t | 0,0 | 0,1 | 0,2 | 0,3 | 0.4 | 0,5 | 0,6 |
θ | 1,5708 | 1.3737 | 0,7971 | -0,0437 | -0,8688 | -1,4104 | -1,5689 |
θ | 1,5708 | 1,3533 | 0.7611 | -0,0418 | -0.8332 | -1,3938 | -1.5686 |
φ(t) | 1,5710 | 1.3737 | 0.7938 | -0,0473 | -0,8696 | -1.4077 | -1.5631 |
t | 0.7 | 0,8 | 0,9 | 1,0 | 1,1 | 1,2 | 1,3 |
θ | -1,3331 | -0,7228 | 0,1308 | 0,9374 | 1,4434 | 1,5632 | 1,2889 |
θ | -1,3090 | -0,6870 | 0,1253 | 0,9028 | 1,4304 | 1,5619 | 1,2609 |
φ(t) | -1,3299 | -0,7216 | 0,1297 | 0,9371 | 1,4448 | 1,5631 | 1,2869 |
, , , , . , , . , , , ( ) . , , , - . , , , T , , .. , k > 0. f(t)
- . , , a0, 1, b1, 2, b2,... , , , . t = 0; 0,4 1 ( ) ,
φ(t) . 7.5; , . , , , .
. 7.19. ,
, . , (. 7.19), , , ;
, . , , .. , .
. , , :
|
|
(7.34)
, , , ( 2 / 2 ). (7.34)
(7.35)
: < ω ≥ ω. , (7.35) . : < ω
, - , φ - ( φ θ0 v0). k ≥ ω
θ0 v0.
(7.34), , , (7.34) (7.35) .
. F(t), , (7.34) F(t) . : F(t) = F0 cos λt, λ - . :
(7.36)
. (7.36)
(7.37)
, (7.37), . : ( < ω) λ. , t >> 1 /k, , λ ω1 λ ≈ ω1 - , . (7.37) , , :
(7.38)
, .
, , , k = 0 λ ≈ ω1 (. 7.20-7.22), , , (7.38) , ; .
. 7.20.
= 0,5; ω = π /2, λ = π, f = 2 π.
. 7.21.
k = 0; ω = 889 π /9000, λ = π/ 9, f = π /70
(7.36). , . : ( ) , , λ ≈ ω .. , , . - . , , , , , , . .
|
|
. 7.22. k = 0; ω = 889 π /9000, λ = π/ 9, f = π /70
. , , , , . .
- , , , , , . , , , ,
(7.39)
ω(t) , . ω 2 (t):
λ - ω 2 (t).
(7.39)
(7.40) - , - , , . , λ ω0, , , , ,... α . . 7.23 α, .
. 7.23
: , , . , .
, , ? - α (, 0,1) γ (, 0,3), , (7.40). τ = ω0t,
(7.41)
. , γ (, 0,01) α, (7.41), , , . α (, α = 0,2) γ .. - .
, (7.40), . . , sin θ (7.39), . , , γ α, γ, . - .
|
|
. , θ(t) ( - , , x(t), y(t) ).
, , (.. ), , , .. ,
(7.42)
( , , ω ):
:
, , . ;
-, ;
- , ;
;
, ;
.
, .
, . , sin θ , , , .