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Principle of Least Action in Continuum Mechanics

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Variational Principles of Continuum Mechanics

Part of the book series: Interaction of Mechanics and Mathematics ((IMM))

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Abstract

As we discussed in Sect. 2.6, for reversible processes the governing equations of mechanics must have a Hamiltonian structure, and accordingly a principle of least action must exist. In another extreme case, when the inertial effects and the internal interactions described by the internal energy can be ignored, variational principles also exist, but they are due to the special structure of the models rather than to the laws of Nature. In this chapter we consider the principle of least action in continuum mechanics of reversible processes and some related issues. The variational principles for dissipative processes are presented in the second part of the book along with the other variational features of the classical continuum models.

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References

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Authors and Affiliations

  1. Department of Mechanical Engineering, Wayne State University, 48202, Detroit, MI, USA

    V.L. Berdichevsky (Professor of Mechanics)

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  1. V.L. Berdichevsky
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Correspondence to V.L. Berdichevsky .

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© 2009 Springer-Verlag Berlin Heidelberg

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Berdichevsky, V. (2009). Principle of Least Action in Continuum Mechanics. In: Variational Principles of Continuum Mechanics. Interaction of Mechanics and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88467-5_4

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  • DOI: https://doi.org/10.1007/978-3-540-88467-5_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88466-8

  • Online ISBN: 978-3-540-88467-5

  • eBook Packages: EngineeringEngineering (R0)

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