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Topic: Time derivative

	Derivative - Wikipedia, the free encyclopedia
		Velocity (instantaneous velocity; the concept of average velocity predates calculus) is the derivative (with respect to time) of an object's position.
		Acceleration is the derivative (with respect to time) of an object's velocity, that is, the second derivative (with respect to time) of an object's position.
		The common thread is that the derivative at a point serves as a linear approximation of the function at that point.
	en.wikipedia.org /wiki/Derivative (2316 words)

	Encyclopedia :: encyclopedia : Derivative (Site not responding. Last check: 2007-10-12)
		Points on the graph of a function where the derivative is undefined or equals zero are called critical points or sometimes stationary points (in the case where the derivative equals zero).
		Acceleration is the derivative (with respect to time) of an object's velocity.
		Jerk is the derivative (with respect to time) of an object's acceleration.
	www.hallencyclopedia.com /Derivative (2198 words)

	Learn more about Derivative in the online encyclopedia. (Site not responding. Last check: 2007-10-12)
		The derivative of a function at a certain point is a measure of the rate at which that function is changing as an argument undergoes change.
		Derivatives are defined by taking the limit of a secant slope, as its two points of intersection (with f(x)) converge; the secant approaches a tangent.
		Velocity (instantaneous velocity; the concept of average velocity predates calculus) is the derivative (with repsect to time) of an object's position.
	www.onlineencyclopedia.org /d/de/derivative.html (1551 words)

	Total derivative - Wikipedia, the free encyclopedia
		In mathematics, a total derivative is a combination of partial derivatives.
		This expression is often used in physics for a gauge transformation of the Lagrangian, as two Lagrangians that differ only by the total time derivative of a function of time and the n generalized coordinates lead to the same equations of motion.
		Since the exterior derivative is a natural operator, in a sense that can be given a technical meaning, such equations are intrinsic and geometric.
	en.wikipedia.org /wiki/Total_derivative (388 words)

	derivative action in pid control (Site not responding. Last check: 2007-10-12)
		Derivative control is selected for systems that have long lags or high capacitances, where it can give large amount of corrections to a rapidly changingerror signal while the error is still small.
		Derivative action is responsible for generating an output which is proportional to the rate of change of error singal with respect to time.
		One way to apply derivative effect is to use the rate of change of input, the D tuning parameter, and the controller scan time to calculate an offset to the current input value, which is added to the actual input for the P calculation.
	www.control.com /1026168765/index_html (1103 words)

	Derivative (Site not responding. Last check: 2007-10-12)
		Category:Calculus In mathematics, the derivative of a function is one of the two central concepts of calculus.
		(The other one is the antiderivative, the inverse of the derivative.) The derivative of a function at a point measures the rate at which the function's value changes as the function's argument changes.
		Arguably the most important application of calculus to physics is the concept of the "'''time derivative'''" — the rate of change over time — which is required for the precise definition of several important concepts.
	derivative.kiwiki.homeip.net (2300 words)

	Time Derivative of a Vector in a Rotating Coordinate System
		This says that the time derivative of a vector can be constructed from its apparent time derivative in the rotating frame plus the vector which is the vector cross product of the rotation vector for the frame and the vector itself.
		There are number of places in the literature where the time derivatives of the unit basis vectors are derived from the above formula on the basis of the argument that such unit vectors are just special cases of position vectors to which the formula applies.
		This is in valid because the formula has to be derived from the determination of the time derivatives of those basis vectors.
	www.applet-magic.com /rotating.htm (492 words)

	What is PID - Tutorial
		Derivative action adds phase lead and is used to compensate for the lag introduced by integral action.
		With derivative action, the controller output is proportional to the rate of change of the measurement or error.
		The process is typical with a dead time of 4 and lag time of 10.
	www.expertune.com /tutor.html#FineTune (801 words)

	General result for the time derivative of any operator (Site not responding. Last check: 2007-10-12)
		The proof of Ehrenfest's theorem proceeds directly and in a similar manner to the proof of the continuity equation: we begin with the time derivatives in the statement we wish to prove and then replace the time derivatives using the TDSE.
		It applies to the time derivative of the average of any physical observable and depends only on the TDSE and the fact that the Hamiltonian operator, being associated with the observable E, is always Hermitian.
		The time derivative of the average of an observable
	people.ccmr.cornell.edu /~muchomas/8.04/Lecs/lec_TDSE/node7.html (178 words)

	Acceleration article - Acceleration physics derivative velocity vector length time units metre/second² - ... (Site not responding. Last check: 2007-10-12)
		Acceleration is the time rate of change of velocity, and at any point on a v-t graph, it is given by the gradient of the tangent to that point
		In physics, acceleration (symbol: a) is defined as the rate of change (or time derivative) of velocity.
		After defining his theory of special relativity, Albert Einstein realized that forces felt by objects undergoing constant acceleration are indistinguishable from those in a gravitational field, and thus defined general relativity (which also resolved how gravity's effects could be limited by the speed of light, but that is another story).
	www.what-means.com /encyclopedia/Acceleration (562 words)

	Industry automatic control fundamentals .
		The derivative time in minutes is the time that the open loop proportional plus derivative response is ahead of the response due to proportional alone.
		This derivative response is combined with the proportional response, and-in addition, as the reset in the controller sees the error increase, it drives the valve farther still.
		This new value is the result of the reset action during the time that the measurement was away from the set point, and compensates for the load change which caused the original upset.
	www.sapiensman.com /automatic_control/automatic_control4.htm (1063 words)

	The Neupert effect as a function of Temperature
		Bottom--The time derivatives of the energy for each component (same colors), plotted along with the hard X-ray time profile as seen in the HXT-M2 and HI channels (arbitrarily scaled, green line), covering the energy range above 33 keV.
		The high-T derivative peaks before the HXR's and goes to zero at the end of the HXR burst, consistent with the Neupert effect.
		At the same time, there's a more gradual heating mechanism, unrelated to the hard X-rays, that is slowly heating low-T plasma; this extra heating lasts until 2 minutes after the HXR burst.
	sprg.ssl.berkeley.edu /~jimm/neupert.html (1681 words)

	Hamiltonian
		These Euler-Lagrange equations assert that the partial time derivative of the partial derivative of the Lagrangian relative to the speed component minus the partial derivative of the Lagrangian relative to the corresponding position component (for a given direction in space) exactly vanishes.
		Secondly, that the time derivative of the momentum component is the negative partial derivative of the Hamiltonian with respect to the corresponding position component.
		The finite time (t) canonical transformation is determined from the condition that the new Hamiltonian (K) be exactly zero and its corresponding positions (Q) and momenta (P) are constant in time along the trajectory with vanishing time derivatives.
	www.qedcorp.com /pcr/pcr/hamilton.html (1214 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-12)
		This instantaneous rate of change is called the derivative." Let me try to explain why: If you have an equation that describes an object's property over a time period, the "derivative" is the rate of change of that property at any instant in the time period.
		If the equation is drawn on a graph, the derivative can also be determined by finding the slope of the graph at a particular point in time.
		An example of using the graphing method of calculating the derivative is to graph the equation and find the slope at the point in time that you want the derivative.
	mathforum.org /library/drmath/view/53399.html (346 words)

	Motion relative to moving frames
		Time derivatives and frames: The derivative of any variable with respect to time provides information on how it is changing with time.
		Since the same event when viewed from different frames may result in different observations, the time derivative of an event when taken relative to one frame may be different from the time derivative taken relative to another frame.
		The derivative of this gives the relation between the acceleration as observed from the two frames.
	em-ntserver.unl.edu /NEGAHBAN/EM373/note17/note.htm (488 words)

	Determinism - Wikipedia, the free encyclopedia
		Determinism in the West is often associated with Newtonian physics, which depicts the physical matter of the universe as operating according to a set of fixed, knowable laws.
		Since molecules are in constant thermal motion, the exact timing of the radioactive decay that produced the fatal alpha particle matters.
		The time dependent Schrödinger equation gives the first time derivative of the quantum state.
	en.wikipedia.org /wiki/Determinism (4233 words)

	Derivatives (General Concepts)
		The derivative of a function is one of the two central objects of study in calculus.
		The derivative of a function is another function whose values measure the rate of change of the original function’s values.
		The derivative is for functions whose graphs are not straight lines what the slope is for straight lines.
	www.math.uncc.edu /~bjwichno/fall2004-math1242-006/Review_Calc_I/lec_deriv.htm (1362 words)

	TIME DERIVATIVE ANALYSIS (Site not responding. Last check: 2007-10-12)
		M is the molecular weight expressed in Kg/mole and SPEED is the angular velocity of the rotor expressed in units of (RPM/1000).
		/2 which is the time interval between the scans being subtracted to generate dc/dt.
		For ordinary analysis, not involving estimation of diffusion coefficients, the time interval may be doubled without introducing serious dispersion.
	www.bbri.org /faculty/stafford/dcdt/Rule_of_thumb.html (263 words)

	unit1 (Site not responding. Last check: 2007-10-12)
		These derivatives are used to create equations that describe various physical, chemical, and biological processes that affect the movement of contaminants.
		Another derivative example is the derivative with respect to time.
		For example, a large positive value of the time derivative would tell you that the concentration is increasing (since positive value) at a high rate (since large value); a negative value tells you that the concentration is decreasing over time (since negative value).
	www.usfca.edu /envsci/envs654/unit1/unit1bk1.htm (558 words)

	Gennert and Negahdaripour's Optical Flow
		are the time derivatives of the multiplier and the offset respectively.
		We use Neumann boundary conditions where the normal component of the derivative of the four unknowns is set to zero on the boundary.
		It is possible to model the noise, the velocity components, and the transformation fields as Brownian processes and derive expressions for the regularization coefficients in terms of the variances of the underlying stochastic processes (cf, [11]).
	iacl.ece.jhu.edu /~gupta/papers/IPMI95/node3.html (449 words)

	Karl's Calculus Tutor - 4.3 Derivatives: More Rules to Live By
		In words, the derivative of the quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator all over the denominator squared.
		Recall that in section 3.1, we were interested in the train's position as a function of time, and particularly as a function of time as measured by the professor's watch.
		When the station clock appears to be gaining time on the professor's watch, the train appears, by the watch, to be going faster than it does by the station clock.
	www.karlscalculus.org /calc4_3.html (3741 words)

	analogy.nb (Site not responding. Last check: 2007-10-12)
		The electric field E equals minus the time derivative of A minus c times the gradient of phi.
		The momentum pi super mu equals h times the square root of G times the derivative of the Lagrange density of electromagnetism with respect to the time derivative of A super mu over c equals negative F super mu zero.
		The four-vector the derivative of t with respect to tau, the derivative of R with respect to tau goes to the derivative of t with respect to the absolute value of R, the derivative of R with respect to the absolute value of R equals the four-vector zero, the unit three-vector R hat.
	world.std.com /~sweetser/quaternions/gravity/analogy/s.html (5019 words)

	Finite Difference Time Domain (FDTD) Technique
		This can be simplified to state that the change in the E field (the time derivative) is dependent on the change in the H field across space (the Curl).
		The new value of the H field is dependent on the old value of the H field (hence the difference in time), and also dependent on the difference in the E field on either side of the H field point.
		FDTD is a time domain technique, and when a time-domain pulse (such as a Gaussian pulse) is used as the source pulse, then a wide frequency range is solved with only one simulation.
	www.pas.rochester.edu /~icpark/Vinos/whatisfdtd.html (936 words)

	Karl's Calculus Tutor - The Dance of the Derivatives (Related Rates)
		The key phrases that indicate time to be the independent variable are "how fast," "how often," "at what speed," "at what rate is this or that changing," and so on.
		In the doggie problem it stated the thickness of the paper, the rate the paper was being pulled, and the radius at which you were to establish the rate (observe that the thickness is neither a dependent nor an independent variable -- it is a constant.
		At the same time a Brooklyn-bound runner on the bridge is passing the tower on the Staten Island side (the towers are at either end of the span, so the runner is entering the span).
	www.karlscalculus.org /calc8_1.html (6009 words)

	SPECTRAL DERIVATIVES
		The structure of time t in QM is one of a universal Newtonian variable that is algebraically "central", i.e., considered as a legitimate operator, which it is not, it commutes with all operators, and can therefore be said conceptually to be in the center of the algebra of observables.
		Conceptually we will distinguish the apparently continuous time parameter of QM which is presumed operationally referred to a large laboratory clock from the time told by the clock that is the system itself.
		Accommodating the structure of the Heisenberg picture where the operators are time dependent and not the Hilbert space vectors means that one should also be able to extend the notion of spectral derivative to express the spectral derivative of an operator with respect to another operator.
	graham.main.nc.us /~bhammel/SPDER/I.html (2138 words)

	Experimental Investigation of Acceleration and Velocity Fields in Turbulent Channel Flow (Site not responding. Last check: 2007-10-12)
		In addition, the broad streamwise extent and shallow inclination angle of the two-point correlations of streamwise velocity are consistent with this large-scale vortex organization, while the wall-normal velocity correlations and the two-point velocity cross-correlations are consistent with the character of the individual vortices.
		The velocity time derivatives are associated predominantly with small scales in both space and time.
		Examination of instantaneous and estimates of the conditionally averaged velocity time-derivative fields indicates that the smaller-scale vortices leave a convective imprint upon the time derivatives.
	ltcf.tam.uiuc.edu /Publications/2001/Chr01.html (564 words)

	Sensible heat flux estimation by flux variance and half-order time derivative methods
		This study is the first to contrast two similarity theory methods, the flux variance and the half-order time derivative, over a wide range of atmospheric stability and surface roughness conditions.
		The half-order time derivative method was found to be sensitive to the parameterization of the eddy diffusivity, especially for the grass and bare soil field sites.
		Overall, the flux variance method was able to reproduce the measured sensible heat flux with greater accuracy than the half-order time derivative methods for the three experiment sites.
	www.agu.org /pubs/crossref/2001/2001WR900021.shtml (246 words)

	Derivative of Acceleration (Site not responding. Last check: 2007-10-12)
		In physics, jerk (in British English, jolt), also called surge, is the derivative of acceleration with respect to time (or the third derivative of displacement).
		Yank is mass times jerk, or equivalently, the derivative of force with respect to time.
		You know,more time derivatives on the position vector are not welcome for various reasons.Take the Lorentz-Dirac reaction force.It has the third time derivative.It poses problems with the causality.Newtonian physics,however,seems to accomodate the time varying acceleration.Thankfully,in quantum physics the problems generated by more than 2 time derivatives are absent.There's no such thing as force,nor acceleration.
	www.physicsforums.com /showthread.php?threadid=78841 (521 words)

	Macroscopic derivation of hydrodynamic equations (Site not responding. Last check: 2007-10-12)
		We derived the hydrodynamic equations from the molecular dynamics of a dilute gas for which the mean free path is small compared to the length scale.
		Hence the hydrodynamic equations derived for dilute gases should also hold for dense fluids which can be regarded as continua at the macroscopic level.
		The macroscopic derivations will make the reader feel more familiar with the hydrodynamic equations, since these derivations are based on notions close to our everyday experience.
	grus.berkeley.edu /~jrg/ay202/node61.html (416 words)

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