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2 results

  • 4 - Vector Theorems

  • 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 202-315

  • Summary

    Formulation and application of the vector theorems (linear momentum theorem and the angular momentum theorem) for the case of systems with constant matter. Those theorems relate the rate of change of a vector associated with the system (the linear momentum and the angular momentum about a point, respectively) to the net interactions (forces and moments) exerted on the system. Three different versions of the angular momentum theorem are presented: about a point fixed to a Galilean frame, about the system's center of mass, and about a point moving relative to a Galilean frame. Rotational dynamics, where the behavior of rigid bodies is often counterintuitive, is analyzed in a general and rigorous way. The dynamic role of the principal axes of inertia is discussed through several didactic examples. The formulation of the vector theorems in non-Galilean frames is also included. An appendix is devoted to the static and dynamic balancing of a rotor.

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.