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