The term Lagrangian refers to any of several mathematical concepts developed by Joseph Louis Lagrange:
- In physics, the Lagrangian is a function that characterizes the dynamics of a system.
- In optimization theory, the Lagrangian is used to solve constrained optimization problems; see Lagrange multipliers.
- In calculus of variations, the Lagrangian is a functional whose extrema are to be determined; see Calculus of variations.
- 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.
- 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.
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