|
Painlevé Paradox
In rigid-body dynamics, the Painlevé paradox (also called frictional paroxysms by Jean Jacques Moreau) is the paradox that results from inconsistencies between the contact and Coulomb models of friction. It is named for former French prime minister and mathematician Paul Painlevé. To demonstrate the paradox, a hypothetical system is constructed where analysis of the system requires assuming the direction of the frictional force. Using that assumption, the system is solved. However, once the solution is obtained, the final direction of motion is determined to contradict the assumed direction of the friction force, leading to a paradox. This result is due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law, especially when dealing with large coefficients of friction. There exist, however, simple examples which prove that the Painlevé paradoxes can appear even for small, realistic friction. Explanations Si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid-body Dynamics
In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are ''rigid'' (i.e. they do not deform under the action of applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body. This excludes bodies that display fluid, highly elastic, and plastic behavior. The dynamics of a rigid body system is described by the laws of kinematics and by the application of Newton's second law (kinetics) or their derivative form, Lagrangian mechanics. The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Jacques Moreau
Jean Jacques Moreau (31 July 1923 – 9 January 2014) was a French mathematician and mechanician. He normally published under the name J. J. Moreau. Moreau was born in Blaye. He received his doctorate in mathematics from the University of Paris, then became a researcher at the Centre National de la Recherche Scientifique. He was appointed Professor of Mathematical Models in Physics at Poitiers University and later Professor of General Mechanics at University of Montpellier II. He was emeritus professor in the Laboratoire de Mécanique et Génie Civil, a joint research unit of the university and the CNRS. Moreau's principal works have been in non-smooth mechanics and convex analysis. He is considered one of the founders of convex analysis, where several fundamental and now classical results have his name (Moreau's lemma of the two cones, Moreau's envelopes, Moreau-Yosida's approximations, Fenchel-Moreau's theorem, etc.). He founded the Convex Analysis Group in the 1970s at Montp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact 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 soli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb 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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Painlevé
Paul Painlevé (; 5 December 1863 – 29 October 1933) was a French mathematician and statesman. He served twice as Prime Minister of the Third Republic: 12 September – 13 November 1917 and 17 April – 22 November 1925. His entry into politics came in 1906 after a professorship at the Sorbonne that began in 1892. His first term as prime minister lasted only nine weeks but dealt with weighty issues, such as the Russian Revolution, the American entry into the war, the failure of the Nivelle Offensive, quelling the French Army Mutinies and relations with the British. In the 1920s as Minister of War he was a key figure in building the Maginot Line. In his second term as prime minister he dealt with the outbreak of rebellion in Syria's Jabal Druze in July 1925 which had excited public and parliamentary anxiety over the general crisis of France's empire. Biography Early life Painlevé was born in Paris. Brought up within a family of skilled artisans (his father was a draughtsma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Differential Equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to how is thought of as an unknown number to be solved for in an algebraic equation like . However, it is usually impossible to write down explicit formulas for solutions of partial differential equations. There is, correspondingly, a vast amount of modern mathematical and scientific research on methods to Numerical methods for partial differential equations, numerically approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematics, pure mathematical research, in which the usual questions are, broadly speaking, on the identification of general qualitative features of solutions of various partial differential equations, such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Jacques Moreau
Jean Jacques Moreau (31 July 1923 – 9 January 2014) was a French mathematician and mechanician. He normally published under the name J. J. Moreau. Moreau was born in Blaye. He received his doctorate in mathematics from the University of Paris, then became a researcher at the Centre National de la Recherche Scientifique. He was appointed Professor of Mathematical Models in Physics at Poitiers University and later Professor of General Mechanics at University of Montpellier II. He was emeritus professor in the Laboratoire de Mécanique et Génie Civil, a joint research unit of the university and the CNRS. Moreau's principal works have been in non-smooth mechanics and convex analysis. He is considered one of the founders of convex analysis, where several fundamental and now classical results have his name (Moreau's lemma of the two cones, Moreau's envelopes, Moreau-Yosida's approximations, Fenchel-Moreau's theorem, etc.). He founded the Convex Analysis Group in the 1970s at Montp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter Lewin Chalk
Walter may refer to: People * Walter (name), both a surname and a given name * Little Walter, American blues harmonica player Marion Walter Jacobs (1930–1968) * Gunther (wrestler), Austrian professional wrestler and trainer Walter Hahn (born 1987), who previously wrestled as "Walter" * Walter, standard author abbreviation for Thomas Walter (botanist) ( – 1789) Companies * American Chocolate, later called Walter, an American automobile manufactured from 1902 to 1906 * Walter Energy, a metallurgical coal producer for the global steel industry * Walter Aircraft Engines, Czech manufacturer of aero-engines Films and television * ''Walter'' (1982 film), a British television drama film * Walter Vetrivel, a 1993 Tamil crime drama film * ''Walter'' (2014 film), a British television crime drama * ''Walter'' (2015 film), an American comedy-drama film * ''Walter'' (2020 film), an Indian crime drama film * ''W*A*L*T*E*R'', a 1984 pilot for a spin-off of the TV series ''M*A*S*H'' * ''W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Paradoxes
A physical paradox is an apparent contradiction in physics, physical descriptions of the universe. While many physical paradoxes have accepted resolutions, others defy resolution and may indicate flaws in scientific theory, theory. In physics as in all of science, contradictions and paradoxes are generally assumed to be artifacts of error and incompleteness because reality is assumed to be completely consistency proof, consistent, although this is itself a philosophical assumption. When, as in fields such as quantum physics and relativity theory, existing assumptions about reality have been shown to break down, this has usually been dealt with by changing our understanding of reality to a new one which remains self-consistent in the presence of the new evidence. Paradoxes relating to false assumptions Certain physical paradoxes defy common sense predictions about physical situations. In some cases, this is the result of modern physics correctly describing the natural world in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
