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  2. Lagrange multiplier - Wikipedia

    en.wikipedia.org/wiki/Lagrange_multiplier

    For example, in economics the optimal profit to a player is calculated subject to a constrained space of actions, where a Lagrange multiplier is the change in the optimal value of the objective function (profit) due to the relaxation of a given constraint (e.g. through a change in income); in such a context is the marginal cost of the ...

  3. Lagrangian (field theory) - Wikipedia

    en.wikipedia.org/wiki/Lagrangian_(field_theory)

    In field theory, the independent variable is replaced by an event in spacetime (x, y, z, t), or more generally still by a point s on a Riemannian manifold.The dependent variables are replaced by the value of a field at that point in spacetime (,,,) so that the equations of motion are obtained by means of an action principle, written as: =, where the action, , is a functional of the dependent ...

  4. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.

  5. Lagrangian mechanics - Wikipedia

    en.wikipedia.org/wiki/Lagrangian_mechanics

    For example, in calculation of the motion of a torus rolling on a horizontal surface with a pearl sliding inside, the time-varying constraint forces like the angular velocity of the torus, motion of the pearl in relation to the torus made it difficult to determine the motion of the torus with Newton's equations. [7] Lagrangian mechanics adopts ...

  6. Lagrangian system - Wikipedia

    en.wikipedia.org/wiki/Lagrangian_system

    A Lagrangian density L (or, simply, a Lagrangian) of order r is defined as an n-form, n = dim X, on the r-order jet manifold J r Y of Y. A Lagrangian L can be introduced as an element of the variational bicomplex of the differential graded algebra O ∗ ∞ ( Y ) of exterior forms on jet manifolds of Y → X .

  7. Lagrangian - Wikipedia

    en.wikipedia.org/wiki/Lagrangian

    Lagrangian mechanics, a formulation of classical mechanics; Lagrangian (field theory), a formalism in classical field theory; Lagrangian point, a position in an orbital configuration of two large bodies; Lagrangian coordinates, a way of describing the motions of particles of a solid or fluid in continuum mechanics

  8. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    For example, renormalization in QED modifies the mass of the free field electron to match that of a physical electron (with an electromagnetic field), and will in doing so add a term to the free field Lagrangian which must be cancelled by a counterterm in the interaction Lagrangian, that then shows up as a two-line vertex in the Feynman diagrams.

  9. Lagrangian and Eulerian specification of the flow field

    en.wikipedia.org/wiki/Lagrangian_and_Eulerian...

    The Lagrangian and Eulerian specifications are named after Joseph-Louis Lagrange and Leonhard Euler, respectively. These specifications are reflected in computational fluid dynamics , where "Eulerian" simulations employ a fixed mesh while "Lagrangian" ones (such as meshfree simulations ) feature simulation nodes that may move following the ...