課件教案-第二十章第20章

§20.5動量(momentof質(zhì)點(diǎn)的動量DO

量mv的叉積，定義為該瞬時質(zhì)

質(zhì)點(diǎn)對點(diǎn)O的動量矩，記

LO(mv) LO(mv)

r mv

kmv

yOx m(yvzzvy)im(zvxxvz)

yvx質(zhì)點(diǎn)對點(diǎn)的動量矩為

D對某一固定軸l

0量對軸的矩（又稱為質(zhì)點(diǎn)對軸的動量矩），0Ll(mv)

LA(mv)l

l0l軸正向的單位矢量2質(zhì)點(diǎn)系的動量質(zhì)點(diǎn)系對某固定點(diǎn)、固定軸的動量設(shè)質(zhì)點(diǎn)系中質(zhì)點(diǎn)D相對于某一固定點(diǎn)Oi

nn nn

LO

l義為質(zhì)點(diǎn)系對該軸的動量矩Ll Ll

Ll(mivi例題 質(zhì)點(diǎn)系對動點(diǎn)的動設(shè)在慣參考系中任意一動點(diǎn)A，其速度為vAvAArvAAr質(zhì)點(diǎn)系中質(zhì)點(diǎn)Di相對于動點(diǎn)A vivA

絕對動量(absolute

絕對動量矩(absolutemomentof將質(zhì)點(diǎn)系中各質(zhì)點(diǎn)的絕對動量mivi對動點(diǎn)A定義為質(zhì)點(diǎn)系對該點(diǎn)的絕對動量矩， n n

LA

LA(mivi)

(mivi

相對動量(relative度的乘積，定義為該質(zhì)點(diǎn)的相對動量。mivri

相對動量矩(relativemomentof

A A

n Lr

(m

)r(mv

質(zhì)點(diǎn)系對動點(diǎn)的絕對動量矩和相對動量矩的關(guān)

(20.26) ri(mivinn

vA

vri

(mivA

nn

(mivri5 r(mv)i

(mr) i

質(zhì)點(diǎn)系質(zhì)心的矢徑公

i1 n n mi

質(zhì)點(diǎn)系質(zhì)心C相對于動點(diǎn)A的矢ArAA

mLA

(mvA

AA6質(zhì)點(diǎn)系對質(zhì)心的動量

CCr(20.29)r

r

LCC質(zhì)點(diǎn)系對不同兩點(diǎn)的動量矩的關(guān)C兩點(diǎn)OA（慣性參考空間中固定點(diǎn)或動點(diǎn)）p pLO

OA

p——7剛體的動量剛體是特殊的質(zhì)點(diǎn)系，剛體運(yùn)動形式的不同其剛體的動量矩的計算法也不同，下面給出幾類簡單運(yùn)動的剛體的動量平移剛體的動量相對速 pvrip

(20.30)CrC

(20.31)

OA

平 LCOC

p

(mvC (mvC zOryx定軸轉(zhuǎn)zOryx坐標(biāo)系 rxi

v

(xi

yj

zk(xk

j

k(xjyivv

m(xi

yj

zk)(xj

yi)(x2i

j

i)(xyj

j

ji

(xzkj

i

(x2i

j

i)(xyj

j

ji

(xzkj

i

(x2k)(y2k)

xzi

m

y)dmJ

m

J

J

(x2m

y2

Jxzi

Jyz

Jzk

J

Jyz

Jzk

Jz

LO OO LO,LO

JO

立

Jxzi

Jyzj

Jzk

隨 置的變化而變化的（由定義知Jz是不變的），i

jkJxz，Jyz，Jzij的（k是不變的矢量）一般平面運(yùn)動剛體的動量

zyOr(20.30)r

x'z

Jy'z'j

Jz

體對點(diǎn)C

Jx'z

Jy'z'

JC