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The centre of percussionCOP is not a unique point on D2 M( M8 J/ B
the barrel since it is defined in terms of a conjugate point in
+ i/ S! ]1 Y% q9 i) J2,6,7
- k( d0 i2 `4 ?( Bthe handle. Each point in the handle is associated with a
# `4 }! q- X; u, J% r* }different COP in the barrel. When a ball strikes a freely; p9 _# M$ W/ Q% S
suspended bat, the bat will translate in the direction of the
8 \4 G D" a7 n8 f0 Gincident ball and it will also rotate about the centre of mass.
5 b$ [/ g' E% Z% UThe combined effects of translation and rotation result in a9 a! `( I/ w2 e% @) v
shift of the actual axis of rotation, away from the centre of
5 J" c1 j$ Z# y9 H: C0 {mass toward the handle. The axis passes through the conju-
* g/ [$ @6 x6 }2 B6 c" Ogate point for that particular impact. If b is the distance from
/ x+ b( w. S# X7 ~! Mthe impact point to the centre of mass, and x is the distance
! y+ `9 }( g7 A& K1 a8 F) ~from the centre of mass to the conjugate point, then xIcm/(Mb) where Icm is the moment of inertiaof the bat; T! V% d& u) m9 L% P, n
about its centre of mass and M is the mass of the bat. Con-
2 N% Y* M$ K3 x4 v7 N O% E4 Q) Nsequently, if the bat is pivoted about an axis through the
3 M* M0 o( i# K1 {conjugate point, and if the ball strikes the corresponding
0 V5 X6 q0 Q( u5 PCOP, then there is no reaction force at the pivot point. It is; z7 f4 }1 D+ U" D1 c6 m
therefore reasonable to expect that every point under the9 q9 H4 v6 F8 [6 x' r
hands will have its own COP and that an impact at any given( `3 P- v# p! H- M; t: Y7 Z, F/ Q
COP will generate zero reaction force at the corresponding
' x* m+ v# ]7 B4 H- M0 ]8: ^2 R1 K1 e7 w) `7 v0 q; M6 h4 C
conjugate point under the hands. Brancazio has suggested7 G1 Y; J3 a, A& q( c% y+ q( w6 r
that the sweet spot zone might therefore encompass all cor-
) t* n; [& m# W$ }4 xresponding COP points along the barrel. There is, however,. l* t! _1 f7 W/ E8 {6 B. s
an uncertainty in this argument since a hand-held bat is not
. h( Q4 W! F$ z: q. A9 w) E% Gfreely suspended, nor is it pivoted about a single axis, and$ B1 O# L) V0 l9 X9 t- r/ G$ v
may behave differently as a result of the reaction forces ex-
) k% v0 l4 G: a% k( {" A) Herted by the two hands. Furthermore, the axis of rotation may
/ O# N( A# n2 z- l& weven shift as a function of time since the ball remains in
8 v* P' Z. a# C% ?; f" n" O" |" L! Fcontact with the bat for about 1.5 ms, the transmission time
( O% z8 ~9 b3 L: F) V3 A7 sof the pulse from the impact point to the hands is about 1 ms,
: [. D. f* R% U, o; Land the impact forces on the hands last for about 20 ms as a
& g0 U% }7 ^% Gresult of the induced vibrations and the induced motion of! c( I4 c P' m2 a7 l
the bat. |
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