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2 results

  • 7 - Lagrange’s Equations

  • Joaquim A. Batlle, Universitat Politècnica de Catalunya, Barcelona, Ana Barjau Condomines, Universitat Politècnica de Catalunya, Barcelona
  • Book:
    Rigid Body Dynamics
    Published online:
    21 March 2022
    Print publication:
    14 April 2022, pp 463-503

  • Summary

    The simplest version of the Lagrange's equations (valid only for holonomic systems whose motion is described through the time derivative of coordinates) is presented as an analytically systematized version of the method of virtual power. They provide the equations of motion of the system from the derivatives of its mechanical energy and the generalized forces associated with the nonconservative interactions. Two methods to calculate the constraint unknowns are given. The first one is based on that simple version of the Lagrange's equations, while the second one leads to the Lagrange's equations with multipliers. Hamilton's principle is presented as the gateway to analytical dynamics. Finally, the equilibrium configurations of an n degree of freedom system are considered.

Rigid Body Dynamics
  • Joaquim A. Batlle, Ana Barjau Condomines
  • Published online:
    21 March 2022
    Print publication:
    14 April 2022
  • Building up from first principles and simple scenarios, this comprehensive introduction to rigid body dynamics gradually introduces readers to tools to address involved real-world problems, and cutting-edge research topics. Using a unique blend of conceptual, theoretical and practical approaches, concepts are developed and rigorously applied to practical examples in a consistent and understandable way. It includes discussion of real-world applications including robotics and vehicle dynamics, and over 40 thought-provoking fully worked examples to cement readers' understanding. Providing a wealth of resources allowing readers to confidently self-assess – including over 100 problems with solutions, over 400 high quality multiple choice questions, and end-of-chapter puzzles dealing with everyday situations – this is an ideal companion for undergraduate students in aerospace, civil and mechanical engineering.