, . , .
. , , .
, , , .
.
(S) .
1 2, , 1 2, ().
.
- . - , , .
= (t) ( ).
- 1 - 2. Dt D = 2 1 , DS (. .).
y
DS
D
1 2
O x
dt, ½ d ½= dS.
, Dt:
= . (1.3.13)
: v = ½ ½= . (1.3.14)
.
:
. (1.3.15)
, , , , . S, t, :
v = S / t. (1.3.16)
, .
, D Dt, , , Dt 0:
. (1.3.17)
.
:
; (1.3.18)
. (1.3.19)
:
Þ .
:
; . (1.3.20)
.
- (, ), ( ) x (t), y (t), z (t):
; ; . (1.3.21)
. (1.3.22)
, :
|
|
; (1.3.23)
:
; ;
:
. (1.3.24)
.
(1.3.25)
, (1.3.26)
, .
t . . , = n.
n () . . , . (R = = ¥).
:
, (1.3.27)
.
:
t = eR, (1.3.28)
v = wR, (1.3.29)
a n = v 2/ R. (1.3.30)
w , e .
10. - , = 1 /2, = 2 /, = 1 . . 2 : 1) , ; 2) ; 3) .
: ;
= 1 /2, = 2 /, = 1 ;
t = 2 c.
: S, v, a.
. , 2 (1.3.23) (1.3.21):
, x = At 2 = 1×(22) = 4 (), y = Bt = 2×2 = 4 (), z = C = 1 ().
(1.3.23) :
= 5,7 ().
, (1.3.23) (1.3.22):
,
,
vx = d (At 2)/ dt = 2 At = 4 (/); vy = d (Bt)/ dt = B = 2 (/);
vz = d (C)/ dt = 0.
v = (42 + 22 + 02)1/2 = 4,5 (/).
ax = d (2 At)/ dt = 2 A = 2 (/2); ay = d (B)/ dt = 0; az = 0,
a = (22 + 02 + 02)1/2 = 2 (/2).
: 5,7 ; 4,5 /; 2 /2.
11. 1 . - , = 1 /3, = 2 /, = 3 . 1 .
: ;
= 1 /3, = 2 /, = 3 ;
t = 1 .
: a n.
. (1.3.30), (1.3.23) (1.3.22):
a n = v 2/ R,
,
.
, :
vx = d (At 3)/ dt = 3 At 2 = 3 (/); vy = d (Bt)/ dt = B = 2 (/);
vz = d (C)/ dt= 0.
v = (32 + 22 + 02)1/2 = 3,6 (/); a n = v 2/ R = 3,62/1 = (13 /2).
: 13 /2.
1.3.6.
() , .
.
, , . .
- (, ) Dt Dj .
|
|
( ) dj , dj, , .
, ( ), .
(1.3.31)
. ( ) , , , .
w = j / t. (1.3.32)
t = T j = 2 p:
w = 2 p / T Þ T = w /2 p, (1.3.33)
.
:
n = 1/ = w /2 p. (1.3.34)
, ()
. (1.3.35)
( ). .
:
. (1.3.36)
() :
. (1.3.37)
12. 1 , j (t) = t 3. 1 : 1) ; 2) . = 1 /3.
: j (t) = t 3,
R = 1 ,
t = 1 .
: 1) t/ n; 2) a.
. (1.3.28) (1.3.30) (1.3.29), (1.3.31) (1.3.35):
t = eR, e = dw / dt, w = dj / dt = d (t 3) dt = 3 At 2 = 3(/). e = d (3 At 2) dt = 6 At = 6 (/2), t = 6 (/2).
: a n = v 2/ R, : v = wR = 3 (/), a n= 32/1 = 9 (/2).
:
t/ a n = 6/9 = 0,67.
(1.3.27):
= (92 + 62)1/2 = 10,8 (/2).
: 0,67; 10,8 /2.
13. 1 ,
j (t) = t 3 t 2. ,
= 1 /3, = 1 /2?
: j (t) = t 3 t 2;
R = 1 ;
= 1 /3, = 1 /2.
: t.
. , : w = 0.
, (1.3.31):
, w = dj / dt = d [ t 3 t 2]/ dt = 3 At 2
2 Bt.
, , :
3 At 2 2 Bt = 0 Þ t (3 At 2 B) = 0.
:
t 1 = 0 t 2 = 2 B /3 A = 0,67 ().
: 0,67 .