Euler's Equation

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Euler's equation [′ȯi·lərz i¦kwā·zhən]

(mathematics)

Euler-Lagrange equation

Euler’s Equation

(1) A differential equation of the form

where a₀, . . ., a_n are constants. When x > 0, equation (*) reduces, by the substitution x = e^t, to a linear differential equation with constant coefficients. Equation (*) was studied by L. Euler in 1740. The equation

reduces to it through the substitution x’ = ax + b.

(2) A differential equation of the form

where X(x) = a₀x⁴ + a₁x³ + a₂x² + a₃x + a₄ and Y(y) = a₀y⁴ + a₁y³ + a₂y² + a₃y + a₄. Euler considered this equation in a number of works, the first of which dates from 1753. He showed that the general solution of the equation is a symmetric polynomial of degree 4 in x and y. This result provided the basis for the theory of elliptic integrals.

(3) A differential equation of the form

which is used in the calculus of variations to search for extrema of the integral

The equation was derived by L. Euler in 1744.

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No references found			After presenting the foundations in a form free from any coordinate system, the author follows with a chapter on the technique of writing Navier-Stokes equations and Euler's equations in general steady and nonsteady curvilinear coordinates, as well as the essential aspects of vorticity and stream functions. Fluid dynamics; theoretical and computational approaches, 3d ed by SciTech Book News Euler's equation was a product of human reason--not observation--but its constants are critical to the fundamental relativistic quantum physics that has been experimentally shown to underlie our material world. To the editors. (Correspondence) by Commonweal He converted the problem into an equivalent mathematical form that enabled him to pick out candidates likely to satisfy Euler's equation. The curious power of large numbers by Peterson, Ivars / Science News			Eukman, Christiaan EULA Eulamellibranchia Eulenburg's disease Eulenburg, Philipp, Fürst zu Eulenspiegel, Till Euler Euler Angles Euler Characteristic Euler characteristic of a topological space X Euler diagram Euler equation Euler equations of motion Euler force Euler formula for long columns Euler method Euler Number Euler number 1 Euler number 2 Euler Numbers Euler Phi-Function Euler Substitutions Euler transformation Euler's Constant Euler's criterion Euler's Equation Euler's Equations Euler's equations of motion Euler's expansion Euler's Formula Euler's Integral Euler's numbers Euler's phi function Euler's spiral Euler's theorem Euler, Leonhard Euler, Ulf Svante Von Euler-Chelpin Euler-Chelpin, Hans Karl August Simon Von Euler-Fourier Formulas Euler-Lagrange equation Euler-Maclaurin formula Euler-Maclaurin Summation Formula Euler-Rodrigues parameter Eulerian coordinates Eulerian correlation Eulerian description Eulerian equation Eulerian graph Eulerian nutation Eulerian path			Euler numbers Euler path Euler phi-function Euler polyhedron theorem Euler quadratic residue theorem Euler rotation Euler Substitutions Euler summation formula Euler theorem Euler theorem on homogeneous functions Euler totient rule Euler totient theorem Euler tour Euler trail Euler transformation Euler Venn diagram Euler walk Euler wenn diagram Euler zeta function Euler's angle Euler's Box Euler's Box Euler's circles Euler's constant Euler's criterion Euler's Equation Euler's equation of motion Euler's equations Euler's equations of motion Euler's expansion Euler's formula Euler's formula for polyhedra Euler's formula in complex analysis Euler's forward method Euler's generalization Euler's homogeneous function theorem Euler's Integral Euler's method Euler's numbers Euler's phi function Euler's polyhedron formula Euler's polyhedron theorem Euler's quadratic residue theorem Euler's spiral Euler's summation formula Euler's theorem Euler's theorem on homogeneous functions Euler's totient function Euler's totient rule Euler's totient theorem

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