Examples in Mechanics

Typical examples provide pictorial meanings.
Rotation, its eigenvector [Gol, p.118, l.−6p.119, l.5], and its trace [Gol, p.124, (484)].
 Physical phenomena raise questions that lead to a theory's development.
 Theory: Linear algebra. Example: Euler's theorem on the motion of a rigid body [Gol, p.119, l.13p.123, l.18].
 Theory: Stoke's theorem. Example: Maxwell's equations.
 A typical example may make the meaning of a definition complete.
[Coh, p.95, (A14)] explains why we require [Coh, p.96, (A7)] in the definition of scalar product.
 Examples eliminate confusion.
Suppose two concept A and B
(e.g. Equilibrium &
steady state: [Lev1, p.4, l.3p.5, l.9]) are so similar that they are easily confused with each other. For
example, A requires conditions I and II; B requires condition I only. To truly
understand the subtle distinction between A and B, we must find an example that
satisfies condition I but does not satisfy condition II.
 Examples allow us to check the consistency among theories [Jack, p.123, l.8l.7].
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