Lagrangian (disambiguation)

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The term Lagrangian refers to any of several mathematical concepts developed by Joseph Louis Lagrange:

Mathematical sciences[edit]

  • In optimization theory, the Lagrangian function is used to solve constrained minimization problems; see Lagrange multipliers.
    • The method of approximating a difficult constrained problem with an easier problem having an enlarged feasible set (allowing but penalizing some violation of constraints), is called Lagrangian relaxation.
    • The problem of maximizing the value of the Lagrangian function, in terms of the Lagrange-multiplier variable, is the Lagrangian dual problem.
  • In symplectic geometry, a Lagrangian submanifold is a special class of submanifolds, with dimension half the dimension of the ambient space and where the symplectic form vanishes identically.
  • Lagrangian system

Physics[edit]

  • Lagrangian mechanics is a formulation of classical mechanics for particles, in which the Lagrangian summarizes the dynamics of a system.
  • Lagrangian (field theory) is a formulation of classical field theory for continua and fields, in which the Lagrangian density (often simply called the Lagrangian) summarizes the dynamics of a system.
  • In orbital mechanics, the Lagrangian points are stable and meta-stable points of a two body system.
  • In continuum mechanics, Lagrangian coordinates are a way of describing the motions of particles of a solid or fluid.