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Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
Further time derivatives have also been named, as snap or jounce (fourth derivative), crackle (fifth derivative), and pop (sixth derivative). [ 12 ] [ 13 ] The seventh derivative is known as "Bang," as it is a logical continuation to the cycle.
Many other fundamental quantities in science are time derivatives of one another: force is the time derivative of momentum; power is the time derivative of energy; electric current is the time derivative of electric charge; and so on. A common occurrence in physics is the time derivative of a vector, such as velocity or displacement. In dealing ...
Since acceleration differentiates the expression involving position, it can be rewritten as a second derivative with respect to time: a = d 2 s d t 2 . {\displaystyle a={\frac {d^{2}s}{dt^{2}}}.} Since, for the purposes of mechanics such as this, integration is the opposite of differentiation, it is also possible to express position as a ...
Suppose that a function represents the position of an object at the time. The first derivative of that function is the velocity of an object with respect to time, the second derivative of the function is the acceleration of an object with respect to time, [29] and the third derivative is the jerk. [36]
The concept of acceleration is a covariant derivative concept. In other words, in order to define acceleration an additional structure on M {\displaystyle M} must be given. Using abstract index notation , the acceleration of a given curve with unit tangent vector ξ a {\displaystyle \xi ^{a}} is given by ξ b ∇ b ξ a {\displaystyle \xi ^{b ...
When considering where to put your money for retirement, you may have to choose between an IRA and an annuity.These financial “vehicles” are set up to ensure guaranteed income down the road ...
The derivatives of scalars, vectors, and second-order tensors with respect to second-order tensors are of considerable use in continuum mechanics.These derivatives are used in the theories of nonlinear elasticity and plasticity, particularly in the design of algorithms for numerical simulations.