BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 3, 2012 91
when we consider the initial condition ( )
C
Ω = t , (16)
I
Ω 0 = 0.
3. If the parameters defined Δ ≠ 0 and C=0, Eq. (11) becomes
d
I
Ω + ΔΩ = 0 . (17)
dt
Solving the characteristic equation is obtained solution
Ω=Ω
Δ
e − t
I
0
where: Ω 0 is the angular velocity value Ω at baseline, considered to t = 0.
If, however, the initial velocity is zero, that is
Ω 0 = 0,
in (18) becomes apparent
Ω = 0,
and
ω= ω a
,
which is understandable because the disturbance is absent, that is C = 0. Where
Ω ≠ 0 , 0
solution of the Eq. (17) equation remains to form (18).
4. A final case under consideration is given to values Δ = 0 , C = 0.
In this case, Eq. (12) is also a simplified form, that is
dΩ I = 0,
(19)
dt
with solution
Ω =Ω , 0 (20)
same question with respect to Ω
0
, as for 3.
With the developed model, based on the solutions (14), (16), (18) and
(20) can be extremely useful analysis of the stability of the vehicle propulsion
system operation. The first case analyzed is the situation defined by
Δ < 0,
that is
tan δ rω
< tan δ mω
.
In this case, the angular velocity decreases or increases indefinitely to a
change in operating point position a; that, in this case the operating point is
unstable.
In the second case, considering the situation
(18)