Paraconical Pendulum
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Paraconical Pendulum
The paraconical pendulum is a type of pendulum invented in the 1950s by Maurice Allais, a French researcher. During the 1950s, Maurice Allais conducted six marathon series of long-term observations, during each of which his team manually operated and manually monitored his pendulum non-stop over about a month. The objective was to investigate possible changes over time of the characteristics of the motion, hypothesized to yield information about asymmetries of inertial space (sometimes described as "aether flow"). Characterization and experiments The defining feature of the "paraconical" or "ball-borne" pendulum is that the pendulum's fulcrum is the changing point of contact between a spherical metal ball and a flat surface on which the ball rests. The pendulum therefore loses energy to rolling friction but not sliding friction, and is able to swing freely in both dimensions (forward-backward and side-to-side), similar to an ordinary conical pendulum. The main difference between ...
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Pendulum
A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum and also to a slight degree on the amplitude, the width of the pendulum's swing. Pendulums were widely used in early mechanical clocks for timekeeping. The regular motion of pendulums was used for timekeeping and was the world's most accurate timekeeping technology until the 1930s. The pendulum clock invented by Christiaan Huygens in 1656 became the world's standard timekeeper, used in homes and offices for 270 years, and ...
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Maurice Allais
Maurice Félix Charles Allais (31 May 19119 October 2010) was a French physicist and economist, the 1988 winner of the Nobel Memorial Prize in Economic Sciences "for his pioneering contributions to the theory of markets and efficient utilization of resources", along with John Hicks (Value and Capital, 1939) and Paul Samuelson (The Foundations of Economic Analysis, 1947), to neoclassical synthesis. They formalize the self-regulation of markets, which Keynes refuted but reiterated some of Allais's ideas. Born in Paris, France, Allais attended the Lycée Lakanal, graduated from the École Polytechnique in Paris and studied at the École nationale supérieure des mines de Paris. His academic and other posts have included being Professor of Economics at the École Nationale Supérieure des Mines de Paris (since 1944) and Director of its Economic Analysis Centre (since 1946). In 1949, he received the title of doctor-engineer from the University of Paris, Faculty of Science. He also ...
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Inertial Space
In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame, the laws of nature can be observed without the need to correct for acceleration. All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity, or, equivalently, Newton's first law of motion holds. Such frames are known as inertial. Some physicists, like Isaac Newton, originally thought that one of these frames was absolute — the one approximated by the fixed stars. However, this is not required for the definition, and it is now known that those stars are in fact moving, relative to o ...
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Fulcrum
A fulcrum (: fulcra or fulcrums) is the support about which a lever pivots. Fulcrum may also refer to: Companies and organizations * Fulcrum (Anglican think tank), a Church of England think tank * Fulcrum Press, a British publisher of poetry * Fulcrum Wheels, a bicycle wheel manufacturer in Italy * The Fulcrum, an American news site Entertainment * ''Fulcrum'' (annual), a United States literary periodical * Fulcrum (''Chuck''), the enemy spy organization on the TV series ''Chuck'' * ''Fulcrum'' (newspaper), a student newspaper at the University of Ottawa * ''Fulcrum'' (sculpture), a 1987 sculpture in London by Richard Serra * The Fulcrum (comics), a supreme being in the Marvel Comics universe * Ahsoka Tano, a character in the animated series ''Star Wars Rebels'' who uses the alias Fulcrum ** Agent Alexsandr Kallus, a character from the same series who took the alias Fulcrum after Ahsoka Tano. Other * Fulcrum (Antarctica), a geological formation in Antarctica * Fulcrum (dru ...
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Rolling Friction
Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body (such as a ball, tire, or wheel) rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc., is recovered when the pressure is removed. Two forms of this are hysteresis losses (see below), and permanent (plastic) deformation of the object or the surface (e.g. soil). Note that the slippage between the wheel and the surface also results in energy dissipation. Although some researchers have included this term in rolling resistance, some suggest that this dissipation term should be treated separately from rolling resistance because it is due to the applied torque to the wheel and the resultant slip between the wheel and ground, which is called slip loss or slip resistance. In addition, only the so-called slip resistance involves friction, therefore the name "rolling frict ...
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Sliding Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. Types of friction include dry, fluid, lubricated, skin, and internal -- an incomplete list. The study of the processes involved is called tribology, and has a history of more than 2000 years. Friction can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Another important consequence of many types of friction can be wear, which may lead to performance degradation or damage to components. It is known that frictional energy losses account for about 20% of the total energy expenditure of the world. As briefly discussed later, there are many different contributors to the retarding force in friction, ranging from asperity deformation to the generation of charges and changes in local structure. When two bodies in contact move relative to each other, due to these various ...
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Conical Pendulum
A conical pendulum consists of a weight (or bob) fixed on the end of a string or rod suspended from a pivot. Its construction is similar to an ordinary pendulum; however, instead of swinging back and forth along a circular arc, the bob of a conical pendulum moves at a constant speed in a circle or ellipse with the string (or rod) tracing out a cone. The conical pendulum was first studied by the English scientist Robert Hooke around 1660 as a model for the orbital motion of planets. In 1673 Dutch scientist Christiaan Huygens calculated its period, using his new concept of centrifugal force in his book ''Horologium Oscillatorium''. Later it was used as the timekeeping element in a few mechanical clocks and other clockwork timing devices. Uses During the 1800s, conical pendulums were used as the timekeeping element in a few clockwork timing mechanisms where a smooth motion was required, as opposed to the unavoidably jerky motion provided by ordinary pendulums. Two examples were m ...
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Foucault Pendulum
The Foucault pendulum or Foucault's pendulum is a simple device named after French physicist Léon Foucault, conceived as an experiment to demonstrate the Earth's rotation. If a long and heavy pendulum suspended from the high roof above a circular area is monitored over an extended period of time, its plane (geometry), plane of oscillation appears to change spontaneously as the Earth makes its 24-hourly rotation. This effect is greatest at the poles and diminishes with lower latitude until it no longer exists at Earth's equator. The pendulum was introduced in 1851 and was the first experiment to give simple, direct evidence of the Earth's rotation. Foucault followed up in 1852 with a Foucault's gyroscope experiment, gyroscope experiment to further demonstrate the Earth's rotation. Foucault pendulums today are popular displays in science museums and universities. History Foucault was inspired by observing a thin flexible rod on the axis of a lathe, which vibrated in the sam ...
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Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ...
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Allais Effect
The Allais effect is the alleged anomalous behavior of pendulums or gravimeters which is sometimes purportedly observed during a solar eclipse. The effect was first reported as an anomalous precession of the plane of oscillation of a Foucault pendulum during the solar eclipse of June 30, 1954 by Maurice Allais, a French polymath who later won the Nobel Prize in Economics. Allais reported another observation of the effect during the solar eclipse of October 2, 1959 using the paraconical pendulum he invented. This study earned him the 1959 Galabert Prize of the French Astronautical Society and made him a laureate of the U.S. Gravity Research Foundation for his 1959 memoir on gravity. The veracity of the Allais effect remains controversial among the scientific community, as its testing has frequently met with inconsistent or ambiguous results over more than five decades of observation. Experimental observations Maurice Allais emphasized the "dynamic character" of the e ...
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Double Pendulum
In physics and mathematics, in the area of dynamical systems, a double pendulum, also known as a chaotic pendulum, is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamical systems, dynamic behavior with a butterfly effect, strong sensitivity to initial conditions. The motion of a double pendulum is governed by a pair of coupled ordinary differential equations and is chaos theory, chaotic. Analysis and interpretation Several variants of the double pendulum may be considered; the two limbs may be of equal or unequal lengths and masses, they may be simple pendulums or compound pendulums (also called complex pendulums) and the motion may be in three dimensions or restricted to one vertical plane. In the following analysis, the limbs are taken to be identical compound pendulums of length and mass , and the motion is restricted to two dimensions. In a compound pendulum, the mass is distributed along its length. If the d ...
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