
making the equilibrium point inherently unstable. Consequently, the state trajectory will move
outwards from the origin in state space.
The reverse is true whenever (cx
2
F
0
) > 0. In this case, the damping term is positive and energy
is dissipated from the system. The state trajectory spirals inward to points where the total energy in
the system is lower. Clearly, a locus of points must exist in state space to function as a transition
between the two phenomena. The locus must be a closed curve, namely, the limit cycle.
Example 2.12
For the mechanical system described by Equation 2.167
(a) Convert the system model to state variable form.
(b) Numerical ...