even dominant as speeds of material objects approach the speed of light, which cannot be exceeded. Relativistic corrections are also needed for quantum mechanics, although General relativity has not been integrated; the two theories remain incompatible, a hurdle which must be overcome in developing the Grand Unified Theory.

History

Main articles: History of classical mechanics and History of quantum mechanics
This section requires expansion.

Antiquity

Main article: Aristotelian mechanics

The main theory of mechanics in antiquity was Aristotelian mechanics.[1] A later developer in this tradition was Hipparchus.[2]

Medieval age

Main articles: Physics in medieval Islam, Theory of impetus, and Aristotelian physics: Medieval criticisms

In the Middle Ages, Aristotle's theories were criticized and modified by a number of figures, beginning with John Philoponus in the 6th century, and reaching its peak during the Golden Age of Islam. A central problem was that of projectile motion, which was discussed by Hipparchus and Philoponus. This led to the development of the theory of impetus by the 11th century Persian Avicenna and the 14th century French Jean Buridan, which developed into the modern theories of inertia, velocity, acceleration and momentum. This work and others was developed in 14th century England by the Oxford Calculators such as Thomas Bradwardine, who studied and formulated various laws regarding falling bodies.

On the question of a body subject to a constant (uniform) force, the 12th century Jewish-Arab Nathanel (Iraqi, of Baghdad) stated that constant force imparts constant acceleration, while the main properties are uniformly accelerated motion (as of falling bodies) was worked out by the 14th century Oxford Calculators.

Early modern age

Two central figures in the early modern age are Galileo Galilei and Isaac Newton. Galileo's final statement of his mechanics, particularly of falling bodies, is his Two New Sciences (1638). Newton's 1687 Philosophiæ Naturalis Principia Mathematica provided a detailed mathematical account of mechanics, using the newly developed mathematics of calculus and providing the basis of Newtonian mechanics.[2]

There is some dispute over priority of various ideas: Newton's Principia is certainly the seminal work and has been tremendously influential, and the systematic mathematics therein did not and could not have been stated earlier because calculus had not been developed. However, many of the ideas, particularly as pertain to inertia (impetus) and falling bodies had been developed and stated by earlier researchers, both the then-recent Galileo and the less-known medieval predecessors. Precise credit is at times difficult or contentious because scientific language and standards of proof changed, so whether medieval statements are equivalent to modern statements or sufficient proof, or instead similar to modern statements and hypotheses is often debatable.

Modern age

Two main modern developments in mechanics are general relativity of Einstein, and quantum mechanics, both developed in the 20th century based in part on earlier 19th century ideas.

Types of mechanical bodies

Thus the often-used term body needs to stand for a wide assortment of objects, including particles, projectiles, spacecraft, stars, parts of machinery, parts of solids, parts of fluids (gases and liquids), etc.

Other distinctions between the various sub-disciplines of mechanics, concern the nature of the bodies being described. Particles are bodies with little (known) internal structure, treated as mathematical points in classical mechanics. Rigid bodies have size and shape, but retain a simplicity close to that of the particle, adding just a few so-called degrees of freedom, such as orientation in space.

Otherwise, bodies may be semi-rigid, i.e. elastic, or non-rigid, i.e. fluid. These subjects have both classical and quantum divisions of study.

For instance, the motion of a spacecraft, regarding its orbit and attitude (rotation), is described by the relativistic theory of classical mechanics, while the analogous movements of an atomic nucleus are described by quantum mechanics.

Sub-disciplines in mechanics

The following are two lists of various subjects that are studied in mechanics.

Note that there is also the "theory of fields" which constitutes a separate discipline in physics, formally treated as distinct from mechanics, whether classical fields or quantum fields. But in actual practice, subjects belonging to mechanics and fields are closely interwoven. Thus, for instance, forces that act on particles are frequently derived from fields (electromagnetic or gravitational), and particles generate fields by acting as sources. In fact, in quantum mechanics, particles themselves are fields, as described theoretically by the wave function.

Classical mechanics

The following are described as forming Classical mechanics:

Quantum mechanics

The following are categorized as being part of Quantum mechanics:

Professional organizations

See also

References

  1. ^ "A history of mechanics". René Dugas (1988). p.19. ISBN 0486656322
  2. ^ a b "A Tiny Taste of the History of Mechanics". The University of Texas at Austin.

Further reading

External links

Categories: Mechanics | Greek loanwords

 

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