Abstract
This chapter explains the basic principles of the theory of the calculus of variations. Having defined what a functional is, the technique for identifying its minima through the calculus of variations is presented for the classes of problems of interest for the development of the aeroelastic models presented in Part I of the textbook. A specific application of the calculus of variations aimed at defining the equation that governs the dynamics of a bending beam as a result of Hamilton's variational principle is discussed in detail to show the potential of this approach.
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References
Aleksandrov, A.D., Kolmogorov, A.N., Lavrent’ev, M.A.: Mathematics. Its Content, Methods, and Meaning, 6th edn. The MIT Press, Cambridge (1989)
Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Dover Publications Inc., New York (2000)
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Gennaretti, M. (2024). Elements of the Calculus of Variations. In: Fundamentals of Aeroelasticity. Springer, Cham. https://doi.org/10.1007/978-3-031-53379-2_8
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DOI: https://doi.org/10.1007/978-3-031-53379-2_8
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Online ISBN: 978-3-031-53379-2
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