理论力学
description
Transcript of 理论力学
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2011.9
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2008
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tx,y,z (r,j,z) (r,q) (r, q, j)
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1
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(x,y,z)
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()()()
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k
kn3nks=3n-ks
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dt=0
21.11.21.31.4
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sks
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n3ns=3n-kk
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ABOAFAOBF
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3
d r
cR
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1.dt=0dt02.3.
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0
00
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0()
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2928517046Fq1q2l1l231.91.101.11
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RR/3
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10
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T
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L=T-V
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2rqr1= r err2= (r-L) ez
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141.61.81.131.14
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t1t2
t1t2qitqi(t)t1t2
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Sq(t)l*dq(t)dq(t)0l
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q(t)q(t)+l*d(t)Sl
q(t)Sl=0S(l)
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ddq=ddq
dq(t)0
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SS
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qx
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aeteq
zerxet
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51.161.181.201.21
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Lxxl
S
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qx
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0
D d
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T
dt
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LA=TA-VALB=TB-VBL=LA+LB
0LL
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f(q,t)
f0
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P251.5
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61.241.251.261.28
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ss2st=0
Ci
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H
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Lt
T=T2H=T+VH
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wzxy
T0zxy
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0
ds|dr|44 ds4|dr(4)|
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4
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bg
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4
4v0
44
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4 x'=x-v0t=x+ibict b=v0/cxict x' x' (1ib)(gigb) g = (1-b2) -1/2ict')(x')""-igbg)
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dt 4dt 4 u(4) =(dr, icdt)/dt = g(v, ic) 4- mu(4) = (p,iE/c)
71.301.331.361.37
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dr
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dj x,y,zj
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4
4
dSdr(4)(A,ij/c)4e
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x
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44
Fji4
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4
[Fji]|Fji-lI|=0l2
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4 EBEB(EB)2
81.291.341.381.39
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rcrr1r2
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m=m1m2/(m1+m2)
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m1+m2 m V(r) r V(r) 0 J = r x mvzrJxy
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bv0
- |v1'-v2'|=|v1-v2|ee=1e
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v1' = vc + | v1-v2 | e m2 / (m1+m2)v2' = vc - | v1-v2 | e m1 / (m1+m2) vc = (m1v1+m2v2) / (m1+m2) e 111
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F(r)=k/r2 k
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eqh
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r j
b b090
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dWds ds/dWBqAb
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m1m2 v1v2 ~m2m1v'1v'2~em2, em1vcv'1v'292.12.22.3
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m2 v1cv2cv'1cv'2cv'1v'2vc m2m1em2, em1, ????m1
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e=1
- a=m1/m2
- a=m1/m2
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m1
a=m1/m2=e2m11/(e2+1)
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m20 m1=m2
- m20 m1>m2m1m2m1m1m2m1
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p1E1p'1E'1 p2E2p'2E'2 m1 m2
p'1xp'1yp'2xp'2yEE321
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Ei meEf q 1 - cosq = mec2(1/Ef - 1/Ei )
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p+m+mp0mm00m
102.42.52.6
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qi=qi(0)+qi(1)01qi(0)=00
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V(q)
V(0)=0 V/qi=0
2
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T=T2
m q 2 m m
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T 00 m = ( Mij )sxs V0 V0k=(kij ) sxsT0 m =( mij )sxs
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mk
q(A) q(B) q(C) = aq(A) + bq(B) q w q = Re[qw exp(iwt)]
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q = 0 0
w2sss 0 sw=wj 0 qw =qwj
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nnsw20
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qwT
m k w2 w2 m-1k qw
w2 s s s
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q s
Aj aj
Q q R Q Q = R-1q
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Q
j=1,2,,s
w2 s w2j
Q
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qj=0 swj
112.72.82.9
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w=0
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q1q2
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v v
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F
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elt l
ql00l2sl0qlT
lcll*
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lj qljj=1,2,..,slj+s
ljAjljAj Aj = A*j+s lj = l*j+s122.102.112.13
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3kkK
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q(a)(t)q(b)(t) q(c)(t)=q(a)(t) - q(b)(t)
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qi(t) = qi ei wot qi qi(t) w0
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1
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1
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w0max
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0
sljlj+sqljj=1,2,,s
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2.122.142.1513
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A
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j 2p
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5
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14