2/13/2023 0 Comments Dirac live™ 7.2![]() However, we note that the Dirac delta function is not strictly a function, although for many purposes it can be manipulated as such and can be formally defined as a generalised function or as a distribution that is also a measure. The delta function not only enables the equations to be simplified, but it also allows the motion of the baseball to be calculated by only considering the total impulse of the bat against the ball, rather than requiring the details of how the bat transferred energy to the ball. ![]() ![]() For example, to calculate the dynamics of a baseball being hit by a bat, approximating the force of the bat hitting the baseball by a delta function is a useful device. This function is very useful as an approximation for a tall narrow spike function, namely an impulse. The function δ( x) has the value zero everywhere except at x = 0, where its value is infinitely large and is such that its total integral is 1. The Dirac delta function is a mathematical construct which is called a generalised function or a distribution and was originally introduced by the British theoretical physicist Paul Dirac. ![]() Ngamta Thamwattana, in Modelling and Mechanics of Carbon-Based Nanostructured Materials, 2017 2.2 Dirac Delta Function: δ( x)
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