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

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Acoustics and Ultrasonics
  • Mechanical Engineering

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  • 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