# Classical mechanics

Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors. In physics, classical mechanics and quantum mechanics are the two major sub-fields of mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The term classical mechanics was coined in the early 20th century to describe the system of physics begun by Isaac Newton and many contemporary 17th century natural philosophers, building upon the earlier astronomical theories of Johannes Kepler, which in turn were based on the precise observations of Tycho Brahe and the studies of terrestrial projectile motion of Galileo. The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz, and others. Similarly, Related:  Theories in Physics

Aerodynamics A vortex is created by the passage of an aircraft wing, revealed by smoke. Vortices are one of the many phenomena associated with the study of aerodynamics. Formal aerodynamics study in the modern sense began in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag have been recorded much earlier. Most of the early efforts in aerodynamics worked towards achieving heavier-than-air flight, which was first demonstrated by Wilbur and Orville Wright in 1903. History Modern aerodynamics only dates back to the seventeenth century, but aerodynamic forces have been harnessed by humans for thousands of years in sailboats and windmills,[1] and images and stories of flight appear throughout recorded history,[2] such as the Ancient Greek legend of Icarus and Daedalus.[3] Fundamental concepts of continuum, drag, and pressure gradients, appear in the work of Aristotle and Archimedes.[4] Fundamental concepts Flow classification

Theory of relativity The theory of relativity, or simply relativity in physics, usually encompasses two theories by Albert Einstein: special relativity and general relativity.[1] Concepts introduced by the theories of relativity include: Measurements of various quantities are relative to the velocities of observers. In particular, space contracts and time dilates.Spacetime: space and time should be considered together and in relation to each other.The speed of light is nonetheless invariant, the same for all observers. The term "theory of relativity" was based on the expression "relative theory" (German: Relativtheorie) used in 1906 by Max Planck, who emphasized how the theory uses the principle of relativity. Scope The theory of relativity transformed theoretical physics and astronomy during the 20th century. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, along with ushering in the nuclear age. Two-theory view History

Perturbation theory (quantum mechanics) In the theory of quantum electrodynamics (QED), in which the electron–photon interaction is treated perturbatively, the calculation of the electron's magnetic moment has been found to agree with experiment to eleven decimal places. In QED and other quantum field theories, special calculation techniques known as Feynman diagrams are used to systematically sum the power series terms. The problem of non-perturbative systems has been somewhat alleviated by the advent of modern computers. Time-independent perturbation theory is one of two categories of perturbation theory, the other being time-dependent perturbation (see next section). We begin[3] with an unperturbed Hamiltonian H0, which is also assumed to have no time dependence. For simplicity, we have assumed that the energies are discrete. We now introduce a perturbation to the Hamiltonian. The energy levels and eigenstates of the perturbed Hamiltonian are again given by the Schrödinger equation: Our goal is to express En and where . . .

Old quantum theory The main tool was Bohr–Sommerfeld quantization, a procedure for selecting out certain discrete set of states of a classical integrable motion as allowed states. These are like the allowed orbits of the Bohr model of the atom; the system can only be in one of these states and not in any states in between. The theory did not extend to chaotic motions. Basic principles The basic idea of the old quantum theory is that the motion in an atomic system is quantized, or discrete. where the are the momenta of the system and the are the corresponding coordinates. are integers and the integral is taken over one period of the motion at constant energy (as described by the Hamiltonian). In order for the old quantum condition to make sense, the classical motion must be separable, meaning that there are separate coordinates in terms of which the motion is periodic. Examples Harmonic oscillator a result which was known well before, and used to formulate the old quantum condition. . . and . as

Tesla Turbine: Engine of the 21st Century? The Tesla Turbine could far surpass the efficiency of the internal combustion engine. Recuperative hydraulics can be used for low-speed, high-torque needs. by Sterling D. AllanPure Energy Systems NewsCopyright © 2007 MUNISING, MICHIGAN, USA -- Nikola Tesla created an engine design nearly 100 years ago that is as much as three or four times more efficient than the combustion engine design that has dominated for reasons other than science. At the time of his invention around 1909, Tesla was able to demonstrate a fuel efficiency of 60% with his bladeless turbine design. The politics of his day impeded Tesla's design from being implemented. Enter Environmental Scientist, Ken Reili , CEO of Phoenix Navigation & Guidance, Inc. Rieli and his associates in the popular Phoenix Turbine Builders Club that he founded, have resurrected and improved Tesla's Turbine design. In addition to transportation, potential applications range from home generators to public utilities to locomotive power. Modern Data

Acoustics Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. The word "acoustic" is derived from the Greek word ἀκουστικός (akoustikos), meaning "of or for hearing, ready to hear"[2] and that from ἀκουστός (akoustos), "heard, audible",[3] which in turn derives from the verb ἀκούω (akouo), "I hear".[4] The Latin synonym is "sonic", after which the term sonics used to be a synonym for acoustics[5] and later a branch of acoustics.[6] Frequencies above and below the audible range are called "ultrasonic" and "infrasonic", respectively. History of acoustics

Thermodynamics Annotated color version of the original 1824 Carnot heat engine showing the hot body (boiler), working body (system, steam), and cold body (water), the letters labeled according to the stopping points in Carnot cycle Thermodynamics applies to a wide variety of topics in science and engineering. Historically, thermodynamics developed out of a desire to increase the efficiency and power output of early steam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot (1824) who believed that the efficiency of heat engines was the key that could help France win the Napoleonic Wars.[1] Irish-born British physicist Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854:[2] "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency." Introduction A thermodynamic system can be defined in terms of its states. History Etymology

M-theory M-theory is a theory in physics that unifies all consistent versions of superstring theory. The existence of such a theory was first conjectured by Edward Witten at the string theory conference at the University of Southern California in the summer of 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Background Quantum gravity and strings One of the deepest problems in modern physics is the problem of quantum gravity. Number of dimensions In everyday life, there are three familiar dimensions of space (up/down, left/right, and forward/backward), and there is one dimension of time (later/earlier). Despite the obvious relevance of four-dimensional spacetime for describing the physical world, there are several reasons why physicists often consider theories in other dimensions. Dualities Main articles: S-duality and T-duality A diagram of string theory dualities. and winding number in the dual description. .

Interference (wave propagation) Swimming Pool Interference[1] Interference of waves from two point sources. Magnified-image of coloured interference-pattern in soap-film. The black "holes" are areas where the film is very thin and there is a nearly total destructive interference. Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Geometrical arrangement for two plane wave interference Interference fringes in overlapping plane waves A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle. It can be seen that the two waves are in phase when and are half a cycle out of phase when Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. and df is known as the fringe spacing. The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout. A point source produces a spherical wave. for to where

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