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 a p ...
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Pendulum
A pendulum is 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. From the first scientific investigations of the pendulum around 1602 by Galileo Galilei, 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 1658 became the world's standard timekeeper, used in homes and offices for 270 years, and ac ...
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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, that Keynes refuted, while reiterating some of his 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 held t ...
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Inertial Space
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. It is a frame in which an isolated physical object — an object with zero net force acting on it — is perceived to move with a constant velocity (it might be a zero velocity) or, equivalently, it is a frame of reference in which Newton's first law of motion holds. All inertial frames are in a state of constant, rectilinear motion with respect to one another; in other words, an accelerometer moving with any of them would detect zero acceleration. It has been observed that celestial objects which are far away from other objects and which are in uniform motion with respect to the cosmic microwave background radiation maintain such uniform motion. Measurements in one inertial frame can be converted to measurements in another by a simple ...
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Fulcrum
A fulcrum 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 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 (drumming), part of a percussionist's grip * Fulcrum weeder, a gar ...
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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. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into ''static friction'' (" stiction") between non-moving surfaces, and ''kinetic friction'' between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities (see Figure 1). *Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other. *Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces. *Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body. *Internal friction is the force resisting motion between the elements making up a so ...
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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, the bob of a conical pendulum moves at a constant speed in a circle 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 mechanisms to turn the lenses of ...
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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. A long and heavy pendulum suspended from the high roof above a circular area was monitored over an extended time period, showing that the plane of oscillation rotated. The pendulum was introduced in 1851 and was the first experiment to give simple, direct evidence of the Earth's rotation. Foucault pendulums today are popular displays in science museums and universities. Original Foucault pendulum The first public exhibition of a Foucault pendulum took place in February 1851 in the Meridian of the Paris Observatory. A few weeks later, Foucault made his most famous pendulum when he suspended a brass-coated lead bob (physics), bob with a wire from the dome of the Panthéon, Paris. The proper period of the pendulum was approximately 2\pi\sqrt\approx 16.5 \,\mathrm. Because the latitude of its location was \ph ...
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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. 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, a dynamical system has a State ...
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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 went on to win 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 eff ...
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Double Pendulum
In physics and mathematics, in the area of dynamical systems, a double pendulum also known as a chaos pendulum is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. The motion of a double pendulum is governed by a set of coupled ordinary differential equations and is 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 the 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 mass is evenly distributed, then the center of mass o ...
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