6. .
.
: , ,
,
.
. .
: , , .
:
V ();
V ();
r = r(t) ;
γ , .. V ( - );
φ ( V );
η ( N );
ψ ( N V).
( , ) , , .. γ0 (γ ) :
γ0(t) = 0, t0 ≤ t ≤ tf,(1)
t0, tf - .
1.
V V . (.. ) :
r = V cos φ - V, (2)
φr = - V sin φ. (3)
,
(4)
(5)
φ0 ϵ [0, π]. (3) (4) , φ r → 0 φ → 0.
r (4) (3),
(6)
:
w ≤ 2 t ϵ [t0, tf], ( ) .
(7)
w ≥ 2 | φ | , w < 2 , cos φ = w/2.
, , , , ( , ) , , , . , , . , , , .
|
|
, -: . . , . .
( ) , γ0:
γ0(t) = γ0, t0 ≤ t ≤ tf,(8)
γ0 ,
(V / V) |sin γ0| ≤ 1, (9)
, , .
(. 1)
(10)
(11)
,
(12)
(13)
(14)
,
(12)
r (12)
(15)
a = w sin γ0 = 1 (16)
(17)
r (15) (11), w = φ
(18)
(19)
, a > sin φ0 a > sin φ. (20)
a < sin φ0 a < sin φ, (21)
(11) (15)
(22)
(23)
(15) , r → 0 sin φ → a,
φ → φ = arcsin a = arcsin (w sin γ0). (24)
sin φ = a [0, π] : φ1 = φ φ2 = π - φ. . , φ0 ϵ [0, π] γ0 ϵ [0, av]. γ0 (9). (11), 0 < φ0 < φ φ > 0 φ → φ, φ < φ0 < φ2 φ < 0 φ → φ, φ2 < φ0 ≤ π φ > 0 φ → 2 π + φ, .. φ φ. φ0 = φ2, , φ → φ.
(18) (19) φ → φ, ,
. (9) (π/2 < φ0 < π) γ0 , a < sin φ0 γ0 ≤ arcsin (v sin φ0), v = V/V.
|
|
: , .
, γ0 , . , φ = 0, , . , , - , γ0. , .