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3.2 ELECTRONICS AND MECHANICS 41
Software
Digital electronics
Abstraction components Rigid/elastic
Electronic
bodies
Electric/magnetic Mechanical continua
fields
Electronics Mechanics
Figure 3.1 Levels of abstraction for electronic and mechanical models
only been possible to differentiate between two levels of abstraction, the contin-
uum level and the level of multibody systems in which rigid and elastic bodies are
each considered as a unit. In particular, we cannot neglect the continuum level for
the consideration of systems since an electro-mechanical transformation, e.g. sen-
sors and actuators, occasionally cannot be abstracted to the multibody level. The
demonstrators from the chapter on micromechatronics are a good example of this.
3.2.2 Analogies
Analogies on the level of electronic components and mechanical bodies repre-
sent the predominant theme running through the joint consideration of electronics
and mechanics. By this we mean that electronics and mechanics can be described
using equations that have the same structure. This is also made clear by the fact
that the equations from both mechanics and electronics can be derived from the
Lagrange principle, see Maißer and Steigenberger [252] and Section 6.2.2. ‘Lan-
grange approach’. The analogies between electronics and mechanics will first be
explained by means of an example, see Ogata [300]. The diagram on the left-hand
side of Figure 3.2 shows a simple mass-spring-damper system.
The differential equation describing the system is as follows:
m¨x + b˙x + kx = F (3.1)
First we have to find out which variables can be identified as being analogous with
one another. One possibility is to associate forces with currents and velocities with
voltages. In order to construct an analogue circuit, let us now consider the mechan-
ical system more closely. In this all forces act upon the mass, i.e. upon a point, and
correspondingly add up to zero. In electronics this corresponds with the situation
