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Analytic mechanics
Analytic mechanics is a mathematical science, but it is of high importance
for engineers as it provides analytic solutions to fundamental problems of
engineering mechanics. At the same time it establishes generally applicable
procedures. Mathematical physics texts, such as [5] and [6], laid the founda-
tion for these analytic approaches addressing physical problems.
In the following sections we find analytic solutions for classical mechanical
problems of elasticity utilizing Hamilton’s principle. The most fitting applica-
tion is the excitation of an elastic system by displacing it from its equilibrium
position. In this case the