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The vorticity equation of fluid dynamics describes the evolution of the vorticity ω of a particle of a fluid as it moves with its flow; that is, the local rotation of the fluid (in terms of vector calculus this is the curl of the flow velocity). The governing equation is: where D Dt is the material derivative operator, u is the flow ...
v. t. e. In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function 's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
The true acceleration at time t is found in the limit as time interval Δt → 0 of Δv/Δt. An object's average acceleration over a period of time is its change in velocity , Δ v {\displaystyle \Delta \mathbf {v} } , divided by the duration of the period, Δ t {\displaystyle \Delta t} .
To state this formally, in general an equation of motion M is a function of the position r of the object, its 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 in 3D are denoted throughout in bold.
is the velocity of the Man relative to the Train, v T ∣ E {\displaystyle \mathbf {v} _{T\mid E}} is the velocity of the T rain relative to E arth. Fully legitimate expressions for "the velocity of A relative to B" include "the velocity of A with respect to B" and "the velocity of A in the coordinate system where B is always at rest".
Time-derivatives of position. In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. The higher-order derivatives are less common than the first three; [1][2 ...
Velocity is a physical vector quantity: both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as metres per second (m/s or m⋅s −1). For example, "5 metres per second" is a scalar, whereas "5 ...