Misplaced Pages

#98901

67-665: MIMIC is a further development from MIDAS ( M odified I ntegration D igital A nalog S imulator), which represented analog computer design. Written completely in FORTRAN but one routine in COMPASS , and ran on Control Data supercomputers , MIMIC is capable of solving much larger simulation models. With MIMIC, ordinary differential equations describing mathematical models in several scientific disciplines as in engineering, physics, chemistry, biology, economics and as well as in social sciences can easily be solved by numerical integration and

134-427: A supermassive black hole , which may result in an active galactic nucleus . Galaxies can also have satellites in the form of dwarf galaxies and globular clusters . The constituents of a galaxy are formed out of gaseous matter that assembles through gravitational self-attraction in a hierarchical manner. At this level, the resulting fundamental components are the stars, which are typically assembled in clusters from

201-455: A variable star . An example of this is the instability strip , a region of the H-R diagram that includes Delta Scuti , RR Lyrae and Cepheid variables . The evolving star may eject some portion of its atmosphere to form a nebula, either steadily to form a planetary nebula or in a supernova explosion that leaves a remnant . Depending on the initial mass of the star and the presence or absence of

268-408: A Fourier synthesizer, a tide-predicting machine , which summed the individual harmonic components. Another category, not nearly as well known, used rotating shafts only for input and output, with precision racks and pinions. The racks were connected to linkages that performed the computation. At least one U.S. Naval sonar fire control computer of the later 1950s, made by Librascope, was of this type, as

335-406: A body and an object: It is a body when referring to the frozen nucleus of ice and dust, and an object when describing the entire comet with its diffuse coma and tail . Astronomical objects such as stars , planets , nebulae , asteroids and comets have been observed for thousands of years, although early cultures thought of these bodies as gods or deities. These early cultures found

402-542: A companion, a star may spend the last part of its life as a compact object ; either a white dwarf , neutron star , or black hole . The IAU definitions of planet and dwarf planet require that a Sun-orbiting astronomical body has undergone the rounding process to reach a roughly spherical shape, an achievement known as hydrostatic equilibrium . The same spheroidal shape can be seen on smaller rocky planets like Mars to gas giants like Jupiter . Any natural Sun-orbiting body that has not reached hydrostatic equilibrium

469-428: A comparatively intimate control and understanding of the problem, relative to digital simulations. Electronic analog computers are especially well-suited to representing situations described by differential equations. Historically, they were often used when a system of differential equations proved very difficult to solve by traditional means. As a simple example, the dynamics of a spring-mass system can be described by

536-609: A fully electronic analog computer at Peenemünde Army Research Center as an embedded control system ( mixing device ) to calculate V-2 rocket trajectories from the accelerations and orientations (measured by gyroscopes ) and to stabilize and guide the missile. Mechanical analog computers were very important in gun fire control in World War II, the Korean War and well past the Vietnam War; they were made in significant numbers. In

603-400: A physical panel with connectors or, in more modern systems, as a software interface that allows virtual management of signal connections and routes. Output devices in analog machines can vary depending on the specific goals of the system. For example, they could be graphical indicators, oscilloscopes , graphic recording devices, TV connection module , voltmeter , etc. These devices allow for

670-417: A very wide range of complexity. Slide rules and nomograms are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated. Complex mechanisms for process control and protective relays used analog computation to perform control and protective functions. Analog computers were widely used in scientific and industrial applications even after

737-444: A voltage on a particular wire). Therefore, each problem must be scaled so its parameters and dimensions can be represented using voltages that the circuit can supply —e.g., the expected magnitudes of the velocity and the position of a spring pendulum . Improperly scaled variables can have their values "clamped" by the limits of the supply voltage. Or if scaled too small, they can suffer from higher noise levels . Either problem can cause

SECTION 10

#1732856207099

804-426: A web that spans the observable universe. Galaxies have a variety of morphologies , with irregular , elliptical and disk-like shapes, depending on their formation and evolutionary histories, including interaction with other galaxies, which may lead to a merger . Disc galaxies encompass lenticular and spiral galaxies with features, such as spiral arms and a distinct halo . At the core, most galaxies have

871-683: Is a naturally occurring physical entity , association, or structure that exists within the observable universe . In astronomy , the terms object and body are often used interchangeably. However, an astronomical body or celestial body is a single, tightly bound, contiguous entity, while an astronomical or celestial object is a complex, less cohesively bound structure, which may consist of multiple bodies or even other objects with substructures. Examples of astronomical objects include planetary systems , star clusters , nebulae , and galaxies , while asteroids , moons , planets , and stars are astronomical bodies. A comet may be identified as both

938-430: Is a type of computation machine (computer) that uses physical phenomena such as electrical , mechanical , or hydraulic quantities behaving according to the mathematical principles in question ( analog signals ) to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude ( digital signals ). Analog computers can have

1005-584: Is classified by the IAU as a small Solar System body (SSSB). These come in many non-spherical shapes which are lumpy masses accreted haphazardly by in-falling dust and rock; not enough mass falls in to generate the heat needed to complete the rounding. Some SSSBs are just collections of relatively small rocks that are weakly held next to each other by gravity but are not actually fused into a single big bedrock . Some larger SSSBs are nearly round but have not reached hydrostatic equilibrium. The small Solar System body 4 Vesta

1072-590: Is no need to sort the statements in order of dependencies of the variables, since MIMIC does it internally. Parts of the software organized in overlays are: Consider a predator-prey model from the field of marine biology to determine the dynamics of fish and shark populations. As a simple model, we choose the Lotka–Volterra equation and the constants given in a tutorial. If then with initial conditions The problem's constants are given as: Analog computer An analog computer or analogue computer

1139-522: Is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft. In 1831–1835, mathematician and engineer Giovanni Plana devised a perpetual-calendar machine , which, through a system of pulleys and cylinders, could predict the perpetual calendar for every year from AD 0 (that is, 1 BC) to AD 4000, keeping track of leap years and varying day length. The tide-predicting machine invented by Sir William Thomson in 1872

1206-513: Is striking in terms of mathematics. They can be modeled using equations of the same form. However, the difference between these systems is what makes analog computing useful. Complex systems often are not amenable to pen-and-paper analysis, and require some form of testing or simulation. Complex mechanical systems, such as suspensions for racing cars, are expensive to fabricate and hard to modify. And taking precise mechanical measurements during high-speed tests adds further difficulty. By contrast, it

1273-726: Is the PEAC (Practical Electronics analogue computer), published in Practical Electronics in the January 1968 edition. Another more modern hybrid computer design was published in Everyday Practical Electronics in 2002. An example described in the EPE hybrid computer was the flight of a VTOL aircraft such as the Harrier jump jet . The altitude and speed of the aircraft were calculated by

1340-497: Is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier, where one input is an analog signal, the other input is a digital signal and the output is analog. It acts as an analog potentiometer, upgradable digitally. This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical, as signal processing for radars and generally for controllers in embedded systems . In

1407-405: Is very inexpensive to build an electrical equivalent of a complex mechanical system, to simulate its behavior. Engineers arrange a few operational amplifiers (op amps) and some passive linear components to form a circuit that follows the same equations as the mechanical system being simulated. All measurements can be taken directly with an oscilloscope . In the circuit, the (simulated) stiffness of

SECTION 20

#1732856207099

1474-507: The Andromeda nebula as a different galaxy, along with many others far from the Milky Way. The universe can be viewed as having a hierarchical structure. At the largest scales, the fundamental component of assembly is the galaxy . Galaxies are organized into groups and clusters , often within larger superclusters , that are strung along great filaments between nearly empty voids , forming

1541-498: The Sun located in the center of the Solar System . Johannes Kepler discovered Kepler's laws of planetary motion , which are properties of the orbits that the astronomical bodies shared; this was used to improve the heliocentric model. In 1584, Giordano Bruno proposed that all distant stars are their own suns, being the first in centuries to suggest this idea. Galileo Galilei was one of

1608-484: The photoelectric photometer allowed astronomers to accurately measure the color and luminosity of stars, which allowed them to predict their temperature and mass. In 1913, the Hertzsprung-Russell diagram was developed by astronomers Ejnar Hertzsprung and Henry Norris Russell independently of each other, which plotted stars based on their luminosity and color and allowed astronomers to easily examine stars. It

1675-491: The protoplanetary disks that surround newly formed stars. The various distinctive types of stars are shown by the Hertzsprung–Russell diagram (H–R diagram)—a plot of absolute stellar luminosity versus surface temperature. Each star follows an evolutionary track across this diagram. If this track takes the star through a region containing an intrinsic variable type, then its physical properties can cause it to become

1742-465: The spring constant and g {\displaystyle g} the gravity of Earth . For analog computing, the equation is programmed as y ¨ = − d m y ˙ − c m y − g {\displaystyle {\ddot {y}}=-{\tfrac {d}{m}}{\dot {y}}-{\tfrac {c}{m}}y-g} . The equivalent analog circuit consists of two integrators for

1809-482: The "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi . Educational analog computers illustrated the principles of analog calculation. The Heathkit EC-1, a $ 199 educational analog computer, was made by the Heath Company, US c.  1960 . It

1876-465: The 1950s to the 1970s, general-purpose analog computers were the only systems fast enough for real time simulation of dynamic systems, especially in the aircraft, military and aerospace field. In the 1960s, the major manufacturer was Electronic Associates of Princeton, New Jersey , with its 231R Analog Computer (vacuum tubes, 20 integrators) and subsequently its EAI 8800 Analog Computer (solid state operational amplifiers, 64 integrators). Its challenger

1943-642: The Dumaresq were produced of increasing complexity as development proceeded. By 1912, Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control systems , based on the differential analyser. It was used by the Imperial Russian Navy in World War I . Starting in 1929, AC network analyzers were constructed to solve calculation problems related to electrical power systems that were too large to solve with numerical methods at

2010-428: The advent of digital computers, because at the time they were typically much faster, but they started to become obsolete as early as the 1950s and 1960s, although they remained in use in some specific applications, such as aircraft flight simulators , the flight computer in aircraft , and for teaching control systems in universities. Perhaps the most relatable example of analog computers are mechanical watches where

2077-568: The analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. (Modern digital simulations are much better in this area. Digital arbitrary-precision arithmetic can provide any desired degree of precision.) However, in most cases the precision of an analog computer is absolutely sufficient given the uncertainty of the model characteristics and its technical parameters. Many small computers dedicated to specific computations are still part of industrial regulation equipment, but from

MIMIC - Misplaced Pages Continue

2144-676: The analog part of the computer and sent to a PC via a digital microprocessor and displayed on the PC screen. In industrial process control , analog loop controllers were used to automatically regulate temperature, flow, pressure, or other process conditions. The technology of these controllers ranged from purely mechanical integrators, through vacuum-tube and solid-state devices, to emulation of analog controllers by microprocessors. The similarity between linear mechanical components, such as springs and dashpots (viscous-fluid dampers), and electrical components, such as capacitors , inductors , and resistors

2211-407: The circuit to produce an incorrect simulation of the physical system. (Modern digital simulations are much more robust to widely varying values of their variables, but are still not entirely immune to these concerns: floating-point digital calculations support a huge dynamic range , but can suffer from imprecision if tiny differences of huge values lead to numerical instability .) The precision of

2278-434: The continuous and periodic rotation of interlinked gears drives the second, minute and hour needles in the clock. More complex applications, such as aircraft flight simulators and synthetic-aperture radar , remained the domain of analog computing (and hybrid computing ) well into the 1980s, since digital computers were insufficient for the task. This is a list of examples of early computation devices considered precursors of

2345-515: The early 1970s, analog computer manufacturers tried to tie together their analog computers with a digital computers to get the advantages of the two techniques. In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and collecting data. The digital computer may also participate to the calculation itself using analog-to-digital and digital-to-analog converters . The largest manufacturer of hybrid computers

2412-432: The equation m y ¨ + d y ˙ + c y = m g {\displaystyle m{\ddot {y}}+d{\dot {y}}+cy=mg} , with y {\displaystyle y} as the vertical position of a mass m {\displaystyle m} , d {\displaystyle d} the damping coefficient , c {\displaystyle c}

2479-567: The first astronomers to use telescopes to observe the sky, in 1610 he observed the four largest moons of Jupiter , now named the Galilean moons . Galileo also made observations of the phases of Venus , craters on the Moon , and sunspots on the Sun. Astronomer Edmond Halley was able to successfully predict the return of Halley's Comet , which now bears his name, in 1758. In 1781, Sir William Herschel discovered

2546-521: The human eye were discovered, and new telescopes were made that made it possible to see astronomical objects in other wavelengths of light. Joseph von Fraunhofer and Angelo Secchi pioneered the field of spectroscopy , which allowed them to observe the composition of stars and nebulae, and many astronomers were able to determine the masses of binary stars based on their orbital elements . Computers began to be used to observe and study massive amounts of astronomical data on stars, and new technologies such as

2613-521: The mathematical understanding of the Gibbs phenomenon of overshoot in Fourier representation near discontinuities. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output. The torque amplifier was the advance that allowed these machines to work. Starting in the 1920s, Vannevar Bush and others developed mechanical differential analyzers. The Dumaresq

2680-414: The modern computers. Some of them may even have been dubbed 'computers' by the press, though they may fail to fit modern definitions. The Antikythera mechanism , a type of device used to determine the positions of heavenly bodies known as an orrery , was described as an early mechanical analog computer by British physicist, information scientist, and historian of science Derek J. de Solla Price . It

2747-518: The movements of the bodies very important as they used these objects to help navigate over long distances, tell between the seasons, and to determine when to plant crops. During the Middle-Ages , cultures began to study the movements of these bodies more closely. Several astronomers of the Middle-East began to make detailed descriptions of stars and nebulae, and would make more accurate calendars based on

MIMIC - Misplaced Pages Continue

2814-546: The movements of these stars and planets. In Europe , astronomers focused more on devices to help study the celestial objects and creating textbooks, guides, and universities to teach people more about astronomy. During the Scientific Revolution , in 1543, Nicolaus Copernicus's heliocentric model was published. This model described the Earth , along with all of the other planets as being astronomical bodies which orbited

2881-499: The new planet Uranus , being the first discovered planet not visible by the naked eye. In the 19th and 20th century, new technologies and scientific innovations allowed scientists to greatly expand their understanding of astronomy and astronomical objects. Larger telescopes and observatories began to be built and scientists began to print images of the Moon and other celestial bodies on photographic plates. New wavelengths of light unseen by

2948-561: The patch panel, various connections and routes can be set and switched to configure the machine and determine signal flows. This allows users to flexibly configure and reconfigure the analog computing system to perform specific tasks. Patch panels are used to control data flows , connect and disconnect connections between various blocks of the system, including signal sources, amplifiers, filters, and other components. They provide convenience and flexibility in configuring and experimenting with analog computations. Patch panels can be presented as

3015-654: The period 1930–1945 in the Netherlands, Johan van Veen developed an analogue computer to calculate and predict tidal currents when the geometry of the channels are changed. Around 1950, this idea was developed into the Deltar , a hydraulic analogy computer supporting the closure of estuaries in the southwest of the Netherlands (the Delta Works ). The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport. Project Cyclone

3082-478: The possible construction of such calculators, but he had been stymied by the limited output torque of the ball-and-disk integrators . Several systems followed, notably those of Spanish engineer Leonardo Torres Quevedo , who built various analog machines for solving real and complex roots of polynomials ; and Michelson and Stratton, whose Harmonic Analyser performed Fourier analysis, but using an array of 80 springs rather than Kelvin integrators. This work led to

3149-405: The potentiometer was then equivalent to the formula of the equation being solved. Multiplication or division could be performed, depending on which dials were inputs and which was the output. Accuracy and resolution was limited and a simple slide rule was more accurate. However, the unit did demonstrate the basic principle. Analog computer designs were published in electronics magazines. One example

3216-663: The results of the analysis are listed or drawn in diagrams. It also enables the analysis of nonlinear dynamic conditions . The MIMIC software package, written as FORTRAN overlay programs, executes input statements of the mathematical model in six consecutive passes. Simulation programs written in MIMIC are compiled rather than interpreted. The core of the simulation package is a variable step numerical integrator of fourth-order Runge-Kutta method . Many useful functions related to electrical circuit elements exist besides some mathematical functions found in most scientific programming languages. There

3283-730: The speed of analog computers was their fully parallel computation, but this was also a limitation. The more equations required for a problem, the more analog components were needed, even when the problem wasn't time critical. "Programming" a problem meant interconnecting the analog operators; even with a removable wiring panel this was not very versatile. While a wide variety of mechanisms have been developed throughout history, some stand out because of their theoretical importance, or because they were manufactured in significant quantities. Most practical mechanical analog computers of any significant complexity used rotating shafts to carry variables from one mechanism to another. Cables and pulleys were used in

3350-445: The spring, for instance, can be changed by adjusting the parameters of an integrator. The electrical system is an analogy to the physical system, hence the name, but it is much less expensive than a mechanical prototype, much easier to modify, and generally safer. The electronic circuit can also be made to run faster or slower than the physical system being simulated. Experienced users of electronic analog computers said that they offered

3417-411: The state variables − y ˙ {\displaystyle -{\dot {y}}} (speed) and y {\displaystyle y} (position), one inverter, and three potentiometers. Electronic analog computers have drawbacks: the value of the circuit's supply voltage limits the range over which the variables may vary (since the value of a variable is represented by

SECTION 50

#1732856207099

3484-503: The time. These were essentially scale models of the electrical properties of the full-size system. Since network analyzers could handle problems too large for analytic methods or hand computation, they were also used to solve problems in nuclear physics and in the design of structures. More than 50 large network analyzers were built by the end of the 1950s. World War II era gun directors , gun data computers , and bomb sights used mechanical analog computers. In 1942 Helmut Hölzer built

3551-399: The various condensing nebulae. The great variety of stellar forms are determined almost entirely by the mass, composition and evolutionary state of these stars. Stars may be found in multi-star systems that orbit about each other in a hierarchical organization. A planetary system and various minor objects such as asteroids, comets and debris, can form in a hierarchical process of accretion from

3618-470: The visualization of analog signals and the representation of the results of measurements or mathematical operations. These are just general blocks that can be found in a typical analog computing machine. The actual configuration and components may vary depending on the specific implementation and the intended use of the machine. Analog computing devices are fast; digital computing devices are more versatile and accurate. The idea behind an analog-digital hybrid

3685-529: Was Electronic Associates . Their hybrid computer model 8900 was made of a digital computer and one or more analog consoles. These systems were mainly dedicated to large projects such as the Apollo program and Space Shuttle at NASA , or Ariane in Europe, especially during the integration step where at the beginning everything is simulated, and progressively real components replace their simulated parts. Only one company

3752-653: Was Applied Dynamics of Ann Arbor, Michigan . Although the basic technology for analog computers is usually operational amplifiers (also called "continuous current amplifiers" because they have no low frequency limitation), in the 1960s an attempt was made in the French ANALAC computer to use an alternative technology: medium frequency carrier and non dissipative reversible circuits. In the 1970s, every large company and administration concerned with problems in dynamics had an analog computing center, such as: An analog computing machine consists of several main components: On

3819-492: Was a mechanical calculating device invented around 1902 by Lieutenant John Dumaresq of the Royal Navy . It was an analog computer that related vital variables of the fire control problem to the movement of one's own ship and that of a target ship. It was often used with other devices, such as a Vickers range clock to generate range and deflection data so the gun sights of the ship could be continuously set. A number of versions of

3886-465: Was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems. Project Typhoon was an analog computer developed by RCA in 1952. It consisted of over 4,000 electron tubes and used 100 dials and 6,000 plug-in connectors to program. The MONIAC Computer was a hydraulic analogy of a national economy first unveiled in 1949. Computer Engineering Associates was spun out of Caltech in 1950 to provide commercial services using

3953-685: Was developed in the late 16th century and found application in gunnery, surveying and navigation. The planimeter was a manual instrument to calculate the area of a closed figure by tracing over it with a mechanical linkage. The slide rule was invented around 1620–1630, shortly after the publication of the concept of the logarithm . It is a hand-operated analog computer for doing multiplication and division. As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions . Aviation

4020-665: Was discovered in 1901, in the Antikythera wreck off the Greek island of Antikythera , between Kythera and Crete , and has been dated to c.  150~100 BC , during the Hellenistic period . Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later. Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use. The planisphere

4087-501: Was done by a rotating disc driven by one variable. Output came from a pick-off device (such as a wheel) positioned at a radius on the disc proportional to the second variable. (A carrier with a pair of steel balls supported by small rollers worked especially well. A roller, its axis parallel to the disc's surface, provided the output. It was held against the pair of balls by a spring.) Astronomical object An astronomical object , celestial object , stellar object or heavenly body

SECTION 60

#1732856207099

4154-556: Was first described by Ptolemy in the 2nd century AD. The astrolabe was invented in the Hellenistic world in either the 1st or 2nd centuries BC and is often attributed to Hipparchus . A combination of the planisphere and dioptra , the astrolabe was effectively an analog computer capable of working out several different kinds of problems in spherical astronomy . The sector , a calculating instrument used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots,

4221-572: Was found that stars commonly fell on a band of stars called the main-sequence stars on the diagram. A refined scheme for stellar classification was published in 1943 by William Wilson Morgan and Philip Childs Keenan based on the Hertzsprung-Russel Diagram. Astronomers also began debating whether other galaxies existed beyond the Milky Way , these debates ended when Edwin Hubble identified

4288-414: Was known as offering general commercial computing services on its hybrid computers, CISI of France, in the 1970s. The best reference in this field is the 100,000 simulation runs for each certification of the automatic landing systems of Airbus and Concorde aircraft. After 1980, purely digital computers progressed more and more rapidly and were fast enough to compete with analog computers. One key to

4355-409: Was of great utility to navigation in shallow waters. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location. The differential analyser , a mechanical analog computer designed to solve differential equations by integration , used wheel-and-disc mechanisms to perform the integration. In 1876 James Thomson had already discussed

4422-441: Was programmed using patch cords that connected nine operational amplifiers and other components. General Electric also marketed an "educational" analog computer kit of a simple design in the early 1960s consisting of two transistor tone generators and three potentiometers wired such that the frequency of the oscillator was nulled when the potentiometer dials were positioned by hand to satisfy an equation. The relative resistance of

4489-536: Was the principal computer in the Mk. 56 Gun Fire Control System. Online, there is a remarkably clear illustrated reference (OP 1140) that describes the fire control computer mechanisms. For adding and subtracting, precision miter-gear differentials were in common use in some computers; the Ford Instrument Mark I Fire Control Computer contained about 160 of them. Integration with respect to another variable

#98901