DDA Integrator
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DDA Integrator
A digital differential analyzer (DDA), also sometimes called a digital integrating computer, is a digital implementation of a differential analyzer. The integrators in a DDA are implemented as accumulator (computing), accumulators, with the numeric result converted back to a pulse rate by the overflow of the accumulator. The primary advantages of a DDA over the conventional analog differential analyzer are greater arithmetic precision, precision of the results and the lack of drift/noise/slip/lash in the calculations. The precision is only limited by register size and the resulting accumulated rounding/truncation errors of repeated addition. Digital electronics inherently lacks the temperature sensitive drift (telecommunication), drift and Noise (electronics), noise level issues of analog electronics and the slippage (electronics), slippage and "backlash (engineering), lash" issues of mechanical analog systems. For problems that can be expressed as differential equations, a DDA ca ...
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London
London is the capital and largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary down to the North Sea, and has been a major settlement for two millennia. The City of London, its ancient core and financial centre, was founded by the Romans as '' Londinium'' and retains its medieval boundaries.See also: Independent city ยง National capitals The City of Westminster, to the west of the City of London, has for centuries hosted the national government and parliament. Since the 19th century, the name "London" has also referred to the metropolis around this core, historically split between the counties of Middlesex, Essex, Surrey, Kent, and Hertfordshire, which largely comprises Greater London, governed by the Greater London Authority.The Greater London Authority consists of the Mayor of London and the London Assembly. The London Mayor is distinguished fr ...
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General Purpose Computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These programs enable computers to perform a wide range of tasks. A computer system is a nominally complete computer that includes the hardware, operating system (main software), and peripheral equipment needed and used for full operation. This term may also refer to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of industrial and consumer products use computers as control systems. Simple special-purpose devices like microwave ovens and remote controls are included, as are factory devices like industrial robots and computer-aided design, as well as general-purpose devices like personal computers and mobile devices like smartphones. Computers power the Internet, which links bil ...
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Real-time Computing
Real-time computing (RTC) is the computer science term for hardware and software systems subject to a "real-time constraint", for example from event to system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines". Ben-Ari, Mordechai; "Principles of Concurrent and Distributed Programming", ch. 16, Prentice Hall, 1990, , page 164 Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds. A system not specified as operating in real time cannot usually ''guarantee'' a response within any timeframe, although ''typical'' or ''expected'' response times may be given. Real-time processing ''fails'' if not completed within a specified deadline relative to an event; deadlines must always be met, regardless of system load. A real-time system has been described as one which "controls an environment by receiving data, processing them, and returning the results sufficiently quic ...
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Accuracy
Accuracy and precision are two measures of ''observational error''. ''Accuracy'' is how close a given set of measurements (observations or readings) are to their ''true value'', while ''precision'' is how close the measurements are to each other. In other words, ''precision'' is a description of ''random errors'', a measure of statistical variability. ''Accuracy'' has two definitions: # More commonly, it is a description of only '' systematic errors'', a measure of statistical bias of a given measure of central tendency; low accuracy causes a difference between a result and a true value; ISO calls this ''trueness''. # Alternatively, ISO defines accuracy as describing a combination of both types of observational error (random and systematic), so high accuracy requires both high precision and high trueness. In the first, more common definition of "accuracy" above, the concept is independent of "precision", so a particular set of data can be said to be accurate, precise, both, or n ...
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Rate Multiplier
A digital differential analyzer (DDA), also sometimes called a digital integrating computer, is a digital implementation of a differential analyzer. The integrators in a DDA are implemented as accumulators, with the numeric result converted back to a pulse rate by the overflow of the accumulator. The primary advantages of a DDA over the conventional analog differential analyzer are greater precision of the results and the lack of drift/noise/slip/lash in the calculations. The precision is only limited by register size and the resulting accumulated rounding/truncation errors of repeated addition. Digital electronics inherently lacks the temperature sensitive drift and noise level issues of analog electronics and the slippage and " lash" issues of mechanical analog systems. For problems that can be expressed as differential equations, a DDA can solve them much faster than a general purpose computer (using similar technology). However reprogramming a DDA to solve a different prob ...
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Initial Condition
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted ''t'' = 0). For a system of order ''k'' (the number of time lags in discrete time, or the order of the largest derivative in continuous time) and dimension ''n'' (that is, with ''n'' different evolving variables, which together can be denoted by an ''n''-dimensional coordinate vector), generally ''nk'' initial conditions are needed in order to trace the system's variables forward through time. In both differential equations in continuous time and difference equations in discrete time, initial conditions affect the value of the dynamic variables (state variables) at any future time. In continuous time, the problem of finding a closed form solution for the state variables as a function of time and of the initial conditions is called the initial value p ...
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Magnetic Drum Digital Differential Analyzer
The MADDIDA (Magnetic Drum Digital Differential Analyzer) was a special-purpose digital computer used for solving systems of ordinary differential equations. It was the first computer to represent bits using voltage levels and whose entire logic was specified in Boolean algebra. Invented by Floyd Steele, MADDIDA was developed at Northrop Aircraft Corporation between 1946 and 1949 to be used as a guidance system for the Snark missile. No guidance system, however, resulted from the work on the MADDIDA, and rather it was used for aeronautical research. In 1952, the MADDIDA became the world's top-selling commercial digital computer (albeit a special-purpose machine), six units having been sold. (The general-purpose UNIVAC I delivered its seventh unit in 1954.) Development Development on the project began in March 1946 at Northrop Corporation with the goal of producing a subsonic cruise missile designated "MX-775", which came to be called the Snark. Northrop's parameters for th ...
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ENIAC
ENIAC (; Electronic Numerical Integrator and Computer) was the first programmable, electronic, general-purpose digital computer, completed in 1945. There were other computers that had these features, but the ENIAC had all of them in one package. It was Turing-complete and able to solve "a large class of numerical problems" through reprogramming. Although ENIAC was designed and primarily used to calculate artillery firing tables for the United States Army's Ballistic Research Laboratory (which later became a part of the Army Research Laboratory), its first program was a study of the feasibility of the thermonuclear weapon. ENIAC was completed in 1945 and first put to work for practical purposes on December 10, 1945.* ENIAC was formally dedicated at the University of Pennsylvania on February 15, 1946, having cost $487,000 (), and was heralded as a "Giant Brain" by the press. It had a speed on the order of one thousand times faster than that of electro-mechanical machines; this ...
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Differential Equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of d ...
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Differential Analyzer
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operationally. The original machines could not add, but then it was noticed that if the two wheels of a rear differential are turned, the drive shaft will compute the average of the left and right wheels. A simple gear ratio of 1:2 then enables multiplication by two, Multiplication is just a special case of integration, namely integrating a constant function. History Research on solutions for differential equations using mechanical devices, discounting planimeters, started at least as early as 1836, when the French physicist Gaspard-Gustave Coriolis designed a mechanical device to integrate differential equations of the first order. The first description of a device which could integrate differential equations of any order was published in 18 ...
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Backlash (engineering)
In mechanical engineering, backlash, sometimes called lash, play, or slop, is a clearance or lost motion in a mechanism caused by gaps between the parts. It can be defined as "the maximum distance or angle through which any part of a mechanical system may be moved in one direction without applying appreciable force or motion to the next part in mechanical sequence."p. 1-8 An example, in the context of gears and gear trains, is the amount of clearance between mated gear teeth. It can be seen when the direction of movement is reversed and the slack or lost motion is taken up before the reversal of motion is complete. It can be heard from the railway couplings when a train reverses direction. Another example is in a valve train with mechanical tappets, where a certain range of lash is necessary for the valves to work properly. Depending on the application, backlash may or may not be desirable. Some amount of backlash is unavoidable in nearly all reversing mechanical couplings, ...
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