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See searches and references containing TIME DERIVATIVE!TIME DERIVATIVE
Derivative of a function with respect to time
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable
Time_derivative
Time rate of change of some physical quantity of a material element in a velocity field
In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element
Material_derivative
Type of derivative in mathematics
In mathematics, the derivative of a function at a point is the linear part of the best affine approximation to the function near the point. In one-variable
Derivative (multivariable calculus)
Derivative_(multivariable_calculus)
Higher derivatives of the position vector with respect to time
derivatives of position are generalizations of velocity and acceleration. They are defined as derivatives of the position vector with respect to time
Fourth, fifth, and sixth derivatives of position
Fourth,_fifth,_and_sixth_derivatives_of_position
Instantaneous rate of change (mathematics)
additional prime marks. Higher order derivatives are used in physics; for example, the first derivative with respect to time of the position of a moving object
Derivative
Physics term
mechanics, including fluid dynamics, an upper-convected time derivative or Oldroyd derivative, named after James G. Oldroyd, is the rate of change of
Upper-convected time derivative
Upper-convected_time_derivative
Vector field representation in 3D curvilinear coordinate systems
field A changes in time, the time derivatives should be calculated. For this purpose Newton's notation will be used for the time derivative ( A ˙ {\displaystyle
Vector fields in cylindrical and spherical coordinates
Vector_fields_in_cylindrical_and_spherical_coordinates
Rate of change of acceleration with time
can be expressed as the first time derivative of acceleration, second time derivative of velocity, and third time derivative of position: j = d a d t = d
Jerk_(physics)
On vector derivatives for rotating frames
equation that relates the time derivative of a Euclidean vector as evaluated in a non-rotating coordinate system to its time derivative in a rotating reference
Transport_theorem
Term in mathematics
denotes the derivative of α at time t, the "direction α is pointing" at time t. From a more abstract viewpoint, this is the Fréchet derivative: ( d t α )
Integral_curve
Rate of change of the second derivative
a branch of mathematics, the third derivative or third-order derivative is the rate at which the second derivative, or the rate of change of the rate
Third_derivative
Formulation of classical mechanics
is how fast the particle moves along its path of motion, and is the time derivative of its position, thus v 1 = d r 1 d t , v 2 = d r 2 d t , … , v N =
Lagrangian_mechanics
Branch of physics describing the motion of objects without considering forces
Most frequently, the quantities that kinematics deals with are the time derivatives of these quantities and the relations between them. Objects whose motion
Kinematics
Concept in classical mechanics
{\boldsymbol {\jmath }}}(t)=(-\sin \theta (t),\ \cos \theta (t))\ .} Thus the time derivative of these vectors, which rotate without changing magnitude, is d d t
Rotating_reference_frame
Type of inertial force
the time derivatives of any vector function P of time—such as the velocity and acceleration vectors of an object—will differ from its time derivatives in
Centrifugal_force
Branch of mathematical analysis
Sonin–Letnikov derivative Liouville derivative Caputo derivative Hadamard derivative Marchaud derivative Riesz derivative Miller–Ross derivative Weyl derivative Erdélyi–Kober
Fractional_calculus
Mathematical operation
second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Informally, the second derivative can be
Second_derivative
3D generalization of the Leibniz integral rule
generalization of the Leibniz integral rule. It is used to recast time derivatives of integrated quantities and is useful in formulating the basic equations
Reynolds_transport_theorem
Concept in the analysis of dynamical systems
has continuous first derivatives, is strictly positive for y ≠ 0 {\displaystyle y\neq 0} , and for which the time derivative V ˙ = ∇ V ⋅ g {\displaystyle
Lyapunov_function
Extension of the classical tensor calculus
calculus to deforming manifolds. Central to the CMS is the tensorial time derivative ∇ ˙ {\displaystyle {\dot {\nabla }}} whose original definition was
Calculus_of_moving_surfaces
Type of financial contract
a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has
Derivative_(finance)
Measure of sustained displacement of an object from its initial position
displacement is the rate of change (first time-derivative) of the absement. The dimension of absement is length multiplied by time. Its SI unit is meter second (m·s)
Absement
Historical mathematical concept; form of derivative
fluent (a time-varying quantity, or function) at a given point. Fluxions were introduced by Isaac Newton to describe his form of a time derivative (a derivative
Fluxion
Study of rates of change
the derivative of the position of a moving body with respect to time is the velocity of the body, and the derivative of velocity with respect to time is
Differential_calculus
Description of a quantum-mechanical system
non-relativistic because it contains a first derivative in time and a second derivative in space, and therefore space and time are not on equal footing. Paul Dirac
Schrödinger_equation
Quasilinear first-order ordinary differential equation
of reference (subscripted "in"), Euler's second law states that the time derivative of the angular momentum L equals the applied torque: d L in d t = M
Euler's equations (rigid body dynamics)
Euler's_equations_(rigid_body_dynamics)
Fluid flow in which density remains constant
\rho \,\mathrm {d} V}.} The conservation of mass requires that the time derivative of the mass inside a control volume be equal to the mass flux, J, across
Incompressible_flow
Data-driven algorithm
a series of snapshots of a dynamical system and its corresponding time derivatives, SINDy performs a sparsity-promoting regression (such as LASSO and
Sparse identification of non-linear dynamics
Sparse_identification_of_non-linear_dynamics
Laws in physics about force and motion
This denotes that the instantaneous velocity is the derivative of the position with respect to time. It can roughly be thought of as the ratio between
Newton's_laws_of_motion
Equations that keep static form even if quantities vary in time
keep a static form (do not involve time derivatives) even if some quantities are allowed to vary slowly with time. In electromagnetism it refers to mathematical
Quasistatic_approximation
In continuum mechanics, objective stress rates are time derivatives of stress that do not depend on the frame of reference. Many constitutive equations
Objective_stress_rate
Formalism in classical field theory based on Hamiltonian mechanics
}{\partial t}}\,,} in which the overdot denotes a partial time derivative ∂/∂t, not a total time derivative d/dt. For many fields φi(x, t) and their conjugates
Hamiltonian_field_theory
Function valued in a vector space; typically a real or complex one
indicate the total derivative operator, as in D/Dt. The total derivative differs from the partial time derivative in that the total derivative accounts for
Vector-valued_function
Overview of mechanics based on the least action principle
where in this context the overdot denotes a partial time derivative, not a total time derivative. The Hamiltonian density H {\displaystyle {\mathcal {H}}}
Analytical_mechanics
Method for solving partial differential equations
the distribution of heat energy u in Rn. Indicating by ut (x, t) the time derivative of u(x, t), the initial value problem is { u t ( x , t ) − Δ u ( x
Duhamel's_principle
Differentiation under the integral sign formula
is the exterior derivative of ω with respect to the space variables only and ω ˙ {\displaystyle {\dot {\omega }}} is the time derivative of ω. The above
Leibniz_integral_rule
Description of phase separation
domains, ∂ / ∂ t {\displaystyle \partial /{\partial t}} is the partial time derivative and ∇ 2 {\displaystyle \nabla ^{2}} is the Laplacian in n {\displaystyle
Cahn–Hilliard_equation
Physical quantity
In kinematics, angular acceleration (symbol α, alpha) is the time derivative of angular velocity. Following the two types of angular velocity, spin angular
Angular_acceleration
Theorem in quantum mechanics
named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position and momentum operators x
Ehrenfest_theorem
Rotation of a celestial body's orbital line of apsides
(periapsis) from its primary body. The apsidal precession is the first time derivative of the argument of periapsis, one of the six main orbital elements
Apsidal_precession
Amount of energy transferred or converted per unit time
shaft's angular velocity. Mechanical power is also described as the time derivative of work. In mechanics, the work done by a force F on an object that
Power_(physics)
Mathematical model for describing material deformation under stress
definition of such a derivative requires an excursion into differential geometry but we avoid those issues in this article. The time derivative of F {\displaystyle
Finite_strain_theory
Rate of change in the linear deformation of a material with respect to time
materials science, strain rate is the time derivative of strain of a material. Strain rate has dimension of inverse time and SI units of inverse second, s−1
Strain_rate
Rate at which heat spreads throughout a material
^{2}T.} One way to view thermal diffusivity is as the ratio of the time derivative of temperature to its curvature, quantifying the rate at which temperature
Thermal_diffusivity
Aircraft flight measures
analyze stability, and in real-time flight simulators for training and entertainment. Stability derivatives and control derivatives are related because they
Stability_derivatives
Resistance of a fluid to shear deformation
parcels, which ideally is directly proportional to the strain rate (the time derivative of strain) that arises when fluid parcels are in relative motion, and
Viscosity
Term in applied mathematics
of theories having equations of motion with more than two time derivatives (higher-derivative theories). It is suggested by a theorem of Mikhail Ostrogradsky
Ostrogradsky_instability
Basic law of electromagnetism
the loop. If the surface Σ is not changing in time, the right-hand side equation becomes the time-derivative of the magnetic flux ΦB through the surface:
Faraday's_law_of_induction
Class of constitutive equations for viscoelastic fluids
material for the case of large deformations using the upper-convected time derivative. The model was proposed by James G. Oldroyd. The concept is named after
Upper-convected_Maxwell_model
Mass of a substance which passes per unit of time
surface per time Δ t {\displaystyle \Delta t} . The overdot on m ˙ {\displaystyle {\dot {m}}} is Newton's notation for a time derivative. Since mass is
Mass_flow_rate
Object movement along a circular path
point in the direction of travel along the orbit. The velocity is the time derivative of the displacement: v ( t ) = d d t r ( t ) = d R d t u ^ R ( t )
Circular_motion
Branch of mathematics
mass times its acceleration, which is the time derivative of velocity and thus the second time derivative of spatial position. Starting from knowing
Calculus
Statistical mechanics hypothesis that all microstates are equiprobable for a given energy
viewed by an observer moving with the ensemble—i.e., the convective time derivative is zero. Thus, if the microstates are uniformly distributed in phase
Ergodic_hypothesis
Lawsuit brought by a company shareholder
A shareholder derivative suit is a lawsuit brought by a shareholder on behalf of a corporation against a third party. Often, the third party is an insider
Derivative_suit
Concept in differential equation mathematics
the Newmark- β {\displaystyle \beta } method states that the first time derivative (velocity in the equation of motion) can be solved as, u ˙ n + 1 =
Newmark-beta_method
Short-term changes in the Earth's magnetic field
amortized time derivative of the magnetic field B {\displaystyle \mathbf {B} } , B ˙ {\displaystyle {\dot {\mathbf {B} }}} . The second derivative, B ¨ {\displaystyle
Geomagnetic_secular_variation
Fundamental construction of differential calculus
In mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical
Generalizations of the derivative
Generalizations_of_the_derivative
Type of partial differential equations
^{2}u}{\partial x^{2}}}} The equation has the property that, if u and its first time derivative are arbitrarily specified initial data on the line t = 0 (with sufficient
Hyperbolic partial differential equation
Hyperbolic_partial_differential_equation
Measurable property of a material or system
For time derivatives, specific, molar, and flux densities of quantities, there is no one symbol; nomenclature depends on the subject, though time derivatives
Physical_quantity
Physics theorem
that the masses are constant, G {\displaystyle G} is one-half the time derivative of this moment of inertia: 1 2 d I d t = 1 2 d d t ∑ k = 1 N m k r
Virial_theorem
Property of materials with both viscous and elastic characteristics under deformation
stress or strain rates. For high stress or strain rates/short time periods, the time derivative components of the stress–strain relationship dominate. In
Viscoelasticity
Kellogg's cereal advertising mascots
describe the fourth, fifth and sixth time derivatives of position. The first derivative of position with respect to time is velocity, the second is acceleration
Snap,_Crackle_and_Pop
Statement in classical mechanics
between the forces acting on a system of massive particles and the time derivatives of the momenta of the system itself projected onto any virtual displacement
D'Alembert's_principle
Scheduling algorithm for network transmissions
IO request weight and its length, the algorithm makes sure that the time derivative of the aforementioned function stays below the needed threshold. The
Token_bucket
Equations that describe the behavior of a physical system
velocity (the first time derivative of r, v = dr/dt), and its acceleration (the second derivative of r, a = d2r/dt2), and time t. Euclidean vectors
Equations_of_motion
Apparent paradox with Faraday's law of induction
electromotive force (EMF) is given by the total derivative of the magnetic flux with respect to time t: E = − d Φ B d t , {\displaystyle {\mathcal {E}}=-{\frac
Faraday_paradox
Control loop feedback mechanism
residual steady-state errors that persist over time, eliminating lingering discrepancies. Lastly, the derivative (D) component predicts future error trend
PID_controller
Banach space-valued functions, which provides a criterion for moving a time derivative of a function out of its action (as a functional) on the function itself
Lions–Magenes_lemma
because the time derivative at any point x {\displaystyle x} is always the same, so the amplitude of the wave function never changes in time. Since the
Diffusion_Monte_Carlo
Non-linear second order differential equation and its attractor
is the displacement at time t, x ˙ {\displaystyle {\dot {x}}} is the first derivative of x {\displaystyle x} with respect to time, i.e. velocity, and x
Duffing_equation
Matrix relating a system's generalized coordinate vector and kinetic energy
is a symmetric matrix M that expresses the connection between the time derivative q ˙ {\displaystyle \mathbf {\dot {q}} } of the generalized coordinate
Mass_matrix
Chart indicator of moving average convergence/divergence
series is a filtered measure of the derivative of the input (price) series with respect to time. (The derivative is called "velocity" in technical stock
MACD
Second-order partial differential equation describing motion of mechanical system
where q ˙ ( t ) {\displaystyle {\dot {\boldsymbol {q}}}(t)} is the time derivative of q ( t ) {\displaystyle {\boldsymbol {q}}(t)} . (For those familiar
Euler–Lagrange_equation
Equation of state in cosmology
constant, and a ¨ {\displaystyle {\ddot {a}}} is the second proper time derivative of the scale factor. If we define (what might be called "effective")
Equation_of_state_(cosmology)
System configuration relative to another
relative to a reference configuration. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized"
Generalized_coordinates
Theory of motion and forces for objects close to the speed of light
from classical mechanics do carry over to SR, such as force as the time derivative of momentum (Newton's second law), the work done by a particle as the
Relativistic_mechanics
Frame of reference for an orbit
the orbit equation. The velocity vector, v, is found by taking the time derivative of the position vector: v = r ˙ = ( r ˙ cos θ − r θ ˙ sin θ ) p
Perifocal_coordinate_system
Gradient whose components are spatial derivatives
gradient Lapse rate Grade (slope) Gradiometer Image gradient Time derivative Material derivative Structure tensor Surface gradient Kreyszig, E. (1999). Advanced
Spatial_gradient
In calculus, a parametric derivative is a derivative of a dependent variable with respect to another dependent variable that is taken when both variables
Parametric_derivative
Formulation of classical mechanics
{\dot {q}}_{i}={\frac {dq_{i}}{dt}}\,,} where the overdots denote time derivatives. In Hamiltonian mechanics, the generalized coordinates q1, q2, ...
Routhian_mechanics
Equation relating transport coefficients to correlation functions
\gamma } in terms of the integral of the equilibrium time correlation function of the time derivative of a corresponding microscopic variable A {\displaystyle
Green–Kubo_relations
Magnitude of velocity
(also known as the distance) travelled until time t {\displaystyle t} , the speed equals the time derivative of s {\displaystyle s} : v = d s d t . {\displaystyle
Speed
Four-vector analogue of the gradient operation
{\displaystyle U^{\mu }} with the 4-gradient gives the total derivative with respect to proper time d d τ {\displaystyle {\frac {d}{d\tau }}} : U ⋅ ∂ = U μ
Four-gradient
Type of derivative in differential geometry
In differential geometry, the Lie derivative (/liː/ LEE), formulated by Władysław Ślebodziński and named after Sophus Lie, evaluates the change of a tensor
Lie_derivative
Model of viscoelastic fluids
{\displaystyle {\stackrel {\nabla }{\mathbf {T} }}} is the upper-convected time derivative of stress tensor: T ∇ = ∂ ∂ t T + v ⋅ ∇ T − ( ( ∇ v ) T ⋅ T + T ⋅ (
Oldroyd-B_model
Long period pulsar in the constellation Vela
the neutron star. PSR J0901−4046's period, combined with its period time derivative of 2.25×10−13 second/second, implies a characteristic age of 5.3 million
PSR_J0901−4046
Specialized notation for multivariable calculus
especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate
Matrix_calculus
Electrical engineering concept
Renshaw Carson defined the instantaneous frequency of a signal "as the time derivative of the signal's phase angle." In frequency modulation, instantaneous
Instantaneous phase and frequency
Instantaneous_phase_and_frequency
Computational analysis of vibrations
the mass matrix, [ U ¨ ] {\displaystyle [{\ddot {U}}]} is the 2nd time derivative of the displacement [ U ] {\displaystyle [U]} (i.e., the acceleration)
Modal_analysis_using_FEM
Mathematical representation of Brownian motion
{x} }{dt}}=g(t),} where v is velocity, x is position, d/dt is the time derivative, and g(t) may for instance be white noise. Since velocity changes instantly
Wiener_equation
Electromagnetic equations describing superconductors
conductor. Instead, the time derivative must be kept and cannot be simply removed. This results in the fact that the time derivative of B {\displaystyle \mathbf
London_equations
Instantaneous rate of change of the function
In multivariable calculus, the directional derivative measures the instantaneous rate at which a function changes along a specified vector through a given
Directional_derivative
Greek strategic business analyst, futurist, and physicist
relationship between entropy and complexity as the latter being the time derivative of the former. He has argued that societal complexity may be nearing
Theodore_Modis
and hX(t) is either 1 if the system at time t is in state X or 0 if not. The time-derivative C'(t) starts at time 0 at the transition state theory (TST)
Transition_path_sampling
Value for the flow of probability in quantum mechanics
particle, the integral in the first term of the preceding equation, sans time derivative, is the probability of obtaining a value within V when the position
Probability_current
Process of energy transfer to an object via force application through displacement
defined, so the evaluation of work is said to be path dependent. The time derivative of the integral for work yields the instantaneous power, If the work
Work_(physics)
Partial differential equation describing the evolution of temperature in a region
physics and engineering, it is common to use Newton's notation for time derivatives, so that u ˙ {\displaystyle {\dot {u}}} is used to denote ∂ u ∂ t {\displaystyle
Heat_equation
2 π T s {\displaystyle {\dot {h}}={\frac {2\pi }{T_{s}}}} and the time derivative of the tan q expression is q ˙ 1 cos 2 q = cos φ [ cos h cos
Parallactic_angle
Economics concept
In finance, inflation derivative (or inflation-indexed derivatives) refers to an over-the-counter and exchange-traded derivative that is used to transfer
Inflation_derivative
Physical quantity conserved throughout a motion
quantity A {\displaystyle A} is a constant of the motion if its total time derivative is zero 0 = d A d t = ∂ A ∂ t + { A , H } , {\displaystyle 0={\frac
Constant_of_motion
travel, tourism, insurance
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