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Index notation for tensors
The cross product can alternatively be defined in terms of the Levi-Civita tensor Eijk and a dot product ηmi, which are useful in converting vector notation for tensor applications:
where the indices correspond to vector components. This characterization of the cross product is often expre... | Cross product | Wikipedia | 454 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
When doing this for the next two elements down should "wrap around" the matrix so that after the z component comes the x component. For clarity, when performing this operation for , the next two components should be z and x (in that order). While for the next two components should be taken as x and y.
For then, if ... | Cross product | Wikipedia | 499 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
The cross product is used in calculating the volume of a polyhedron such as a tetrahedron or parallelepiped.
Angular momentum and torque
The angular momentum of a particle about a given origin is defined as:
where is the position vector of the particle relative to the origin, is the linear momentum of the par... | Cross product | Wikipedia | 423 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
This can be thought of as the oriented multi-dimensional element "perpendicular" to the bivector. In a d-dimensional space, Hodge star takes a k-vector to a (d–k)-vector; thus only in d = 3 dimensions is the result an element of dimension one (3–2 = 1), i.e. a vector. For example, in d = 4 dimensions, the cross product... | Cross product | Wikipedia | 428 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
The paradox of the orthonormal basis
Let (i, j, k) be an orthonormal basis. The vectors i, j and k do not depend on the orientation of the space. They can even be defined in the absence of any orientation. They can not therefore be axial vectors. But if i and j are polar vectors, then k is an axial vector for i × j =... | Cross product | Wikipedia | 441 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
In general dimension, there is no direct analogue of the binary cross product that yields specifically a vector. There is however the exterior product, which has similar properties, except that the exterior product of two vectors is now a 2-vector instead of an ordinary vector. As mentioned above, the cross product can... | Cross product | Wikipedia | 303 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
The commutator product could be generalised to arbitrary multivectors in three dimensions, which results in a multivector consisting of only elements of grades 1 (1-vectors/true vectors) and 2 (2-vectors/pseudovectors). While the commutator product of two 1-vectors is indeed the same as the exterior product and yields ... | Cross product | Wikipedia | 388 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
In detail, the 3-dimensional volume form defines a product by taking the determinant of the matrix given by these 3 vectors. By duality, this is equivalent to a function (fixing any two inputs gives a function by evaluating on the third input) and in the presence of an inner product (such as the dot product; more ge... | Cross product | Wikipedia | 468 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
This formula is identical in structure to the determinant formula for the normal cross product in R3 except that the row of basis vectors is the last row in the determinant rather than the first. The reason for this is to ensure that the ordered vectors (v1, ..., vn−1, Λvi) have a positive orientation with respect to (... | Cross product | Wikipedia | 402 | 157092 | https://en.wikipedia.org/wiki/Cross%20product | Mathematics | Algebra | null |
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used. It is often called the inner product ... | Dot product | Wikipedia | 494 | 157093 | https://en.wikipedia.org/wiki/Dot%20product | Mathematics | Algebra | null |
where denotes summation and is the dimension of the vector space. For instance, in three-dimensional space, the dot product of vectors and is:
Likewise, the dot product of the vector with itself is:
If vectors are identified with column vectors, the dot product can also be written as a matrix product
where den... | Dot product | Wikipedia | 499 | 157093 | https://en.wikipedia.org/wiki/Dot%20product | Mathematics | Algebra | null |
Also, by the geometric definition, for any vector and a vector , we note that
where is the component of vector in the direction of . The last step in the equality can be seen from the figure.
Now applying the distributivity of the geometric version of the dot product gives
which is precisely the algebraic definit... | Dot product | Wikipedia | 462 | 157093 | https://en.wikipedia.org/wiki/Dot%20product | Mathematics | Algebra | null |
Its value is the determinant of the matrix whose columns are the Cartesian coordinates of the three vectors. It is the signed volume of the parallelepiped defined by the three vectors, and is isomorphic to the three-dimensional special case of the exterior product of three vectors.
The vector triple product is defined... | Dot product | Wikipedia | 496 | 157093 | https://en.wikipedia.org/wiki/Dot%20product | Mathematics | Algebra | null |
The self dot product of a complex vector , involving the conjugate transpose of a row vector, is also known as the norm squared, , after the Euclidean norm; it is a vector generalization of the absolute square of a complex scalar (see also: Squared Euclidean distance).
Inner product
The inner product generalizes the... | Dot product | Wikipedia | 500 | 157093 | https://en.wikipedia.org/wiki/Dot%20product | Mathematics | Algebra | null |
A dot product function is included in:
BLAS level 1 real , ; complex , , ,
Fortran as or
Julia as or standard library LinearAlgebra as
R (programming language) as for vectors or, more generally for matrices, as
Matlab as or or or
Python (package NumPy) as or or
GNU Octave as , and sim... | Dot product | Wikipedia | 92 | 157093 | https://en.wikipedia.org/wiki/Dot%20product | Mathematics | Algebra | null |
Cut, copy, and paste are essential commands of modern human–computer interaction and user interface design. They offer an interprocess communication technique for transferring data through a computer's user interface. The cut command removes the selected data from its original position, and the copy command creates a d... | Cut, copy, and paste | Wikipedia | 498 | 157115 | https://en.wikipedia.org/wiki/Cut%2C%20copy%2C%20and%20paste | Technology | User interface | null |
Early methods
The earliest editors (designed for teleprinter terminals) provided keyboard commands to delineate a contiguous region of text, then delete or move it. Since moving a region of text requires first removing it from its initial location and then inserting it into its new location, various schemes had to be i... | Cut, copy, and paste | Wikipedia | 465 | 157115 | https://en.wikipedia.org/wiki/Cut%2C%20copy%2C%20and%20paste | Technology | User interface | null |
The IBM Common User Access (CUA) standard also uses combinations of the Insert, Del, Shift and Control keys. Early versions of Windows used the IBM standard. Microsoft later also adopted the Apple key combinations with the introduction of Windows, using the control key as modifier key. For users migrating to Windows fr... | Cut, copy, and paste | Wikipedia | 282 | 157115 | https://en.wikipedia.org/wiki/Cut%2C%20copy%2C%20and%20paste | Technology | User interface | null |
Computer-based editing can involve very frequent use of cut-and-paste operations. Most software-suppliers provide several methods for performing such tasks, and this can involve (for example) key combinations, pulldown menus, pop-up menus, or toolbar buttons.
The user selects or "highlights" the text or file for movin... | Cut, copy, and paste | Wikipedia | 473 | 157115 | https://en.wikipedia.org/wiki/Cut%2C%20copy%2C%20and%20paste | Technology | User interface | null |
The term "copy-and-paste" refers to the popular, simple method of reproducing text or other data from a source to a destination. It differs from cut and paste in that the original source text or data does not get deleted or removed. The popularity of this method stems from its simplicity and the ease with which users c... | Cut, copy, and paste | Wikipedia | 110 | 157115 | https://en.wikipedia.org/wiki/Cut%2C%20copy%2C%20and%20paste | Technology | User interface | null |
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of the mathematical field of combinatorics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a question of the form: "how big must some str... | Ramsey theory | Wikipedia | 413 | 157175 | https://en.wikipedia.org/wiki/Ramsey%20theory | Mathematics | Combinatorics | null |
Van der Waerden's theorem: For any given c and n, there is a number V, such that if V consecutive numbers are coloured with c different colours, then it must contain an arithmetic progression of length n whose elements are all the same colour.
Hales–Jewett theorem: For any given n and c, there is a number H such that... | Ramsey theory | Wikipedia | 345 | 157175 | https://en.wikipedia.org/wiki/Ramsey%20theory | Mathematics | Combinatorics | null |
Results in Ramsey theory typically have two primary characteristics. Firstly, they are unconstructive: they may show that some structure exists, but they give no process for finding this structure (other than brute-force search). For instance, the pigeonhole principle is of this form. Secondly, while Ramsey theory res... | Ramsey theory | Wikipedia | 388 | 157175 | https://en.wikipedia.org/wiki/Ramsey%20theory | Mathematics | Combinatorics | null |
Glass fiber (or glass fibre) is a material consisting of numerous extremely fine fibers of glass.
Glassmakers throughout history have experimented with glass fibers, but mass manufacture of glass fiber was only made possible with the invention of finer machine tooling. In 1893, Edward Drummond Libbey exhibited a dress... | Glass fiber | Wikipedia | 481 | 157606 | https://en.wikipedia.org/wiki/Glass%20fiber | Technology | Materials | null |
The most common type of glass fiber used in fiberglass is E-glass, which is alumino-borosilicate glass with less than 1% w/w alkali oxides, mainly used for glass-reinforced plastics. Other types of glass used are A-glass (Alkali-lime glass with little or no boron oxide), E-CR-glass (Electrical/Chemical Resistance; alum... | Glass fiber | Wikipedia | 206 | 157606 | https://en.wikipedia.org/wiki/Glass%20fiber | Technology | Materials | null |
Pure silica (silicon dioxide), when cooled as fused quartz into a glass with no true melting point, can be used as a glass fiber for fiberglass, but has the drawback that it must be worked at very high temperatures. In order to lower the necessary work temperature, other materials are introduced as "fluxing agents" (i.... | Glass fiber | Wikipedia | 464 | 157606 | https://en.wikipedia.org/wiki/Glass%20fiber | Technology | Materials | null |
The vitreous and crystalline states of silica (glass and quartz) have similar energy levels on a molecular basis, also implying that the glassy form is extremely stable. In order to induce crystallization, it must be heated to temperatures above 1200 °C for long periods of time.
Although pure silica is a perfectly vi... | Glass fiber | Wikipedia | 471 | 157606 | https://en.wikipedia.org/wiki/Glass%20fiber | Technology | Materials | null |
Mechanical properties
The strength of glass is usually tested and reported for "virgin" or pristine fibers—those that have just been manufactured. The freshest, thinnest fibers are the strongest because the thinner fibers are more ductile. The more the surface is scratched, the less the resulting tenacity. Because gla... | Glass fiber | Wikipedia | 368 | 157606 | https://en.wikipedia.org/wiki/Glass%20fiber | Technology | Materials | null |
Formation
The bushing plate is the most important part of the machinery for making the fiber. This is a small metal furnace containing nozzles for the fiber to be formed through. It is almost always made of platinum alloyed with rhodium for durability. Platinum is used because the glass melt has a natural affinity for... | Glass fiber | Wikipedia | 451 | 157606 | https://en.wikipedia.org/wiki/Glass%20fiber | Technology | Materials | null |
Continuous filament process
In the continuous filament process, after the fiber is drawn, a size is applied. This size helps protect the fiber as it is wound onto a bobbin. The particular size applied relates to end-use. While some sizes are processing aids, others make the fiber have an affinity for a certain resin, ... | Glass fiber | Wikipedia | 501 | 157606 | https://en.wikipedia.org/wiki/Glass%20fiber | Technology | Materials | null |
A 1998 study using rats found that the biopersistence of synthetic fibers after one year was 0.04–13%, but 27% for amosite asbestos. Fibers that persisted longer were found to be more carcinogenic.
Glass-reinforced plastic (fiberglass)
Glass-reinforced plastic (GRP) is a composite material or fiber-reinforced plasti... | Glass fiber | Wikipedia | 496 | 157606 | https://en.wikipedia.org/wiki/Glass%20fiber | Technology | Materials | null |
A composite or composite material (also composition material) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or physical properties and are merged to create a material with properties unlike the individual elements. Within the finishe... | Composite material | Wikipedia | 366 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Woody plants, both true wood from trees and such plants as palms and bamboo, yield natural composites that were used prehistorically by humankind and are still used widely in construction and scaffolding.
Plywood, 3400 BC, by the Ancient Mesopotamians; gluing wood at different angles gives better properties than natur... | Composite material | Wikipedia | 441 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Concrete is the most common artificial composite material of all. , about 7.5 billion cubic metres of concrete are made each year.
Concrete typically consists of loose stones (construction aggregate) held with a matrix of cement. Concrete is an inexpensive material resisting large compressive forces, however, susceptib... | Composite material | Wikipedia | 495 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Organic matrix/ceramic aggregate composites include asphalt concrete, polymer concrete, mastic asphalt, mastic roller hybrid, dental composite, syntactic foam, and mother of pearl. Chobham armour is a special type of composite armour used in military applications.
Additionally, thermoplastic composite materials can be... | Composite material | Wikipedia | 410 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Wood is a naturally occurring composite comprising cellulose fibres in a lignin and hemicellulose matrix. Engineered wood includes a wide variety of different products such as wood fibre board, plywood, oriented strand board, wood plastic composite (recycled wood fibre in polyethylene matrix), Pykrete (sawdust in ice m... | Composite material | Wikipedia | 429 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Carbon composite is a key material in today's launch vehicles and heat shields for the re-entry phase of spacecraft. It is widely used in solar panel substrates, antenna reflectors and yokes of spacecraft. It is also used in payload adapters, inter-stage structures and heat shields of launch vehicles. Furthermore, disk... | Composite material | Wikipedia | 457 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Composite materials are created from individual materials. These individual materials are known as constituent materials, and there are two main categories of it. One is the matrix (binder) and the other reinforcement. A portion of each kind is needed at least. The reinforcement receives support from the matrix as the ... | Composite material | Wikipedia | 492 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Martin Hubbe and Lucian A Lucia consider wood to be a natural composite of cellulose fibres in a matrix of lignin.
Cores in composites
Several layup designs of composite also involve a co-curing or post-curing of the prepreg with many other media, such as foam or honeycomb. Generally, this is known as a sandwich struc... | Composite material | Wikipedia | 483 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Methods of fabrication
Normally, the fabrication of composite includes wetting, mixing or saturating the reinforcement with the matrix. The matrix is then induced to bind together (with heat or a chemical reaction) into a rigid structure. Usually, the operation is done in an open or closed forming mould. However, the o... | Composite material | Wikipedia | 501 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Other fabrication methods
Other types of fabrication include casting, centrifugal casting, braiding (onto a former), continuous casting, filament winding, press moulding, transfer moulding, pultrusion moulding, and slip forming. There are also forming capabilities including CNC filament winding, vacuum infusion, wet la... | Composite material | Wikipedia | 462 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
For example, a composite material made up of α and β phases as shown in the figure to the right under isostrain, the Young's modulus would be as follows:where Vα and Vβ are the respective volume fractions of each phase.
This can be derived by considering that in the isostrain case, Assuming that the composite has a uni... | Composite material | Wikipedia | 370 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Though composite stiffness is maximized when fibres are aligned with the loading direction, so is the possibility of fibre tensile fracture, assuming the tensile strength exceeds that of the matrix. When a fibre has some angle of misorientation θ, several fracture modes are possible. For small values of θ the stress re... | Composite material | Wikipedia | 491 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
In contrast to composites, isotropic materials (for example, aluminium or steel), in standard wrought forms, possess the same stiffness typically despite the directional orientation of the applied forces and/or moments. The relationship between forces/moments and strains/curvatures for an isotropic material can be desc... | Composite material | Wikipedia | 418 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Continuous fiber reinforcement
In general, continuous fiber reinforcement is implemented by incorporating a fiber as the strong phase into a weak phase, matrix. The reason for the popularity of fiber usage is materials with extraordinary strength can be obtained in their fiber form. Non-metallic fibers are usually show... | Composite material | Wikipedia | 509 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
The covalently bonded high strength fibers (e.g. carbon fibers) experience mostly elastic deformation before the fracture since the plastic deformation can happen due to dislocation motion. Whereas, metallic fibers have more space to plastically deform, so their composites exhibit a third stage where both fiber and the... | Composite material | Wikipedia | 492 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
At small angles, , the dominant fracture mechanism is the same as with load-fiber alignment, tensile fracture. The resolved force acting upon the length of the fibers is reduced by a factor of from rotation. . The resolved area on which the fiber experiences the force is increased by a factor of from rotation. . Taki... | Composite material | Wikipedia | 505 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
The stiffness matrix and compliance matrix can be reduced to
and
For fiber-reinforced composite, the fiber orientation in material affect anisotropic properties of the structure. From characterizing technique i.e. tensile testing, the material properties were measured based on sample (1-2) coordinate system. The te... | Composite material | Wikipedia | 434 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
Composites can fail on the macroscopic or microscopic scale. Compression failures can happen at both the macro scale or at each individual reinforcing fibre in compression buckling. Tension failures can be net section failures of the part or degradation of the composite at a microscopic scale where one or more of the l... | Composite material | Wikipedia | 335 | 157616 | https://en.wikipedia.org/wiki/Composite%20material | Technology | Material and chemical | null |
The peregrine falcon (Falco peregrinus), also known simply as the peregrine, is a cosmopolitan bird of prey (raptor) in the family Falconidae. A large, crow-sized falcon, it has a blue-grey back, barred white underparts, and a black head. The peregrine is renowned for its speed. It can reach over during its characteri... | Peregrine falcon | Wikipedia | 386 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The peregrine is a highly successful example of urban wildlife in much of its range, taking advantage of tall buildings as nest sites and an abundance of prey such as pigeons and ducks. Both the English and scientific names of this species mean "wandering falcon", referring to the migratory habits of many northern popu... | Peregrine falcon | Wikipedia | 510 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The back and the long pointed wings of the adult are usually bluish black to slate grey with indistinct darker barring (see "Subspecies" below); the wingtips are black. The white to rusty underparts are barred with thin clean bands of dark brown or black. The tail, coloured like the back but with thin clean bars, is lo... | Peregrine falcon | Wikipedia | 418 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The peregrine falcon belongs to a genus whose lineage includes the hierofalcons and the prairie falcon (F. mexicanus). This lineage probably diverged from other falcons towards the end of the Late Miocene or in the Late Pliocene, about 3–8 million years ago (mya). As the peregrine-hierofalcon group includes both Old Wo... | Peregrine falcon | Wikipedia | 276 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
Falco peregrinus anatum, described by Bonaparte in 1838, is known as the American peregrine falcon or "duck hawk"; its scientific name means "duck peregrine falcon". At one time, it was partly included in F. p. leucogenys. It is mainly found in the Rocky Mountains. It was formerly common throughout North America betwee... | Peregrine falcon | Wikipedia | 449 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
, described by John Latham in 1790, it was formerly called F. p. leucogenys and includes F. p. caeruleiceps. It breeds in the Arctic tundra of Eurasia from Murmansk Oblast to roughly Yana and Indigirka Rivers, Siberia. It is completely migratory and travels south in winter as far as South Asia and sub-Saharan Africa. I... | Peregrine falcon | Wikipedia | 429 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
Falco peregrinus japonensis, described by Gmelin in 1788, includes F. p. kleinschmidti, F. p. pleskei, and F. p. harterti, and seems to refer to intergrades with F. p. calidus. It is found from northeast Siberia to Kamchatka (though it is possibly replaced by F. p. pealei on the coast there) and Japan. Northern populat... | Peregrine falcon | Wikipedia | 466 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
, described by Ridgway in 1873, is Peale's falcon and includes F. p. rudolfi. It is found in the Pacific Northwest of North America, northwards from Puget Sound along the British Columbia coast (including the Haida Gwaii), along the Gulf of Alaska and the Aleutian Islands to the far eastern Bering Sea coast of Russia, ... | Peregrine falcon | Wikipedia | 471 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
, the nominate (first-named) subspecies, described by Tunstall in 1771, breeds over much of temperate Eurasia between the tundra in the north and the Pyrenees, Mediterranean region and Alpide belt in the south. It is mainly non-migratory in Europe, but migratory in Scandinavia and Asia. Males weigh , while females weig... | Peregrine falcon | Wikipedia | 412 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
Barbary falcon
The Barbary falcon is a subspecies of the peregrine falcon that inhabits parts of North Africa, from the Canary Islands to the Arabian Peninsula. There was discussion concerning the taxonomic status of the bird, with some considering it a subspecies of the peregrine falcon and others considering it a fu... | Peregrine falcon | Wikipedia | 492 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The peregrine falcon reaches faster speeds than any other animal on the planet when performing the stoop, which involves soaring to a great height and then diving steeply at speeds of over , hitting one wing of its prey so as not to harm itself on impact. The air pressure from such a dive could possibly damage a bird's... | Peregrine falcon | Wikipedia | 360 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The peregrine falcon is host to a range of parasites and pathogens. It is a vector for Avipoxvirus, Newcastle disease virus, Falconid herpesvirus 1 (and possibly other Herpesviridae), and some mycoses and bacterial infections. Endoparasites include Plasmodium relictum (usually not causing malaria in the peregrine falco... | Peregrine falcon | Wikipedia | 400 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
In urban areas, where it tends to nest on tall buildings or bridges, it subsists mostly on a variety of pigeons. Among pigeons, the rock dove or feral pigeon comprises 80% or more of the dietary intake of peregrines. Other common city birds are also taken regularly, including mourning doves, common wood pigeons, common... | Peregrine falcon | Wikipedia | 331 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The peregrine falcon hunts most often at dawn and dusk, when prey are most active, but also nocturnally in cities, particularly during migration periods when hunting at night may become prevalent. Nocturnal migrants taken by peregrines include species as diverse as yellow-billed cuckoo, black-necked grebe, virginia rai... | Peregrine falcon | Wikipedia | 417 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The peregrine falcon is sexually mature at one to three years of age, but in larger populations they breed after two to three years of age. A pair mates for life and returns to the same nesting spot annually. The courtship flight includes a mix of aerial acrobatics, precise spirals, and steep dives. The male passes pre... | Peregrine falcon | Wikipedia | 398 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The pair defends the chosen nest site against other peregrines, and often against ravens, herons, and gulls, and if ground-nesting, also such mammals as foxes, wolverines, felids, bears, wolves, and mountain lions. Both nests and (less frequently) adults are predated by larger-bodied raptorial birds like eagles, large ... | Peregrine falcon | Wikipedia | 450 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
After hatching, the chicks (called "es") are covered with creamy-white down and have disproportionately large feet. The male (called the "") and the female (simply called the "falcon") both leave the nest to gather prey to feed the young. The hunting territory of the parents can extend a radius of from the nest site. ... | Peregrine falcon | Wikipedia | 467 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
Peregrine falcons handled by falconers are also occasionally used to scare away birds at airports to reduce the risk of bird-plane strikes, improving air-traffic safety. They were also used to intercept homing pigeons during World War II.
Peregrine falcons have been successfully bred in captivity, both for falconry an... | Peregrine falcon | Wikipedia | 446 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
Decline due to pesticides
The peregrine falcon became an endangered species over much of its range because of the use of organochlorine pesticides, especially DDT, during the 1950s, '60s, and '70s. Pesticide biomagnification caused organochlorine to build up in the falcons' fat tissues, reducing the amount of calcium i... | Peregrine falcon | Wikipedia | 463 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
Some controversy has existed over the origins of captive breeding stock used by the Peregrine Fund in the recovery of peregrine falcons throughout the contiguous United States. Several peregrine subspecies were included in the breeding stock, including birds of Eurasian origin. Due to the local extinction of the easter... | Peregrine falcon | Wikipedia | 497 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
In England, peregrine falcons have become increasingly urban in distribution, particularly in southern areas where inland cliffs suitable as nesting sites are scarce. The first recorded urban breeding pair was observed nesting on the Swansea Guildhall in the 1980s. In Southampton, a nest prevented restoration of mobile... | Peregrine falcon | Wikipedia | 423 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The Peregrine, by J. A. Baker, is widely regarded as one of the best nature books in English written in the twentieth century. Admirers of the book include Robert Macfarlane, Mark Cocker, who regards the book as "one of the most outstanding books on nature in the twentieth century" and Werner Herzog, who called it "the... | Peregrine falcon | Wikipedia | 211 | 157626 | https://en.wikipedia.org/wiki/Peregrine%20falcon | Biology and health sciences | Accipitriformes and Falconiformes | null |
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relative to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis. It pl... | Moment of inertia | Wikipedia | 416 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
The moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics—both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis. For a point-like ... | Moment of inertia | Wikipedia | 444 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
The moment of inertia of a rotating flywheel is used in a machine to resist variations in applied torque to smooth its rotational output. The moment of inertia of an airplane about its longitudinal, horizontal and vertical axes determine how steering forces on the control surfaces of its wings, elevators and rudder(s) ... | Moment of inertia | Wikipedia | 510 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
The force of gravity on the mass of a simple pendulum generates a torque around the axis perpendicular to the plane of the pendulum movement. Here is the distance vector from the torque axis to the pendulum center of mass, and is the net force on the mass. Associated with this torque is an angular acceleration, , of... | Moment of inertia | Wikipedia | 490 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
Center of oscillation
A simple pendulum that has the same natural frequency as a compound pendulum defines the length from the pivot to a point called the center of oscillation of the compound pendulum. This point also corresponds to the center of percussion. The length is determined from the formula,
or
The second... | Moment of inertia | Wikipedia | 505 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
Consider the kinetic energy of an assembly of masses that lie at the distances from the pivot point , which is the nearest point on the axis of rotation. It is the sum of the kinetic energy of the individual masses,
This shows that the moment of inertia of the body is the sum of each of the terms, that is
Thus, m... | Moment of inertia | Wikipedia | 447 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
The moment of inertia of a thin rod with constant cross-section and density and with length about a perpendicular axis through its center of mass is determined by integration. Align the -axis with the rod and locate the origin its center of mass at the center of the rod, then where is the mass of the rod.
The mo... | Moment of inertia | Wikipedia | 488 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
If a system of particles, , are assembled into a rigid body, then the momentum of the system can be written in terms of positions relative to a reference point , and absolute velocities :
where is the angular velocity of the system and is the velocity of .
For planar movement the angular velocity vector is directe... | Moment of inertia | Wikipedia | 511 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
Kinetic energy
The kinetic energy of a rigid system of particles moving in the plane is given by
Let the reference point be the center of mass of the system so the second term becomes zero, and introduce the moment of inertia so the kinetic energy is given by
The moment of inertia is the polar moment of inertia o... | Moment of inertia | Wikipedia | 501 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
Then, the skew-symmetric matrix obtained from the relative position vector , can be used to define,
where defined by
is the symmetric inertia matrix of the rigid system of particles measured relative to the center of mass .
Kinetic energy
The kinetic energy of a rigid system of particles can be formulated in terms... | Moment of inertia | Wikipedia | 472 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
The first term is the inertia matrix relative to the center of mass. The second and third terms are zero by definition of the center of mass . And the last term is the total mass of the system multiplied by the square of the skew-symmetric matrix constructed from .
The result is the parallel axis theorem,
where is... | Moment of inertia | Wikipedia | 500 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
For the same object, different axes of rotation will have different moments of inertia about those axes. In general, the moments of inertia are not equal unless the object is symmetric about all axes. The moment of inertia tensor is a convenient way to summarize all moments of inertia of an object with one quantity. It... | Moment of inertia | Wikipedia | 473 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
Alternate inertia convention
There are some CAD and CAE applications such as SolidWorks, Unigraphics NX/Siemens NX and MSC Adams that use an alternate convention for the products of inertia. According to this convention, the minus sign is removed from the product of inertia formulas and instead inserted in the inertia... | Moment of inertia | Wikipedia | 487 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
Body frame
Let the body frame inertia matrix relative to the center of mass be denoted , and define the orientation of the body frame relative to the inertial frame by the rotation matrix , such that,
where vectors in the body fixed coordinate frame have coordinates in the inertial frame. Then, the inertia matrix of... | Moment of inertia | Wikipedia | 508 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
A practical example of this mathematical phenomenon is the routine automotive task of balancing a tire, which basically means adjusting the distribution of mass of a car wheel such that its principal axis of inertia is aligned with the axle so the wheel does not wobble.
Rotating molecules are also classified as asymme... | Moment of inertia | Wikipedia | 253 | 157700 | https://en.wikipedia.org/wiki/Moment%20of%20inertia | Physical sciences | Classical mechanics | null |
A hybrid vehicle is one that uses two or more distinct types of power, such as submarines that use diesel when surfaced and batteries when submerged. Other means to store energy include pressurized fluid in hydraulic hybrids.
Hybrid powertrains are designed to switch from one power source to another to maximize both f... | Hybrid vehicle | Wikipedia | 508 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
A SHEPB prototype made by David Kitson in Australia in 2014 used a lightweight brushless DC electric motor from an aerial drone and small hand-tool sized internal combustion engine, and a 3D printed drive system and lightweight housing, altogether weighing less than 4.5 kg. Active cooling keeps plastic parts from softe... | Hybrid vehicle | Wikipedia | 485 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
North America
In the US, General Electric made a locomotive with sodium–nickel chloride (Na-NiCl2) battery storage. They expect ≥10% fuel economy.
Variant diesel electric locomotive include the Green Goat (GG) and Green Kid (GK) switching/yard engines built by Canada's Railpower Technologies, with lead acid (Pba) batt... | Hybrid vehicle | Wikipedia | 375 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
Hybrid systems are regularly in use for trucks, buses and other heavy highway vehicles. Small fleet sizes and installation costs are compensated by fuel savings, with advances such as higher capacity, lowered battery cost, etc. Toyota, Ford, GM and others are introducing hybrid pickups and SUVs. Kenworth Truck Company ... | Hybrid vehicle | Wikipedia | 479 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
Newer hybrid ship-propulsion schemes include large towing kites manufactured by companies such as SkySails. Towing kites can fly at heights several times higher than the tallest ship masts, capturing stronger and steadier winds.
Aircraft
The Boeing Fuel Cell Demonstrator Airplane has a Proton-Exchange Membrane (PEM) f... | Hybrid vehicle | Wikipedia | 455 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
In 1899, Henri Pieper developed the world's first petro-electric hybrid automobile. In 1900, Ferdinand Porsche developed a series-hybrid using two motor-in-wheel-hub arrangements with an internal combustion generator set providing the electric power; Porsche's hybrid set two-speed records.
While liquid fuel/electric hy... | Hybrid vehicle | Wikipedia | 439 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
In addition to vehicles that use two or more different devices for propulsion, some also consider vehicles that use distinct energy sources or input types ("fuels") using the same engine to be hybrids, although to avoid confusion with hybrids as described above and to use correctly the terms, these are perhaps more cor... | Hybrid vehicle | Wikipedia | 440 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
Hydraulic hybrid and pneumatic hybrid vehicles use an engine or regenerative braking (or both) to charge a pressure accumulator to drive the wheels via hydraulic (liquid) or pneumatic (compressed gas) drive units. In most cases the engine is detached from the drivetrain, serving solely to charge the energy accumulator.... | Hybrid vehicle | Wikipedia | 402 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
Although petro-hydraulic hybrid technology has been known for decades and used in trains as well as very large construction vehicles, the high costs of the equipment precluded the systems from lighter trucks and cars. In the modern sense, an experiment proved the viability of small petro-hydraulic hybrid road vehicles ... | Hybrid vehicle | Wikipedia | 321 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
Research is underway in large corporations and small companies. The focus has now switched to smaller vehicles. The system components were expensive which precluded installation in smaller trucks and cars. A drawback was that the power driving motors were not efficient enough at part load. A British company (Artemis In... | Hybrid vehicle | Wikipedia | 508 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
In January 2011 industry giant Chrysler announced a partnership with the US Environmental Protection Agency (EPA) to design and develop an experimental petro-hydraulic hybrid powertrain suitable for use in large passenger cars. In 2012 an existing production minivan was adapted to the new hydraulic powertrain for asses... | Hybrid vehicle | Wikipedia | 468 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
On-road examples include Honda Civic Hybrid, Honda Insight 2nd generation, Honda CR-Z, Honda Accord Hybrid, Mercedes Benz S400 BlueHYBRID, BMW 7 Series hybrids, General Motors BAS Hybrids, Suzuki S-Cross, Suzuki Wagon R and Smart fortwo with micro hybrid drive.
Power-split or series-parallel hybrid
In a power-split hy... | Hybrid vehicle | Wikipedia | 503 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
When describing cars, the battery of a series-hybrid is usually charged by being plugged in—but a series-hybrid may also allow for a battery to only act as a buffer (and for regeneration purposes), and for the electric motor's power to be supplied constantly by a supporting engine. Series arrangements have been common ... | Hybrid vehicle | Wikipedia | 460 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
For some users, this type of vehicle may also be financially attractive so long as the electrical energy being used is cheaper than the petrol/diesel that they would have otherwise used. Current tax systems in many European countries use mineral oil taxation as a major income source. This is generally not the case for ... | Hybrid vehicle | Wikipedia | 424 | 157736 | https://en.wikipedia.org/wiki/Hybrid%20vehicle | Technology | Basics_7 | null |
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