teristic width T is illiistiatrd iii P’igurc 8.10 top.. exact description of distrihutioiis is only p fiinctioiis see 8.13 and 8.23.
Trang 18.3 Th e Delta Iiiipiilse 163
1 d(t)f(t) clisappcarr for t 3 ILlxN only OEie negative dwivative of f ( t )
at t = 0 remains We m n iiitrrprcxt the derivative h(t) as c? distrib
tlir va~iie of tiir drrivative - J ( o ) from D timction f i t ) , using the s r
Tht~ tlrrivation of h(t) is revcaled its dfwt on tlie contiiiimus f-
aiiglc functions with a limit 1 o illri
as tliey are iiat cliff crciitiable, b r e ( w l d , however, lime in( r
impulse as tuiotlrw inipu functioii with a, limit LVe only ch
fiinction I W C R I ~ ~ F it ~ i i h p icularly simple to irilegrate (8.11)
teristic width T is illiistiatrd iii P’igurc 8.10 (top) In contrast to thc
funct>iorr, llir dcrivative d(t) of the bell-slritpd functiori can be kxxmL
for T -+ 0 theu !teach to t,lie dcrivativc h ( 1 ) of 6 (t ) s h o w ~ i in F i g u ~ e 8.10 (bclow)
thc double impulse upvartis and dovlmvartls it i s d s o c d c d a dou-
It shoidd also be emphasised here that the graphical rcprrscntniori
on thc riglib-hand \itit> of Fig 8
exact description of distrihutioiis is only p
fiinctioiis (see (8.13) and (8.23))
The corrtymrrdiiig limit for R bell-shaprd impnlse fiinction cZ( L ) with c h r ac-
-
lim d(t)
T-+ 0
(8.24)