ballmea
smakethee
ergyKassmallaspossibleAccordi
gtomecha
icalk
owledge
K
A
2

L
0
EIL2yydxdx20x2t
2
2
3
Whereisthede
sityAisthecrosssectio
EistheYou
gmodulusa
dIisthemome
tofi
ertia
x
Whereisthebestplacetoreceivetheball
y
Figure223Vibratio
ofthebatThemecha
icmodeloftheca
tileveris
2y4yA2EI4ftx
4
Withi
itialco
ditio
s
yx00tA
dthebou
daryco
ditio
syx00
yy2yy0t0，Lt0，0t020t0xxx
5
6
Experime
tsshowthatthestro
gestimpactofballbatcollisio
isi
themiddleoftheco
tactperiodThereforefistake
asthefollowi
gsimplefu
ctio

5
fTeam6336
Page6of13
2Ftftxtt2F1t
0t
tx0xx0x2
tttx0xx0x2
7
Ourpurposeofourstudyistofi
dtherelatio
shipbetwee
Ka
dx0soweca
fi
dthe“sweetspot”throughe
ergya
alysisTosolvepartialdiffere
tialequatio
46Galerki
’smethodisappliedFora
ygive
fu
ctio
xwehaveco
cludedfromtheequatio
4that
Ay
L0
t
EIyxxxxfxdx0
8
Let
4Lytxx3BtxCtxL23
9
Whichfitthebou
daryco
ditio
sBa
dCareu
k
ow
fu
ctio
sSubstitutefu
ctio
9a
d4LxxxL23i
tur
i
toequatio
8weobtai
thefollowi
gordi
arydiffere
tialequatio
s
74F8LAL6BtAL7Ct20EIL2Bdx2x0dx9031523
41AL7BtAL8CtEI8BtL36CtL4315280Fdx3x0L23dxx0Ldx23
10


11


Withi
itialvalues
B0B00C0C00
Wethe
useRu
geKuttamethodtosolvetheequatio
systema
dthe
substitutethesolutio
BCi
tofu
ctio
9the
umericalsolutio
ofmodel46isobtai
edThe
extstepiscomputi
gthee
ergy3Substitutethe
umericalsolutio
ofyi
toequatio
3a
dusi
g
umericaldiffere
tiatio
a
d
umericali
tegralmethodsthee
ergyca
becomputedfora
ygive
parametersThealgorithmsa
dtheprogramsca
befou
di
theappe
dices24The
umericalresultsa
da
alysisUsi
gourmodela
dabove
umericalmethodswe
owa
alyzetherelatio
shipbetwee
thee
ergytra
sferredtothebata
dthelocatio
theballhitWecalculate
6
fTeam6336
Page7of13
e
ergycorrespo
di
gtoeverypoi
to
thebata
ddrawafigurebelow
Figure3
Byobservi
gthefigure3weca
drawtheco
clusio
thatatthe22i
chestotheha
dlethee
ergytra
sferredtother