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Tumbling (rigid Body)
In classical mechanics, Poinsot's construction (after Louis Poinsot) is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion has four constants: the kinetic energy of the body and the three components of the angular momentum, expressed with respect to an inertial laboratory frame. The angular velocity vector \boldsymbol\omega of the rigid rotor is ''not constant'', but satisfies Euler's equations. The conservation of kinetic energy and angular momentum provide two constraints on the motion of \boldsymbol\omega. Without explicitly solving these equations, the motion \boldsymbol\omega can be described geometrically as follows: * The rigid body's motion is entirely determined by the motion of its inertia ellipsoid, which is rigidly fixed to the rigid body like a coordinate frame. * Its inertia ellipsoid rolls, without slipping, on the invariable plane, with the cent ... [...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] |
Inertial Reference Frame
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques Philippe Marie Binet
Jacques Philippe Marie Binet (; 2 February 1786 – 12 May 1856) was a French mathematician, physicist and astronomer born in Rennes; he died in Paris, France, in 1856. He made significant contributions to number theory, and the mathematical foundations of matrix algebra which would later lead to important contributions by Arthur Cayley, Cayley and others. In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now known as ''Binet's theorem''. He is also recognized as the first to describe the rule for matrix multiplication, multiplying matrices in 1812, and ''Binet's formula'' expressing Fibonacci numbers in closed form is named in his honour, although the same result was known to Abraham de Moivre a century earlier. Career Binet graduated from l'École Polytechnique in 1806, and returned as a teacher in 1807. He advanced in position until 1816 when he became an inspector of studies at l'École. He held this post until ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tennis Racket Theorem
The tennis racket theorem or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with three distinct principal moments of inertia. It has also been dubbed the Dzhanibekov effect, after Soviet Union, Soviet cosmonaut Vladimir Dzhanibekov, who noticed one of the theorem's logical consequences whilst in space in 1985. The effect was known for at least 150 years prior, having been described by Louis Poinsot in 1834 and included in standard physics textbooks such as Classical Mechanics (Goldstein), ''Classical Mechanics'' by Herbert Goldstein throughout the 20th century. The theorem describes the following effect: rotation of an object around its first and third Moment of inertia#Principal axes, principal axes is stable, whereas rotation around its second principal axis (or intermediate axis) is not. This can be demonstrated by the following experiment: Hold a tennis racket at its handle, with its face being horizo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dzhanibekov Effect
The tennis racket theorem or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with three distinct principal moments of inertia. It has also been dubbed the Dzhanibekov effect, after Soviet cosmonaut Vladimir Dzhanibekov, who noticed one of the theorem's logical consequences whilst in space in 1985. The effect was known for at least 150 years prior, having been described by Louis Poinsot in 1834 and included in standard physics textbooks such as ''Classical Mechanics'' by Herbert Goldstein throughout the 20th century. The theorem describes the following effect: rotation of an object around its first and third principal axes is stable, whereas rotation around its second principal axis (or intermediate axis) is not. This can be demonstrated by the following experiment: Hold a tennis racket at its handle, with its face being horizontal, and throw it in the air such that it performs a full rotation around its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Tumblers (small Solar System Bodies)
This is a list of tumblers, that is, small Solar System bodiess or moons that do not rotate in a fairly constant manner with a constant period. Instead of rotating around a constant axis or around an axis that itself moves evenly, they appear to tumble (see Poinsot's ellipsoid for an explanation). For true tumbling, the three moments of inertia must be different. If two are equal, then the axis of rotation will simply precess in a circle. As of 2018, there are 3 natural satellites and 198 confirmed or likely tumblers out of a total of nearly 800,000 discovered small Solar System bodies. The data is sourced from the "Lightcurve Data Base" (LCDB). The tumbling of a body can be caused by the torque from asymmetrically emitted radiation known as the YORP effect. Note that the rotation periods given below are apparent periods and are not constant for a tumbler. There is another definition of rotation, sometimes called intrinsic rotation, that relates to how the point on the object wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moons Of Pluto
The dwarf planet Pluto has five natural satellites. In order of distance from Pluto, they are Charon, Styx, Nix, Kerberos, and Hydra. Charon, the largest, is mutually tidally locked with Pluto, and is massive enough that Pluto and Charon are sometimes considered a binary dwarf planet. History The innermost and largest moon, Charon, was discovered by James Christy on 22 June 1978, nearly half a century after Pluto was discovered. This led to a substantial revision in estimates of Pluto's size, which had previously assumed that the observed mass and reflected light of the system were all attributable to Pluto alone. Two additional moons were imaged by astronomers of the Pluto Companion Search Team preparing for the ''New Horizons'' mission and working with the Hubble Space Telescope on 15 May 2005, which received the provisional designations S/2005 P 1 and S/2005 P 2. The International Astronomical Union officially named these moons Nix (Pluto II, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperion (moon)
Hyperion , also known as Saturn VII, is the eighth-largest moon of Saturn. It is distinguished by its highly irregular shape, chaotic rotation, low density, and its unusual sponge-like appearance. It was the first non- rounded moon to be discovered. Discovery Hyperion was independently discovered by William Cranch Bond and his son George Phillips Bond in the United States, and William Lassell in the United Kingdom in September 1848. Name The moon is named after Titan Hyperion, the god of watchfulness and observation, and the elder brother of Cronus (the Greek equivalent of the Roman god Saturn). It is also designated ''Saturn VII''. The adjectival form of the name is ''Hyperionian''. Hyperion's discovery came shortly after John Herschel had suggested names for the seven previously known satellites of Saturn in his 1847 publication ''Results of Astronomical Observations made at the Cape of Good Hope''. William Lassell, who saw Hyperion two days after William ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2-manifold
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solid figures; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space. Topological surfaces are sometimes equipped with additional information, such as a Riemannian metric or a complex structure, that connects them to other disciplines within mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical world. In general In mathematics, a surface is a geometrical shape that resembles a deformed plane. The most familiar examples arise as boundaries of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus
In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanarity, coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a donut or doughnut. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution, also known as a ring torus. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a Lemon (geometry), spindle torus (or ''self-crossing torus'' or ''self-intersecting torus''). If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a ''toroid'', as in a square toroid. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphere
A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the center (geometry), ''center'' of the sphere, and the distance is the sphere's ''radius''. The earliest known mentions of spheres appear in the work of the Greek mathematics, ancient Greek mathematicians. The sphere is a fundamental surface in many fields of mathematics. Spheres and nearly-spherical shapes also appear in nature and industry. Bubble (physics), Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is spherical Earth, often approximated as a sphere in geography, and the celestial sphere is an important concept in astronomy. Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres rolling, roll smoothly in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient Vector
In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of f. If the gradient of a function is non-zero at a point p, the direction of the gradient is the direction in which the function increases most quickly from p, and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to minimize a function by gradient descent. In coordinate-free terms, the gradient of a function f(\mathbf) may be defined by: df=\nabla f \cdot d\mathbf where df is the total infinitesimal change in f for an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
