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Appendix D: Rigid-Body Mass Properties

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Abstract

This Appendix shows an efficient algorithm to compute the mass properties of 3D polyhedra. The mass properties include the total volume, total mass, center of mass, and inertia tensor. These quantities are used in the physically based modeling of the dynamics and interactions of objects in the simulated world.

Keywords

  • Volume Integral
  • Mass Property
  • Body Frame
  • Surface Integral
  • Line Integral

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 9.1
Fig. 9.2

References

  1. Alonso, M., Finn, E.J.: Fundamental University Physics. Addison-Wesley, Reading (1967)

    Google Scholar 

  2. Beer, F.P., Johnston, E.R.: Vector Mechanics for Engineers: vol. 1—Statics. McGraw-Hill, New York (1977)

    Google Scholar 

  3. Kallay, M.: Computing the moment of inertia of a solid defined by a triangle mesh. J. Graph. Tools 11(2), 51–58 (2006)

    CrossRef  Google Scholar 

  4. Lien, S.-L., Kajiya, J.T.: A symbolic method for calculating the integral properties of arbitrary non-convex polyhedra. IEEE Comput. Graph. Appl. 4(10), 34–41 (1984)

    Google Scholar 

  5. Lee, Y.T., Requicha, A.A.G.: Algorithms for computing the volume and other integral properties of solids. (1) Known methods and open issues. Commun. ACM 25(9), 635–641 (1982)

    MathSciNet  CrossRef  Google Scholar 

  6. Lee, Y.T., Requicha, A.A.G.: Algorithms for computing the volume and other integral properties of solids. (2) A family of algorithms based on representation conversion and cellular approximation. Commun. ACM 25(9), 642–650 (1982)

    MathSciNet  CrossRef  Google Scholar 

  7. Mirtich, B.V.: Fast and accurate computation of polyhedral mass properties. J. Graph. Tools 1(2), 31–50 (1996)

    CrossRef  Google Scholar 

  8. Mirtich, B.V.: Impulse-based dynamic simulation of rigid body systems. PhD Thesis, University of California, Berkeley (1996)

    Google Scholar 

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Coutinho, M.G. (2013). Appendix D: Rigid-Body Mass Properties. In: Guide to Dynamic Simulations of Rigid Bodies and Particle Systems. Simulation Foundations, Methods and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-4417-5_9

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  • DOI: https://doi.org/10.1007/978-1-4471-4417-5_9

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4416-8

  • Online ISBN: 978-1-4471-4417-5

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