The Art of the Helicopter John Watkinson - Karatunov.net

44 The Art of the Helicopter
It will be clear that the behaviour just noted has a direct parallel in the behaviour of
an electronic damped tuned circuit consisting of an inductor, a capacitor and a resistor
and the mathematics of both are one and the same. This is more than just a convenience
because it means that an unwanted mechanical resonance or phase change in a control
system can be suppressed by incorporating at some point a suitable electronic circuit
designed to have the opposite characteristic. Additionally by converting mechanical
parameters into electrical parameters the behaviour of a mechanism can be analysed
as if it were an electronic circuit.
2.13 Sidebands
It was seen in Figure 2.17 that a sinusoidal function is a rotation resolved in one axis.
In order to obtain a purely sinusoidal motion, the motion on the other axis must be
eliminated. Conceptually this may be achieved by having a contra-rotating system in
which there is one rotation at +ω and another at −ω. Figure 2.25(a) shows that the
sine components of these two rotations will be in the same phase and will add, whereas
Fig. 2.25 (a) A sinusoidal motion can be considered as the sum of contra-rotations which cancel the cosine
components. (b) When two sinusoids are multiplied, the effect is that one rotation is carried around by the other.
A difference frequency exists because the forward rotation of one signal carries round the backward rotation of
the other which makes it slow down. The sum frequency is obviously rotating faster.