title: Yamaha Motor Company

text: In the early 1969s, Yamaha added reed-valve induction to its previously piston-ported designs to produce the twin-cylinder RD and single-cylinder RS families, with variants in a number of capacities. There was a persistent, but apocryphal, rumour to the effect that "RD" indicated "race developed". In fact, "R" appears to have indicated "reed valved", "D" the twin (or "double") cylinder models and "S" the single-cylinder models. The RD family would be developed through the 1970s and 1980s, gaining solid wheels, water-cooling, YPVS, and other newer technology 'til they had little in common with the original variants (before being supplanted by the TZR). The RS family was produced for many years in a large number of variants by Yamaha and then Escorts Limited in India without losing its resemblance to its progenitors. In addition to the RD and RS standards, Yamaha also manufactured small standards with stamped steel frames and rotary disc-valved motors such as the Yamaha FS1, and step-through V-50 and V-80 designs. Its Enduro trail bike was replaced by the DT models. Not until 1976 would Yamaha answer the other Japanese brands with a multi-cylinder four stroke of their own. The XS-750 (and later 850) a 750cc triple cylinder machine with shaft final drive was introduced almost seven years after Honda's breakthrough bike. Yamaha's first four-cylinder model, the XS-1100 followed in 1978, again with shaft drive. Despite being heavier and more touring oriented than its rivals it produced an impressive string of victories in endurance racing.


title: Yamaha Motor Company

text: The 1970s also saw some of the first dedicated off-road bikes for off-road racing and recreation. Yamaha was an early innovator in dirt-bike technology, and introduced the first single-shock rear suspension, the trademarked "Monoshock" of 1973. It appeared in production on the 1974 Yamaha YZ-250, a model which is still in production, making it Yamaha's longest continuous model and name.


title: Yamaha Motor Company

text: Yamaha continued racing throughout the 1960s and 1970s with increasing success in several formats. The decade of the 1970s was capped by the XT500 winning the first Paris-Dakar Rally in 1979.


title: Yamaha Motor Company

text: By 1980 the combination of consumer preference and environmental regulation made four strokes increasingly popular. Suzuki ended production of their GT two stroke series, including the flagship water-cooled two-stroke 750cc GT-750 in 1977. Kawasaki, who had considerable success throughout the 1970s with their two-stroke triples of 250cc, 350cc, 400cc, 500cc and 750cc ended production of road-going two strokes in 1980. Yamaha bucked this trend and continued to refine and sell two-strokes for the street into the 1980s. These bikes were performance oriented, water-cooled twin cylinder machines, designed to achieve excellent performance taking advantage of the lower weight of two strokes. The RZ-250 of 1980 was the progenitor of this series. The RZ-350, the largest displacement model, was a popular hot-rod bike of the 1980s and continued to be sold in some countries into the early 1990s.


title: Yamaha Motor Company

text: Throughout the 1980s the motorcycle industry gradually went from building a few basic but versatile models designed to work well in many roles, to offering many more specialized machines designed to excel in particular niches. These included racing and performance street riding, touring, motocross racing, enduro and recreational off-road riding, and cruising. Yamaha branched out from the relatively small number of UJMs (Universal Japanese Motorcycle) at the start of the decade to a much larger set of offerings in several clearly defined markets at the end of the decade.


title: Yamaha Motor Company

text: The XV750 of 1981 featured an air-cooled V-twin four-stroke engine and cruiser styling, and was one of the first Japanese cruiser style motorcycles. By the end of the 1980s Yamaha had offered dozens of cruiser styled bikes in a variety of displacements and engine configurations.


title: Yamaha Motor Company

text: The RZV500 was one of the first "repli-racers", a near copy of Kenny Roberts competition GP bike, it featured a liquid-cooled two-stroke motor of 500cc displacement in a V4 configuration, along with a perimeter frame and full fairing.


title: Yamaha Motor Company

text: A more popular and practical high-performance model for the street was introduced in 1985, the FZ750. It was an innovative 750cc four-stroke inline four cylinder model. It was the first motorcycle to feature a five-valve cylinder head, something Yamaha became well known for. It also featured a cylinder block canted forward at 45 degrees, and a box-section steel perimeter frame. Production of the FZ continued until 1991.


title: Yamaha Motor Company

text: Another bike that was performance-oriented was the Yamaha RX-Z, introduced in 1985 as a two-stroke naked sport bike, related to the Yamaha RX-135 and Yamaha RD-135, borrowing its chassis and platform. Originally equipped with a five speed transmission and a solid front disc brake rotor with rear drum brakes, it was popular in Malaysia and Singapore. After a few years on the market, the engine was upgraded with the installation of a six-speed transmission, together with a newer instrument panel and handlebar switches, as well as a cross-drilled front disc brake rotor, while the rear remained with the drum brakes. The design was unchanged until it was updated in 2004, with the rear lights being borrowed by the Yamaha Y125Z and a new headlight. It was also installed with a catalytic converter, which reduced its horsepower to 19bhp. However, the maximum torque remained unchanged but the low-end torque was improved compared to the early models. Some owners of the earlier RX-Z motorcycles may have problems during take-off because the engine tends to stall when an inexperienced rider tries to take off in the first gear. However, the problem was resolved in the new model. In Malaysia, this bike was associated with street racers and was featured in many Malay movies. In 2011, after 26 years, it was discontinued.


title: Yamaha Motor Company

text: In 1998 Yamaha marketed a 1000cc four cylinder road bike called the YZF 'R1', this model introduced a new style of gearbox design which shortened the overall length of the motor/gearbox case, to allow a more compact unit. This, in turn allowed the motor to be placed in the frame further forward, designed to improve handling in a short wheel-based frame.


title: Yamaha Motor Company

text: In 1995, Yamaha announced the creation of Star Motorcycles, a new brand name for its cruiser series of motorcycles in the American market. In other markets, Star motorcycles are still sold under the Yamaha brand. This was an attempt to create a brand identity more closely aligned with the cruiser market segment, one of the largest and most lucrative in the USA.


title: Yamaha Motor Company

text: In 2007, Yamaha established the Philippine operations and distributes Yamaha motorcycles under the corporate name of Yamaha Motor Philippines, Inc., one of more than 20 worldwide subsidiaries operating on all continents.


title: Yamaha Motor Company

text: Yamaha purchased small engine maker Subaru Industrial Power Products from Subaru in October 2017. Subaru's engines powered lawnmowers, generators and water pumps and have since been rebranded as Yamaha.


title: Yamaha Motor Company

text: In motorcycle racing Yamaha has won 39 world championships, including seven in MotoGP and 10 in the preceding 500 cc two-stroke class, and two in World Superbike. In addition Yamaha have recorded 210 victories at the Isle of Man TT and head the list of victories at the Sidecar TT with 40. Past Yamaha riders include: Jarno Saarinen Giacomo Agostini, Bob Hannah, Heikki Mikkola, Bruce Anstey, Kenny Roberts, Eddie Lawson, Wayne Rainey, Jeremy McGrath, Stefan Merriman, Dave Molyneux, Ian Hutchinson, Phil Read, Chad Reed, Ben Spies, Jorge Lorenzo, and nine-time world champion Valentino Rossi.


title: Yamaha Motor Company

text: The Yamaha YZ450F won the AMA Supercross Championship two years in a row, in 2008 with Chad Reed, and 2009 James Stewart. Yamaha was the first to build a production monoshock motocross bike (1975 for 250 and 400, 1976 for 125) and one of the first to have a water-cooled motocross production bike (1977 in works bikes, 1981 in off-the-shelf bikes). Yamaha's first Motocross competition four-stroke bike, the YZ400F, won the 1998 USA outdoor national Championship with factory rider Doug Henry.


title: Yamaha Motor Company

text: Since 1962, Yamaha made production road racing Grand Prix motorcycles that any licensed road racer could purchase. In 1970, non-factory privateer teams dominated the 250 cc World Championship with Great Britain's Rodney Gould winning the title on a Yamaha TD2.


title: Yamaha Motor Company

text: Yamaha also sponsors several professional ATV riders in several areas of racing, such as cross country racing and motocross. Yamaha has had success in cross country with their YFZ450, ridden by Bill Ballance, winning 9 straight titles since 2000. Yamaha's other major rider, Traci Cecco, has ridden the YFZ450 to 7 titles, with the first in 2000. In ATV motocross, Yamaha has had success with Dustin Nelson and Pat Brown, both who race the YFZ450. Pat Brown's best season was a 3rd place title in 2007, while Nelson has had two 1st place titles in the Yamaha/ITP Quadcross, one in 2006 and the other in 2008.


title: Yamaha Motor Company

text: In 2021, Yamaha has won several competitions, such as British Superbike with Tarran Mackenzie, MotoAmerica with Jake Gagne, MFJ Superbike with Katsuyuki Nakasuga, WorldSSP with Dominique Aegerter, and several other competitions.


title: Yamaha Motor Company

text: Their 2022 MotoGP lineup consists of Fabio Quartararo and Franco Morbidelli, with Toprak Razgatlıoğlu and Andrea Locatelli in World Superbikes. Yamaha's Superbike World Championship team since 2016 has been delivered by Crescent Racing.


title: Yamaha Motor Company

text: The first Yamaha rider to ever win a World Superbike was Ben Spies in 2009. Then in 2021, Toprak Razgatlıoğlu managed to become world champion.


title: Yamaha Motor Company

text: Yamaha produced Formula One engines from 1989 to 1997 (with a one-year break in 1990), initially for the Zakspeed team, in 1991 for the Brabham BT60Y, in 1992 for the Jordan 192, from 1993 to 1996 for Tyrrell, and in 1997 for the Arrows A18. The Yamaha Engines never won a race (Damon Hill nearly did so at the 1997 Hungarian Grand Prix), drivers including Damon Hill, Ukyo Katayama, Mark Blundell and Mika Salo scored some acceptable results with Blundell achieving a surprise 3rd place at the 1994 Spanish Grand Prix and Hill with 2nd at the aforementioned 1997 Hungarian Grand Prix, this partly was considered to be due to Yamaha collaborating with the John Judd Engine Organization to create a better and reliable engine however there were questions raised as to whether the Yamaha Engines used from 1993 until 1997 were just Judd engines with the Yamaha branding on top of this.


title: Yamaha Motor Company

text: 1994 was considered to be Yamaha's most successful year in terms of points accrued, apart from the Podium achieved by Blundell in Spain the Yamaha engine in the Tyrrell Car achieved 4 Fifth Place finishes and 1 Sixth Place finish over the course of the season, However, due to the inconsistency of the engine over the years they were often unreliable and were usually regarded as not very powerful, the Yamaha powered engine never secured a Fastest Lap or Pole Position despite being on the grid for nearly a decade.


title: Yamaha Motor Company

text: After the conclusion of the 1997 Formula One Season, Yamaha decided to pull out of the sport, a possible reason for this was due to a disagreement with Arrows regarding the 1998 engine's identification, Yamaha wished to carry out work on the engine with their engineers while Arrows wished for their own engineers to work on the engine instead while still having it badged as a Yamaha engine.


title: Yamaha Motor Company

text: Yamaha Motor is a highly diversified company which produces products for a large number of industries and consumer market segments:


title: Yamaha Motor Company

text: Yamaha has built engines for other manufacturers' vehicles beginning with the development and production of the Toyota 2000GT (1967). The cylinder head from the Toyota 4A-GE engine was developed by Yamaha and built at Toyota's Shimayama plant alongside the 4A and 2A engines.


title: Yamaha Motor Company

text: In 1984, executives of the Yamaha Motor Corporation signed a contract with the Ford Motor Company to develop, produce, and supply compact 60° 3.0 Liter DOHC V6 engines for transverse application for the 1989–95 Ford Taurus SHO. From 1993 to 1995, the SHO engine was produced in 3.0 and 3.2 Liter versions. Yamaha jointly designed the 3.4 Liter DOHC V-8 engine with Ford for the 1996–99 SHO. Ford and Yamaha also developed the Zetec-SE branded 4-cylinder engines used in several Ford cars like the small sports car Ford Puma.


title: Yamaha Motor Company

text: From 2005 to 2010, Yamaha produced a 4.4 Litre V8 for Volvo. The B8444S engines were used in the XC90 and S80 models, whilst also adapted to 5.0L configuration for Volvo's foray into the V8 Supercars with the S60. British sportscar maker Noble also uses a bi-turbo version of the Volvo V8 in their M600.


title: Yamaha Motor Company

text: All performance-oriented cylinder heads on Toyota/Lexus engines were designed and/or built by Yamaha. Some examples are the 1LR-GUE engine found on the 2010–2012 Lexus LFA, the 2UR-GSE found in Lexus ISF, the 3S-GTE engine found on the Toyota MR2 and Toyota Celica GT4/All-Trac, the 2ZZ-GE engine found on the 1999–2006 Toyota Celica GT-S and Lotus Elise Series 2, and the Toyota 4GR-FSE engine found on the Lexus IS250.


title: Yamaha Motor Company

text: Yamaha also tunes engines for manufacturers, such as Toyota, so Yamaha logos are on Toyota S engines.


title: Yamaha Motor Company

text: Yamaha also tried to produce a supercar in the 1990s, named the Yamaha OX99-11. It was made as a supercar to have a Yamaha Formula 1 engine as its powerplant and have Formula 1 technology in it. Even though their engines did not win a Grand Prix, by 1991 the team had produced a new engine, the OX99, and approached a German company to design an initial version of the car. Yamaha was not pleased with the result as it was too similar to sport cars of that time, so it contacted IAD to continue working on the project. By the beginning of 1992, just under 12 months after starting to work on the project, IAD came with an initial version of the car. The car's design was undertaken by Takuya Yura, and was originally conceived as a single seater; however, Yamaha requested a two-seater vehicle and a tandem seating arrangement was suggested which was in keeping with Yamaha's motorcycle expertise. This resulted in a radical and somewhat outrageous design based on Group C cars of the time, with features such as the cockpit-locking roof. It also shared the same chassis as the Formula 1 car, to try to give the consumer market a pure Formula 1 experience. Eventually disagreements with IAD over the budget made Yamaha take the project to its own Ypsilon Technology which was given six months to finish the project, otherwise it would be terminated. To make matters worse, Japan was in the midst of an economic downturn, which made Yamaha believe there would be no customers for the car, and so the project was cancelled in 1994 after many delays, with only 3 prototypes in existence.


title: Wyvern

text: The wyvern in its various forms is important in heraldry, frequently appearing as a mascot of schools and athletic teams (chiefly in the United States, United Kingdom, and Canada). It is a popular creature in European literature, mythology, and folklore. Today, they are often used in fantasy literature and video games. The wyvern in heraldry and folklore is rarely fire-breathing, unlike four-legged dragons.


title: Wyvern

text: According to the "Oxford English Dictionary", the word is a development of Middle English "wyver" (attested fourteenth century), from Anglo-French "wivre" (cf. French "guivre" and "vouivre"), which originate from Latin "vīpera", meaning "viper", "adder", or "asp". The concluding ""–n"" had been added by the beginning of the 17th century, when John Guillim in 1610 describes the ""wiverne"" as a creature that "partake[s] of a Fowle in the Wings and Legs ... and doth resemble a Serpent in the Taile". John Gibbon in 1682 emphasises that it "hath but two Legs".


title: Wyvern

text: Conversely, medievalist William Sayers proposes a more complex origin for the term. He notes that the Anglo-French "guivre" and its Middle English derivative ceased to retain the original sense of "venomous snake" after the Latin term was re-introduced into medieval Latin, freeing them up to take an alternate meaning. Adducing another meaning of "wiver" (this time Old English) and "guivre", "light javelin", and noting partial resemblances between the size and shape of javelins and snakes, plus the later medieval era's increasing use of heavy armor and decreasing use of light javelins, he proposes that the concepts of "venomous snake" and "light javelin" were melded to produce a new term for a previously unimagined concept of flying snake, a kind of dragon.


title: Wyvern

text: The concept of winged snakes, mythical creatures similar to wyverns, is common in cultures around the Mediterranean, with a notable example being the Egyptian goddess Wadjet. The oldest creatures outright referred to as "winged dragons" are Helios's chariot steeds, which aid Medea.


title: Wyvern

text: Since the sixteenth century, in English, Scottish, and Irish heraldry, the key difference has been that a wyvern has two legs, whereas a dragon has four. This distinction is not commonly observed in the heraldry of other European countries, where two-legged dragon-like creatures are called dragons.


title: Wyvern

text: The wyvern frequently features in modern fantasy fiction, though its first literary appearances may have been in medieval bestiaries.


title: Wyvern

text: The wyvern is a frequent charge in English heraldry and vexillology, also occasionally appearing as a supporter or crest.


title: Wyvern

text: A wyvern is typically depicted resting upon its legs and tail, but may be depicted with its claws in the air and only supported by its tail. On occasion, a wyvern may be depicted as wingless and with its tail nowed.


title: Wyvern

text: A white ("Argent") wyvern formed the crest of the Borough of Leicester as recorded at the heraldic visitation of Leicestershire in 1619: "A wyvern sans legs argent strewed with wounds gules, wings expanded ermine." The term "sans legs" may not imply that the wyvern was "without legs", rather than its legs are not depicted, being hidden or folded under. This was adopted by the Midland Railway in 1845 when it became the crest of its unofficial coat of arms. The company asserted that the "wyvern was the standard of the Kingdom of Mercia", and that it was "a quartering in the town arms of Leicester". However, in 1897 the "Railway Magazine" noted that there appeared "to be no foundation that the wyvern was associated with the Kingdom of Mercia". It has been associated with Leicester since the time of Thomas, 2nd Earl of Lancaster and Leicester (c. 1278–1322), the most powerful lord in the Midlands, who used it as his personal crest.


title: Wyvern

text: A green Wyvern stands in the emblem of the ancient and historical Umbrian city of Terni, the dragon is called by the citizens with the name of Thyrus. A sable wyvern on a white background with endorsed wings forms the coat of arms of the Tilley family.


title: Wyvern

text: The arms of the Worshipful Society of Apothecaries depict a wyvern, symbolising disease, being overcome by Apollo, symbolising medicine.


title: Wyvern

text: Wyvern Zilant is depicted on the coat of arms of the city of Kazan, the capital of the Republic of Tatarstan.


title: Wyvern

text: The wyvern is also a fairly popular commercial logo or mascot, especially in Wales and what was once the West Country Kingdom of Wessex, but also in Herefordshire and Worcestershire, as the rivers Wye and Severn run through Hereford and Worcester respectively. A local radio station was formerly called Wyvern FM. Vauxhall Motors had a model in its range in the 1950s called the Wyvern. The Westland Wyvern was a British single-seat carrier-based multi-role strike aircraft built by Westland Aircraft that served in the 1950s, seeing active service in the 1956 Suez Crisis.


title: Kinetic bombardment

text: A kinetic bombardment or a kinetic orbital strike is the hypothetical act of attacking a planetary surface with an inert kinetic projectile from orbit (orbital bombardment), where the destructive power comes from the kinetic energy of the projectile impacting at very high speeds. The concept originated during the Cold War.


title: Kinetic bombardment

text: Typical depictions of the tactic are of a satellite containing a magazine of tungsten rods and a directional thrust system. When a strike is ordered, the launch vehicle brakes one of the rods out of its orbit and into a suborbital trajectory that intersects the target. The rods would typically be shaped to minimize air resistance and maximize velocity upon impact.


title: Kinetic bombardment

text: Kinetic bombardment has the advantage of being able to deliver projectiles from a very high angle at a very high speed, making them extremely difficult to defend against. In addition, projectiles would not require explosive warheads, and—in the simplest designs—would consist entirely of solid metal rods, giving rise to the common nickname "rods from God". Disadvantages include the technical difficulties of ensuring accuracy and the high costs of positioning ammunition in orbit.


title: Kinetic bombardment

text: During the Korean and Vietnam Wars, there was limited use of the Lazy Dog bomb, a kinetic projectile shaped like a conventional bomb but only about and . A piece of sheet metal was folded to make the fins and welded to the rear of the projectile. These were dumped from aircraft onto enemy troops and had the same effect as a machine gun fired vertically. Similar flechette projectiles have been used since the first World War.


title: Kinetic bombardment

text: In the 1980s, another kinetic swarm system was conceptualized as a potential part of the Strategic Defense Initiative, there codenamed Brilliant Pebbles.


title: Kinetic bombardment

text: "Project Thor" was an idea for a weapons system that launches telephone pole-sized kinetic projectiles made from tungsten from Earth's orbit to damage targets on the ground. Jerry Pournelle created the concept while working in operations research at Boeing in the 1950s before becoming a science-fiction writer.


title: Kinetic bombardment

text: A system described in the 2003 United States Air Force report called "Hypervelocity Rod Bundles" was that of , tungsten rods that are satellite-controlled and have global strike capability, with impact speeds of Mach 10.


title: Kinetic bombardment

text: The bomb would naturally contain a large kinetic energy because it moves at orbital velocities, around in orbit and at impact. As the rod reenters Earth's atmosphere it would lose most of the velocity, but the remaining energy would cause considerable damage. Some systems are quoted as having the yield of a small tactical nuclear bomb. These designs are envisioned as a bunker buster. As the name suggests, the 'bunker buster' is powerful enough to destroy a nuclear bunker. With 6–8 satellites on a given orbit, a target could be hit within 12–15 minutes from any given time, less than half the time taken by an ICBM and without the launch warning. Such a system could also be equipped with sensors to detect incoming anti-ballistic missile-type threats and relatively light protective measures to use against them (e.g. Hit-To-Kill Missiles or megawatt-class chemical laser). The time between deorbit and impact would only be a few minutes, and depending on the orbits and positions in the orbits, the system would have a worldwide range. There would be no need to deploy missiles, aircraft or other vehicles.


title: Kinetic bombardment

text: In the case of the system mentioned in the 2003 Air Force report above, a tungsten cylinder impacting at has a kinetic energy equivalent to approximately . The mass of such a cylinder is itself greater than , so the practical applications of such a system are limited to those situations where its other characteristics provide a clear and decisive advantage—a conventional bomb/warhead of similar weight to the tungsten rod, delivered by conventional means, provides similar destructive capability and is far more practical and cost-effective.


title: Kinetic bombardment

text: The highly elongated shape and high mass of the projectiles are intended to enhance sectional density (and therefore minimize kinetic energy loss due to air friction) and maximize penetration of hard or buried targets. The larger device is expected to be quite effective at penetrating deeply buried bunkers and other command and control targets.


title: Kinetic bombardment

text: The weapon would be very hard to defend against. It has a very high closing velocity and small radar cross-section. Launch is difficult to detect. Any infrared launch signature occurs in orbit, at no fixed position. The infrared launch signature also has a much smaller magnitude compared to a ballistic missile launch. The system would also have to cope with atmospheric heating from re-entry, which could melt non-tungsten components of the weapon.


title: Kinetic bombardment

text: The phrase "rods from God" is also used to describe the same concept. An Air Force report called them "hypervelocity rod bundles".


title: Kinetic bombardment

text: In the mid-1960s, popular science interest in orbital mechanics led to a number of science fiction stories which explored their implications. Among these was "The Moon Is a Harsh Mistress" by Robert A. Heinlein, in which the citizens of the Moon bombard the Earth with rocks wrapped in iron containers which are in turn fired from an electromagnetic launch system at Earth-based targets.


title: Kinetic bombardment

text: In the 1970s and 1980s, this idea was refined in science fiction novels such as "Footfall" by Larry Niven and Jerry Pournelle (the same Pournelle that first proposed the idea for military use in a non-fiction context), in which aliens use a Thor-type system. During the 1980s and 1990s references to such weapons became a staple of science fiction roleplaying games such as "Traveller", "Shadowrun" and "Heavy Gear" (the first of these games naming such weapons "ortillery", a portmanteau of "orbital artillery"), as well as visual media including "Babylon 5's" "mass drivers", the film "The Last Starfighter", and the film "Starship Troopers", itself an adaptation of the Heinlein novel of the same name. A smaller "crowbar" variant is mentioned in "David's Sling" by Marc Stiegler (Baen, 1988). Set in the Cold War, the story is based on the use of (relatively inexpensive) information-based "intelligent" systems to overcome an enemy's numerical advantage. The orbital kinetic bombardment system is used first to destroy the Soviet tank armies that have invaded Europe and then to take out Soviet ICBM silos prior to a nuclear strike.


title: Kinetic bombardment

text: In Neal Stephenson's "Anathem," a kinetic bombardment weapon is deployed from orbit to trigger the eruption of a dormant volcano.


title: Kinetic bombardment

text: The repurposing of space colonies for use in kinetic bombardment (referred as a "colony drop") is a frequent element of the "Gundam" franchise and is central to the plots of "", and "", while a more limited bombardment is key to the climax of "".


title: Kinetic bombardment

text: From the mid-1990s, kinetic weapons as science fiction plot devices appeared in video games. Appearing in "Syndicate Wars" as a player-usable weapon, it also featured prominently in the plots of other video games, such as "Tom Clancy's EndWar", "Mass Effect 2", "", and "Halo".


title: Kinetic bombardment

text: "Halo" features the Magnetic Accelerator Cannon (MAC), or Mass Accelerator Cannon, as the primary weapon system employed by the United Nations Space Command (UNSC) on its warships and orbital defense platforms. Essentially large coilguns, MACs are capable of firing a variety of ammunition types varying on the model and bore, ranging from hyper-dense kinetic kill slugs to sub-caliber rounds to semi-autonomous drone missiles. Most predominantly featured in "Halo Wars" and "Halo Wars 2", the MAC is an ability that allows the player to utilize the UNSC "Spirit of Fire"'s point-defense MAC for pinpoint orbital bombardment, allowing the player to heavily damage or destroy enemy units. However, there are variants of the MAC platforms mounted to various ships and stations, with the most powerful being able to fire a 3,000 ton projectile at anywhere between 0.4% and 25% the speed of light.


title: Kinetic bombardment

text: The film "" depicts the destruction of Central London with a tungsten rod dropped from a satellite system.


title: Kinetic bombardment

text: "Orion's Arm" features them as a major weapon type in the galaxy of 10,000 years in the future, where they can be used on planets at speeds up to 99.9% that of light, typically sterilizing a large portion of the target world. They are referred to as Relativistic Kinetic Kill Systems, or RKKS (pronounced "rocks").


title: Inner product space

text: In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in formula_1. Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or "scalar product" of Cartesian coordinates. Inner product spaces of infinite dimension are widely used in functional analysis. Inner product spaces over the field of complex numbers are sometimes referred to as unitary spaces. The first usage of the concept of a vector space with an inner product is due to Giuseppe Peano, in 1898.


title: Inner product space

text: An inner product naturally induces an associated norm, (denoted formula_2 and formula_3 in the picture); so, every inner product space is a normed vector space. If this normed space is also complete (that is, a Banach space) then the inner product space is a Hilbert space. If an inner product space is not a Hilbert space, it can be "extended" by completion to a Hilbert space formula_4 This means that formula_5 is a linear subspace of formula_6 the inner product of formula_5 is the restriction of that of formula_6 and formula_5 is dense in formula_10 for the topology defined by the norm.


title: Inner product space

text: In this article, denotes a field that is either the real numbers formula_11 or the complex numbers formula_12 A scalar is thus an element of . A bar over an expression representing a scalar denotes the complex conjugate of this scalar. A zero vector is denoted formula_13 for distinguishing it from the scalar .


title: Inner product space

text: An "inner product" space is a vector space over the field together with an "inner product", that is a map


title: Inner product space

text: If the positive-definiteness condition is replaced by merely requiring that formula_23 for all , then one obtains the definition of "positive semi-definite Hermitian form". A positive semi-definite Hermitian form formula_24 is an inner product if and only if for all "x", if formula_25 then "x = 0".


title: Inner product space

text: In the following properties, which result almost immediately from the definition of an inner product, and are arbitrary vectors, and and are arbitrary scalars.


title: Inner product space

text: Over formula_19, conjugate-symmetry reduces to symmetry, and sesquilinearity reduces to bilinearity. Hence an inner product on a real vector space is a "positive-definite symmetric bilinear form". The binomial expansion of a square becomes


title: Inner product space

text: Some authors, especially in physics and matrix algebra, prefer to define inner products and sesquilinear forms with linearity in the second argument rather than the first. Then the first argument becomes conjugate linear, rather than the second.


title: Inner product space

text: The real numbers formula_19 are a vector space over formula_19 that becomes an inner product space with arithmetic multiplication as its inner product:


title: Inner product space

text: The complex numbers formula_44 are a vector space over formula_44 that becomes an inner product space with the inner product


title: Inner product space

text: Unlike with the real numbers, the assignment formula_47 does define a complex inner product on formula_12


title: Inner product space

text: More generally, the real formula_49-space formula_50 with the dot product is an inner product space, an example of a Euclidean vector space.


title: Inner product space

text: A function formula_54 is an inner product on formula_50 if and only if there exists a symmetric positive-definite matrix formula_56 such that formula_57 for all formula_58 If formula_56 is the identity matrix then formula_57 is the dot product. For another example, if formula_61 and formula_62 is positive-definite (which happens if and only if formula_63 and one/both diagonal elements are positive) then for any formula_64


title: Inner product space

text: As mentioned earlier, every inner product on formula_66 is of this form (where formula_67 and formula_68 satisfy formula_69).


title: Inner product space

text: where formula_72 is any Hermitian positive-definite matrix and formula_73 is the conjugate transpose of formula_74 For the real case, this corresponds to the dot product of the results of directionally-different scaling of the two vectors, with positive scale factors and orthogonal directions of scaling. It is a weighted-sum version of the dot product with positive weights—up to an orthogonal transformation.


title: Inner product space

text: The article on Hilbert spaces has several examples of inner product spaces, wherein the metric induced by the inner product yields a complete metric space. An example of an inner product space which induces an incomplete metric is the space formula_75 of continuous complex valued functions formula_76 and formula_77 on the interval formula_78 The inner product is


title: Inner product space

text: This space is not complete; consider for example, for the interval the sequence of continuous "step" functions, formula_80 defined by:


title: Inner product space

text: This sequence is a Cauchy sequence for the norm induced by the preceding inner product, which does not converge to a function.


title: Inner product space

text: is an inner product. In this case, formula_85 if and only if formula_86 (that is, formula_87 almost surely), where formula_88 denotes the probability of the event. This definition of expectation as inner product can be extended to random vectors as well.