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Kirchhoff Equations
In fluid dynamics, the Kirchhoff equations, named after Gustav Kirchhoff, describe the motion of a rigid body In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible, when a deforming pressure or deforming force is applied on it. The distance between any two given points on a rigid body rema ... in an ideal fluid. \begin & = \times \boldsymbol\omega + \times \mathbf v + \mathbf Q_h + \mathbf Q, \\ 0pt & = \times \boldsymbol\omega + \mathbf F_h + \mathbf F, \\ 0ptT & = \left( \boldsymbol\omega^T \tilde I \boldsymbol\omega + m v^2 \right) \\ 0pt\mathbf Q_h & = -\int p \mathbf x \times\hat\mathbf n \, d\sigma, \\ 0pt\mathbf F_h & = -\int p \hat\mathbf n \, d\sigma \end where \boldsymbol\omega and \mathbf v are the angular and linear velocity vectors at the point \mathbf x, respectively; \tilde I is the moment of inertia tensor, m is the body's mass; \hat\mathbf n is a unit normal vector to the surface o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav Kirchhoff
Gustav Robert Kirchhoff (; 12 March 1824 – 17 October 1887) was a German chemist, mathematician, physicist, and spectroscopist who contributed to the fundamental understanding of electrical circuits, spectroscopy and the emission of black-body radiation by heated objects. He also coined the term ''black body'' in 1860. Several different sets of concepts are named "Kirchhoff's laws" after him, which include Kirchhoff's circuit laws, Kirchhoff's law of thermal radiation, and Kirchhoff's law of thermochemistry. The Bunsen–Kirchhoff Award for spectroscopy is named after Kirchhoff and his colleague, Robert Bunsen. Life and work Gustav Kirchhoff was born on 12 March 1824 in Königsberg, Prussia, the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke. His family were Lutheranism, Lutherans in the Evangelical Church of Prussia. He graduated from the Albertus University of Königsberg in 1847 where he attended the mathematico-physical seminar directed by Carl Gusta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Body
In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible, when a deforming pressure or deforming force is applied on it. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. Mechanics of rigid bodies is a field within mechanics where motions and forces of objects are studied without considering effects that can cause deformation (as opposed to mechanics of materials, where deformable objects are considered). In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light, where the mass is infinitely large. In quantum mechanics, a rigid body is usually thought of as a collection of point masses. For instance, molecules (consisting of the point masses: electr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal Fluid
In physics, a perfect fluid or ideal fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure . Real fluids are viscous ("sticky") and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are ignored. Specifically, perfect fluids have no shear stresses, viscosity, or heat conduction. A quark–gluon plasma and graphene are examples of nearly perfect fluids that could be studied in a laboratory. Non-relativistic fluid mechanics In classical mechanics, ideal fluids are described by Euler equations. Ideal fluids produce no drag according to d'Alembert's paradox. If a fluid produced drag, then work would be needed to move an object through the fluid and that work would produce heat or fluid motion. However, a perfect fluid can not dissipate energy and it can't transmit energy infinitely far from the object. A flock of birds in the medium of air is an example of a perfect fluid; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Normal Vector
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point. A normal vector is a vector perpendicular to a given object at a particular point. A normal vector of length one is called a unit normal vector or normal direction. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior). In three-dimensional space, a surface normal, or simply normal, to a surface at point is a vector perpendicular to the tangent plane of the surface at . The vector field of normal directions to a surface is known as '' Gauss map''. The word "normal" is also used as an adjective: a line ''normal'' to a plane, the ''normal'' component of a forc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clebsch
Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory. He attended the University of Königsberg and was habilitated at Berlin. He subsequently taught in Berlin and Karlsruhe. His collaboration with Paul Gordan in Giessen led to the introduction of Clebsch–Gordan coefficients for spherical harmonics, which are now widely used in quantum mechanics. Together with Carl Neumann at Göttingen, he founded the mathematical research journal ''Mathematische Annalen'' in 1868. In 1883, Saint-Venant translated Clebsch's work on elasticity into French and published it as ''Théorie de l'élasticité des Corps Solides''. Books by A. Clebsch Vorlesungen über Geometrie(Teubner, Leipzig, 1876-1891) edited by Ferdinand Lindemann. Théorie der binären algebraischen Formen(Teubner, 1872) Theorie der Abelschen Functionenwith P. Gordan (B. G. Teubner, 1866) Theorie der Elasti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanics
Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of an object's position relative to its environment. Theoretical expositions of this branch of physics has its origins in Ancient Greece, for instance, in the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo Galilei, Johannes Kepler, Christiaan Huygens, and Isaac Newton laid the foundation for what is now known as classical mechanics. As a branch of classical physics, mechanics deals with bodies that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as the physical science that deals with the motion of and forces on bodies not in the quantum realm. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics
Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics involved Scientific Revolution, substantial change in the methods and philosophy of physics. The qualifier ''classical'' distinguishes this type of mechanics from physics developed after the History of physics#20th century: birth of modern physics, revolutions in physics of the early 20th century, all of which revealed limitations in classical mechanics. The earliest formulation of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on the 17th century foundational works of Sir Isaac Newton, and the mathematical methods invented by Newton, Gottfried Wilhelm Leibniz, Leonhard Euler and others to describe the motion of Physical body, bodies under the influence of forces. Later, methods bas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rigid Bodies
In physics, a rigid body, also known as a rigid object, is a solid body in which deformation is zero or negligible, when a deforming pressure or deforming force is applied on it. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it. A rigid body is usually considered as a continuous distribution of mass. Mechanics of rigid bodies is a field within mechanics where motions and forces of objects are studied without considering effects that can cause deformation (as opposed to mechanics of materials, where deformable objects are considered). In the study of special relativity, a perfectly rigid body does not exist; and objects can only be assumed to be rigid if they are not moving near the speed of light, where the mass is infinitely large. In quantum mechanics, a rigid body is usually thought of as a collection of point masses. For instance, molecules (consisting of the point masses: electro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
