Lagrangeova

Lagrangeova is a Czech adjectival form meaning “of Lagrange” and is used to name mathematical and physical concepts connected with Joseph-Louis Lagrange (1736–1813), a prominent mathematician and physicist who worked in Italy and France. In Czech scholarly terminology, Lagrangeova forms prefix terms to indicate their origin or authorship by Lagrange, or to honor his contributions in different fields.

One common use is Lagrangeova mechanika, or Lagrangian mechanics, a reformulation of classical mechanics based on the Lagrangian function L = T − V, depending on generalized coordinates q_i, their time derivatives q̇_i, and time t. The equations of motion follow from the Euler–Lagrange equations d/dt(∂L/∂q̇_i) − ∂L/∂q_i = 0. This framework simplifies handling of constraints and coordinate changes, and underpins many modern methods in physics and engineering.

Lagrangeovy multiplikátory are another widely used concept named after Lagrange. They provide a technique for finding extrema of a function subject to constraints by introducing auxiliary multipliers and forming a Lagrangian L(x, λ) = f(x) + λ(g(x) − c), then solving the stationary conditions.

Lagrangeova věta o čtyřech čtvercích is Lagrange’s four-square theorem in number theory, which states that every natural number can be expressed as a sum of four integer squares. The name also appears in other results attributed to Lagrange, including various identities and equations in algebra and mechanics.

Joseph-Louis Lagrange, born in Turin and later working in France, made foundational contributions across analysis, number theory, and celestial mechanics, shaping much of classical and analytical mechanics.