Introduction to Analytical Mechanics

Sohrob Mottaghi, Rene Gabbai, Haym Benaroya

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter presents several of the most important concepts from analytical dynamics. We derive Lagrange’s equation and how it can be used for the derivation of governing equations of motion. It is, especially, useful for the derivation of the equations of motion for systems, discrete or continuous, with more than one degree-of-freedom, where the Newtonian free body diagrams become more difficult to apply. We also derive Hamilton’s principle, an integral energy formulation, also applicable to both discrete and continuous systems, and see how it is related to Lagrange’s equation. Hamilton’s principle is, especially, relevant to the work in Chaps. 4 and 5.

Original languageEnglish (US)
Title of host publicationSolid Mechanics and its Applications
PublisherSpringer Verlag
Pages57-73
Number of pages17
DOIs
StatePublished - Jan 1 2020

Publication series

NameSolid Mechanics and its Applications
Volume260
ISSN (Print)0925-0042
ISSN (Electronic)2214-7764

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Equations of motion
Mechanics

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Mottaghi, S., Gabbai, R., & Benaroya, H. (2020). Introduction to Analytical Mechanics. In Solid Mechanics and its Applications (pp. 57-73). (Solid Mechanics and its Applications; Vol. 260). Springer Verlag. https://doi.org/10.1007/978-3-030-26133-7_3
Mottaghi, Sohrob ; Gabbai, Rene ; Benaroya, Haym. / Introduction to Analytical Mechanics. Solid Mechanics and its Applications. Springer Verlag, 2020. pp. 57-73 (Solid Mechanics and its Applications).
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Mottaghi, S, Gabbai, R & Benaroya, H 2020, Introduction to Analytical Mechanics. in Solid Mechanics and its Applications. Solid Mechanics and its Applications, vol. 260, Springer Verlag, pp. 57-73. https://doi.org/10.1007/978-3-030-26133-7_3

Introduction to Analytical Mechanics. / Mottaghi, Sohrob; Gabbai, Rene; Benaroya, Haym.

Solid Mechanics and its Applications. Springer Verlag, 2020. p. 57-73 (Solid Mechanics and its Applications; Vol. 260).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Mottaghi S, Gabbai R, Benaroya H. Introduction to Analytical Mechanics. In Solid Mechanics and its Applications. Springer Verlag. 2020. p. 57-73. (Solid Mechanics and its Applications). https://doi.org/10.1007/978-3-030-26133-7_3