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1 results

  • 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.