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Dynamic Simulations

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Part of the Simulation Foundations, Methods and Applications book series (SFMA)


This chapter presents an overview of how all techniques covered in this book fit together as independent modules constituting a simulation engine. It discusses in detail a possible architectural design of a computationally efficient implementation of a dynamic-simulation engine for non-penetrating particle and rigid-body systems. In doing so, we are mostly interested in studying algorithms that can produce real-time or near real-time performance. The actual description of the algorithms used in each step of the simulation engine proposed in this book, as well as reference software implementations of several modules that make up the entire simulation, are provided in the remaining chapters and appendices. The main goal of this chapter is to justify the book’s organization, and describe the high-level steps necessary to implement an efficient dynamic-simulation engine.


  • Contact Force
  • Collision Detection
  • Linear Complementarity Problem
  • Collision Time
  • Simulation Engine

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  1. 1.

    In this book, we shall focus the study of particle systems to the case in which particles are approximated by point-mass objects.

  2. 2.

    In this book, we shall sometimes refer to object as a synonym to particle or rigid body.

  3. 3.

    In this book, we assume the object’s geometry is defined by its boundary representation, that is, by its vertices, edges and faces.

  4. 4.

    A value of △t=1/24 corresponds to 24 frames per second of simulation.

  5. 5.

    A value of 4 is a common choice.

  6. 6.

    The value of N should be clamped at a minimum value of one, otherwise the system will end up moving forward in time by more than △t.

  7. 7.

    The closest features between two objects are vertex–face, face–vertex or edge–edge.

  8. 8.

    The direction defined by the line connecting the closest points at t i .

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Coutinho, M.G. (2013). Dynamic Simulations. In: Guide to Dynamic Simulations of Rigid Bodies and Particle Systems. Simulation Foundations, Methods and Applications. Springer, London.

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  • Print ISBN: 978-1-4471-4416-8

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