The restrained gyro-stabilized platform with reasonable response characteristics operates with an approximate equation of motion, neglecting transient effects, as follows: Af where U is a torque applied about the output axis of the controlling gyro.

The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born – Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, thereby simplifying the Schrödinger equation.

Often, ray tracing methods are utilized to approximate the solution to the rendering equation by applying Monte Carlo methods to it.

This is an approximate equation, but holds with good accuracy.

The date and approximate time of a specific full moon ( assuming a circular orbit ) can be calculated from the following equation:

Later, Archimedes used a similar equation to approximate the square root of 3, and found 1351 / 780.

The idea is to replace the derivatives appearing in the differential equation by finite differences that approximate them.

This is an approximate equation that is derived from the incompressible Navier-Stokes equations ( written in spherical coordinate system ) and describes the motion of the radius of the bubble R as a function of time t. Here, μ is the viscosity, p the pressure, and γ the surface tension.

This equation, though approximate, has been shown to give good estimates on the motion of the bubble under the acoustically driven field except during the final stages of collapse.

A difference equation is the discrete equivalent of a differential equation and can be used to approximate the latter or studied in its own right.

Because of simplifications introduced along every step of the way, the corrections are never perfect, and the conditions met by the corrected solution do not perfectly match the equation demanded by reality, but even one cycle of corrections often provides a remarkably better approximate answer to what the real solution should be.

For example, the Mason equation is an approximate analytical expression for the growth of a water droplet based on the effects of heat transport on evaporation and condensation.

On these cases, a new approximate parabolic drag equation can be traced leaving the minimum drag value at zero lift value.

The atmosphere is in approximate hydrostatic equilibrium and hydrostatic equation for atmospheric pressure is given by

Therefore, the significant terms near the origin under this assumption are only those lying on the line and the others may be ignored it produce a simple approximate equation for the curve.

Brick-wall filters that run in realtime are not physically realizable as they have infinite latency ( i. e., its compact support in the frequency domain forces its time response not to have compact support meaning that it is ever-lasting ) and infinite order ( i. e., the response cannot be expressed as a linear differential equation with a finite sum ), but approximate implementations are sometimes used and they are frequently called brick-wall filters.

We want to approximate the solution of the differential equation

See also the sentence under the last equation in the English translation, K < sub > 0 </ sub >-K < sub > 1 </ sub >= 1 / 2 L / c < sup > 2 </ sup > v < sup > 2 </ sup >, and the comment on the symbols used in About this edition that follows the translation A remark placed above it informed that the equation was approximate because the conclusion was only justified if one neglected " magnitudes of fourth and higher orders " of a series expansion.

Coupled-cluster theory provides an approximate solution to the time-independent Schrödinger equation

Weyl conjectured that the Mertens function satisfied the approximate functional-differential equation

Now, you might wonder why we would ever want to get an approximate fit when we could just increase the degree of the polynomial equation and get an exact match.

The `` approximate '' is important, because even after the order of the work has been established by the chance method, the result is not inviolable.

Rhode Island's rate of $.07 per mile is considerably lower than reimburseable rates in the federal government and in industry nationally which approximate a $.09 per mile average.

He concluded that the anaconda's maximum length is 12 or 13 ( perhaps 14 ) meters, which would approximate from 39 to 42 feet ( 14 meters is slightly less than 46 feet ).

To test the hypothesis that all treatments have exactly the same effect, the F-test's p-values closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced.

One Nepōhualtzintzin ( 91 ) represented the number of days that a season of the year lasts, two Nepōhualtzitzin ( 182 ) is the number of days of the corn's cycle, from its sowing to its harvest, three Nepōhualtzintzin ( 273 ) is the number of days of a baby's gestation, and four Nepōhualtzintzin ( 364 ) completed a cycle and approximate a year ( 1 days short ).

This ensures that ΔG and ΔH are nearly the same over a considerable range of temperatures and justifies the approximate empirical Principle of Thomsen and Berthelot, which states that the equilibrium state to which a system proceeds is the one which evolves the greatest amount of heat, i. e. an actual process is the most exothermic one.

Except for a few primitive types such as sponges ( which have no nervous system ) and jellyfish ( which have a nervous system consisting of a diffuse nerve net ), all living animals are bilaterians, meaning animals with a bilaterally symmetric body shape ( that is, left and right sides that are approximate mirror images of each other ).

* Some curves that seem simple, such as the circle, cannot be described exactly by a Bézier or piecewise Bézier curve ; though a four-piece cubic Bézier curve can approximate a circle ( see Bézier spline ), with a maximum radial error of less than one part in a thousand, when each inner control point ( or offline point ) is the distance horizontally or vertically from an outer control point on a unit circle.

More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.

The approximate generation time for Danio rerio is three to four months.

where Fε < sup >- D </ sup > must be the number of units ε required to obtain L. The fractal dimension is the number of the dimensions of the figure being used to approximate the fractal: 0 for a dot, 1 for a line, 2 for a square.

The treatment of larger molecules that contain a few dozen electrons is computationally tractable by approximate methods such as density functional theory ( DFT ).

This does not imply that the solution is an exact one ; they are all approximate quantum mechanical calculations.

In this type of calculation, there is an approximate Hamiltonian and an approximate expression for the total electron density.

If a throw lands out of bounds, unless defined by the hole, the thrower has the option of playing from the previous lie, or playing from the approximate spot where the disc crossed into the out-of-bound territory.

This plaque marks the approximate location where Edgar Poe was born in Boston, Massachusetts.

where d is the number of days since 1 January 2000 00: 00: 00 in the Terrestrial Time scale used in astronomical ephemerides ; for Universal Time ( UT ) add the following approximate correction to d:

Unlike conventional microscopes, where the spatial resolution is limited by the wavelength of the particles which are used for imaging, the FIM is a projection type microscope with atomic resolution and an approximate magnification of a few million times.

From Louisville, the river loses depth very gradually until its confluence with the Mississippi at Cairo, Illinois, where it has an approximate depth of.

* Barter economy replaces organized trade as Romans and other citizens desert their towns for the countryside, where they will be less vulnerable against barbarian raids ( approximate date ).

The present state of knowledge about Kurdish allows, at least roughly, drawing the approximate borders of the areas where the main ethnic core of the speakers of the contemporary Kurdish dialects was formed.

The Erlenmeyer is usually marked on the side ( graduated ) to indicate the approximate volume of contents, and has a spot of ground glass or enamel where it can be labeled with a pencil.

The Celtic king, Belin, rebuilds an earth wall surrounding a few dozen huts and orders a small landing place to be cut into the south side of the wall, along the river front, where a wooden quay is built ( approximate date ).

Straight quotation marks ( or italicized straight quotation marks ) are often used to approximate the prime and double prime, e. g., when signifying feet and inches, arcminutes and arcseconds or minutes and seconds, where the quotation mark symbolises the latter part of the pair.

Instead an approximate correction may be used where Z is substituted with an effective nuclear charge symbolized as Z < sub > eff </ sub >.

Bill Yoshida learned comic book lettering from Ben Oda and was hired in 1965 by Archie Comics, where he averaged 75 pages a week for 40 years for an approximate total of 156, 000 pages.

In the operations research and control literature the field where reinforcement learning methods are studied is called approximate dynamic programming.

By testing historically verifiable cases where we have knowledge of t through non-linguistic data ( e. g. the approximate distance from Classical Latin to modern Romance languages ), Swadesh arrived at the empirical value of approximately 0. 14 for L ( meaning that the rate of replacement constitutes around 14 words from the 100-wordlist per millennium ).

This data does not only include information about the time, duration, originator and recipient of the call, but also the identification of the base station where the call was made from, which equals its approximate geographical location.

In this way it has been possible to determine without excavation the approximate site of lost churches, where the tower still exists.

California Historical Landmark 344, near the intersection of what are now State Routes 33 and 198, marks the approximate site of his headquarters, Arroyo de Cantua, where he was slain.

While the turnpike passes through at an approximate length of 1½ miles, Monroe Township is known for the Turnpike's division ( where it divides into Inner Car Lanes & Outer Truck Lanes ) and its dangerous ( and often-congested ) merge, where the dual-dual configuration ends ( 5 lanes each direction ; 2-3-3-2 ) and becomes a single roadway, consisting of three lanes in each direction ( 3-3 ); the merge is particularly difficult to travel through on Friday afternoons, summertime and on holidays.

The area where Main Street, also known as Montauk Highway, is located today, was the approximate area of the original hamlet known as Good Ground.

Midway, Bamberg County, South Carolina, was the approximate half-way point of the trip, where the weary passengers could have a meal at the new eating place there, and, even take advantage of the new hotel.