High-acceleration linear motors are normally rather short, and are designed to accelerate an object to a very high speed, for example see the railgun.

High-acceleration linear motors have been suggested for a number of uses.

High-acceleration linear motors are difficult to design for a number of reasons.

Pneumatic motors generally convert the compressed air to mechanical work though either linear or rotary motion.

No absolute theoretical limit is known for the size, acceleration or muzzle energy of linear motors.

* Electromagnetic Guns — a page describing research into linear motors at MIT

Many designs have been put forward for linear motors, falling into two major categories, low-acceleration and high-acceleration linear motors.

Low-acceleration linear motors are suitable for maglev trains and other ground-based transportation applications.

The high-acceleration motors are usually of the AC linear induction motor ( LIM ) design with an active three-phase winding on one side of the air-gap and a passive conductor plate on the other side.

The low-acceleration, high speed and high power motors are usually of the linear synchronous motor ( LSM ) design, with an active winding on one side of the air-gap and an array of alternate-pole magnets on the other side.

For cost reasons synchronous linear motors rarely use commutators, so the rotor often contains permanent magnets, or soft iron.

Examples include coilguns and the motors used on some maglev systems, as well as many other linear motors.

Piezoelectric drive is often used to drive small linear motors.

The history of linear electric motors can be traced back at least as far as the 1840s, to the work of Charles Wheatstone at King's College in London, but Wheatstone's model was too inefficient to be practical.

Because of these properties, linear motors are often used in maglev propulsion, as in the Japanese Linimo magnetic levitation train line near Nagoya.

However, linear motors have been used independently of magnetic levitation, as in Bombardier's Advanced Rapid Transit systems worldwide and a number of modern Japanese subways, including Tokyo's Toei Oedo Line.

Outside of public transportation, vertical linear motors have been proposed as lifting mechanisms in deep mines, and the use of linear motors is growing in motion control applications.

Dual axis linear motors also exist.

Mostly used linear motors are LIM ( linear induction motor ), LSM ( linear synchronous motor ).

Comparisons can also look at tests of trend, such as linear and quadratic relationships, when the independent variable involves ordered levels.

Saturated hydrocarbons can also combine any of the linear, cyclic ( e. g., polycyclic ) and branching structures, and they are still alkanes ( no general formula ) as long as they are acyclic ( i. e., having no loops ). They also have single covalent bonds between their carbons.

While most alphabets have letters composed of lines ( linear writing ), there are also exceptions such as the alphabets used in Braille, fingerspelling, and Morse code.

However, the bilinear transformation can also be interpreted as a single linear transformation from the tensor product to Z.

The spaceX * of all linear maps into K ( which is called the algebraic dual space to distinguish it from X ′) also induces a weak topology which is finer than that induced by the continuous dual since X ′ ⊆ X *.

In the complex case, one can also check that the bilinear form is linear over i in one argument, and conjugate linear in the other.

The character function is also used to display the timecode on the preview monitors in linear editing suites.

It can also be used to denote abstract vectors and linear functionals in mathematics.

Over any vector space without topology, we may also notate the vectors by kets and the linear functionals by bras.

* Dynamics is also described by linear operators on the Hilbert space.

This approach also allows preserving the curve definition under all linear or perspective 2D and 3D transforms and projections.

In calculus, this picture also gives a geometric proof of the derivative if one sets and interpreting b as an infinitesimal change in a, then this picture shows the infinitesimal change in the volume of an n-dimensional hypercube, where the coefficient of the linear term ( in ) is the area of the n faces, each of dimension

These linear combinations are also known as Bessel functions of the third kind ; they are two linearly independent solutions of Bessel's differential equation.

In juxtaposition, it also marks a fundamental distinction from western philosophy, in which the dominant view of time is a linear progression.

In 1929, the linear combination of atomic orbitals molecular orbital method ( LCAO ) approximation was introduced by Sir John Lennard-Jones, who also suggested methods to derive electronic structures of molecules of F < sub > 2 </ sub > ( fluorine ) and O < sub > 2 </ sub > ( oxygen ) molecules, from basic quantum principles.

Computationally, a context-sensitive language is equivalent with a linear bounded nondeterministic Turing machine, also called a linear bounded automaton.

This set of languages is also known as NLIN-SPACE, because they can be accepted using linear space on a non-deterministic Turing machine.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

However, Judeo-Christian thought also makes an " innovation of the first importance ", Eliade says, because it embraces the notion of linear, historical time ; in Christianity, " time is no longer the circular Time of the Eternal Return ; it has become linear and irreversible Time ".

Heinrich Zimmer also notes Christianity's emphasis on linear time ; he attributes this emphasis specifically to the influence of Saint Augustine's theory of history.

LPC may also be thought of as a basic perceptual coding technique ; reconstruction of an audio signal using a linear predictor shapes the coder's quantization noise into the spectrum of the target signal, partially masking it.

This was a compromise arrangement for a broadcast time scale: a linear transformation of the BIH's atomic time meant that the time scale was stable and internationally synchronised, while approximating UT1 means that tasks such as navigation which require a source of Universal Time continue to be well served by public time broadcasts.

Betasatellites are small linear single stranded DNA viruses that require a begomovirus to replicate.

Many algorithms, including Support Vector Machines, linear regression, logistic regression, neural networks, and nearest neighbor methods, require that the input features be numerical and scaled to similar ranges ( e. g., to the interval ).

For any two empirical thermometers, this does not require that the relation between their numerical scale readings be linear, but it does require that relation to be strictly monotonic.

For instance, the problem of integer factorization is suspected to require more than a polynomial function of the length of the input as run-time if the input is given in binary, but it only needs linear runtime if the input is presented in unary.

Generally, higher bit rate transmissions require a wider frequency band, though the ratio of bit rate to bandwidth are not linear due to significant innovations in digital signal processing and digital modulation methods.

Despite this, it is common that a driver thunk out to the real mode interrupt in order to initialize screen modes and gain direct access to a card's linear frame buffer, because these tasks would otherwise require handling many hundreds of proprietary variations that exist from card to card.

Considering all rotating ( or linear ) electric motors require synchronism between a moving magnetic field and a moving current sheet for average torque production, there is a clear distinction between an asynchronous motor and synchronous types.

In going from two to three dimensions, Super Mario 64 placed an emphasis on exploration within vast worlds that require the player to complete multiple diverse missions, replacing the linear obstacle courses of traditional platform games.

All linear regulators require an input voltage at least some minimum amount higher than the desired output voltage.

For any two empirical thermometers, this does not require that the relation between their numerical scale readings be linear, but it does require that relation to be strictly monotonic.

The use of infinitesimals will often require the application of calculus whereas circuits analysed by the lumped element model can be solved with linear algebra.

These two scenarios have competing demands — interception requires excellent linear speed, while Within Visual Range or WVR engagements require excellent turn rate, while maintaining speed, rapid acceleration, and availability of control at low speeds and high angle of attack.

The conventions,, and, do have different meanings ( the position of the index determines its valence ( variance ), in that the first may represent a quadratic form, the second a linear transformation, and the distinction is important in contexts that require tensors that aren't orthogonal ( see below ).

A bounded linear operator is generally not a bounded function ; the latter would require that the norm of L ( v ) be bounded for all v, which is not possible unless Y is the zero vector space.

Additionally, the system's linear induction motor did not require physical contact for traction, which meant it would run with equal capacity in snow or icy conditions.

Many linear algebra algorithms require significantly less computational effort when applied to triangular matrices, and this improvement often carries over to Hessenberg matrices as well.

Many linear algebra algorithms require significantly less computational effort when applied to diagonal matrices, and this improvement often carries over to tridiagonal matrices as well.

Hydraulic and air-powered airless pumps have linear motors that require a hydraulic pump or an air compressor, which can be electric or gasoline powered, although an air compressor is usually diesel powered for mobile use or electric for fixed installations.

Compared with a Chebyshev Type I / Type II filter or an elliptic filter, the Butterworth filter has a slower roll-off, and thus will require a higher order to implement a particular stopband specification, but Butterworth filters have a more linear phase response in the pass-band than Chebyshev Type I / Type II and elliptic filters can achieve.

It is estimated that differential cryptanalysis would require 2 < sup > 61 </ sup > chosen plaintexts ( vs. 2 < sup > 47 </ sup > for DES ), while linear cryptanalysis would require 2 < sup > 60 </ sup > known plaintexts ( vs. 2 < sup > 43 </ sup > for DES.