1) :
. . j() - , p .
dx T(x+dx)
j
T(x)
(x,x+dx):
rdx2S/t2=T(sinjx+dx - sinjx)=T(tgjx+dx tgjx)=T(j(x+dx)j(x))=T , r , Þ , S(t,x)=S(t(x/c)).
2) :
()
e=dx/dx, (e>0 , e<0 ).
dm=srdx, (s ), dm(2S/t2)=DF=F(x+Dx)F(x)=Es Þ
msrdx(2S/t2)=Es Þ (2S/t2)=(E/r)(2S/x2) Þ c2=E/r
. . .
().
. .
, s, dx.
dm=r0sdx; r0sdx(2S/t2)=[Px Px+dx]s; p0(2S/t2)= P/x
P@pg
p0
dP = (P/r)p0 dr =c2dr; P/x =c2 (dp/x)=c2 /x[p0(S/x)]=c2po(2S/x2)
(2S/t2)= c2 (2S/x2), c2= P/r, p=p0
:
P=rRT/M; P=const pg; dP/dp= g const pg-1= g P0/r0
: C2=gP0/r0= g RT/M; g=CP/CV.
24. .
25.
() , ,
, , , .
, , .
, , , . (X,Y,Z). : 3+3-1=5 . X1,Y1,Z1 X2,Y2,Z2 , L2=(X2-X1)2+(Y2-Y1)2+(Z2-Z1)2, L
, 3+3+3-3=6 .
:
1. X Y Z
2. X0,Y0,Z0, , X Y Z, .. .
3. x y z, , x0 y0 z0, .
( X Y Z) φ, ψ, Θ, x y z x0 y0 z0 -
|
|
φ ( Z),
ψ ( Z0 Θ Z0 Z),
Θ ( Z0)
, ( ).
,
rAB VA =d rA /dt VB =d rB /dt= VA, .. rAB =const : aA =d VA /dt=d VB /dt= aB
, . , , . , , . , .
. a, - . w: . w = onst, . n=w/2p ( ).
: . S=r´a : S=(r)*a+(a)*r=w*r S=(w*r)=r*w+r*w=re ( )+v*w (=v2/r ). .
:
Δ φ . ω =d φ /dt , . VA: VA = ω× rA ( ) VA=ω rA*sinα=ωρ :
a A=d ω /dt× rA + ω× d rA /dt= ε × rA + ω× VA
e -
aA = at + an - , at = e×rA =e*ρ* t - (t - VA).
an = ω× VA = ω ×(ω × rA )=ω2r n (n )
, .
- , , .
- :
rA = r0 + r`, r` - , .
:
VA = d rA /dt= d r0 /dt+ d r` /dt= V0 + ω × r`
, , X Y Z
V0= -ω×r`
.
|
|
, , - .
:
aA =d VA /dt=d V0 /dt+d ω /dt× r` + ω × d r` /dt= a0+a t+an
a t = e×r` an = ω × d r` /dt= ω ×( ω × r`)= ω *( ω * r`)- r` ( ω * ω) =- ω2 * r `
((ω * r`)=0, .. ω ^ r`)
, . ( , )
2. , (, ) .
s(t,x)=Acos[w (tx/c)]Acos[w (t+x/c)]=2Asin[w x/c]sinw t
w, : ()=2|sin[wx/c]|
26.
, . : dp/dt=F; dL/dt=M; . . , . - . . Z , . . : mdv/dt=F; Jdw/dt=M;
. . . i- m, :
F. , i- , f , i- j- , .. . , , .
(.6) -
,
( k , ),
i- -
) , ;
; . :
, .
(.8) :
(B10)
.