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8120 results in Fluid dynamics and solid mechanics

Page 38 of 406

  • 1 - Particle Dynamics

  • 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 1-78

  • Summary

    Hypotheses and principles of Newtonian mechanics governing the dynamics of particles. Mach’s "empirical propositions” are presented as an alternative to Newton's laws, and the equivalences between both approaches is analyzed. The fundamental law governing particle dynamics (Newton’s second law) is presented both in Galilean and non-Galilean reference frames. A discussion of the frames which appear to behave as Galilean ones (according to the scope of the problem under study) is also included. The most usual interactions between particles are described. Formulation of forces associated with gravitation, springs, dampers, and friction phenomena are provided. Constraint forces on particles are introduced and characterized.

  • 7 - Lagrange’s Equations

  • 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 463-503

  • Summary

    The simplest version of the Lagrange's equations (valid only for holonomic systems whose motion is described through the time derivative of coordinates) is presented as an analytically systematized version of the method of virtual power. They provide the equations of motion of the system from the derivatives of its mechanical energy and the generalized forces associated with the nonconservative interactions. Two methods to calculate the constraint unknowns are given. The first one is based on that simple version of the Lagrange's equations, while the second one leads to the Lagrange's equations with multipliers. Hamilton's principle is presented as the gateway to analytical dynamics. Finally, the equilibrium configurations of an n degree of freedom system are considered.

Page 38 of 406