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8133 results in Fluid dynamics and solid mechanics

Page 40 of 407

  • 6 - The Method of Virtual Power

  • 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 406-462

  • Summary

    The method of virtual power is a powerful tool to obtain the equations of motion and the constriant forces and moments in multibody systems (especially in planar motion). The d'Alembert torsor of inertial forces is defined, and then the concept of virtual motion is introduced. Numerous examples illustrate the application of that method to different mechanical systems.

  • 3 - Mass Distribution

  • 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 151-201

  • Summary

    Introduction of all concepts related to the mass distribution of the system (center of mass and inertia tensor about a point) needed to apply the vector theorems that solve the dynamics of a rigid body. A few theorems that help calculate those elements (Pappus–Guldon theorems, Steiner's theorem) are presented. The qualitative assessment of the inertia tensor from the mass distribution geometry is discussed and illustrated through several examples. Principal directions of inertia (or of rotation) are introduced, and symmetrical and spherical rotors are defined. The inertia ellipsoid (a tool to visualize the inertia tensor) is presented in the last section.

Global Atmospheric and Oceanic Modelling
  • Fundamental Equations
  • Andrew N. Staniforth
  • Published online:
    08 April 2022
    Print publication:
    28 April 2022
  • Combining rigorous theory with practical application, this book provides a unified and detailed account of the fundamental equations governing atmospheric and oceanic fluid flow on which global, quantitative models of weather and climate prediction are founded. It lays the foundation for more accurate models by making fewer approximations and imposing dynamical and thermodynamical consistency, moving beyond the assumption that the Earth is perfectly spherical. A general set of equations is developed in a standard notation with clearly stated assumptions, limitations, and important properties. Some exact, non-linear solutions are developed to promote further understanding and for testing purposes. This book contains a thorough consideration of the fundamental equations for atmospheric and oceanic models, and is therefore invaluable to both theoreticians and numerical modellers. It also stands as an accessible source for reference purposes.

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.

  • STATIONARY MARKOVIAN ARRIVAL PROCESSES: RESULTS AND OPEN PROBLEMS

  • Part of
  • AZAM ASANJARANI, YONI NAZARATHY
  • Journal:
    The ANZIAM Journal / Volume 64 / Issue 1 / January 2022
    Published online by Cambridge University Press:
    22 February 2022, pp. 54-68
    • Article
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  • We consider two classes of irreducible Markovian arrival processes specified by the matrices C and D: the Markov-modulated Poisson process (MMPP) and the Markov-switched Poisson process (MSPP). The former exhibits a diagonal matrix D while the latter exhibits a diagonal matrix C. For these two classes we consider the following four statements: (I) the counting process is overdispersed; (II) the hazard rate of the event-stationary interarrival time is nonincreasing; (III) the squared coefficient of variation of the event-stationary process is greater than or equal to one; (IV) there is a stochastic order showing that the time-stationary interarrival time dominates the event-stationary interarrival time. For general MSPPs and order two MMPPs, we show that (I)–(IV) hold. Then for general MMPPs, it is easy to establish (I), while (II) is shown to be false by a counter-example. For general simple point processes, (III) follows from (IV). For MMPPs, we conjecture that (IV) and thus (III) hold. We also carry out some numerical experiments that fail to disprove this conjecture. Importantly, modelling folklore has often treated MMPPs as “bursty”, and implicitly assumed that (III) holds. However, to the best of our knowledge, proving this is still an open problem.

Page 40 of 407