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searching for Euler–Lagrange equation 9 found (99 total)

Riemannian metric and Lie bracket in computational anatomy (3,650 words) [view diff] exact match in snippet view article find links to article

{d}{dt}}w_{t}-((Dv_{t})w_{t}-(Dw_{t})v_{t})\ .} The Euler–Lagrange equation can be used to calculate geodesic flows through the group which

Contributors to the mathematical background for general relativity (260 words) [view diff] exact match in snippet view article find links to article

approach to solving PDEs; see also parent list) Leonhard Euler (Euler-Lagrange equation, from which the geodesic equation is obtained) Carl Friedrich Gauss

Computational anatomy (16,865 words) [view diff] exact match in snippet view article find links to article

the diffeomorphic shape momentum taken pointwise satisfying the Euler–Lagrange equation for geodesics is determined by its neighbors through spatial derivatives

Dirichlet form (1,330 words) [view diff] exact match in snippet view article find links to article

where A(x){\displaystyle A(x)} is a positive symmetric matrix. The Euler-Lagrange equation of a Dirichlet form is a non-local analogue of an elliptic equations

Biharmonic map (2,107 words) [view diff] exact match in snippet view article find links to article

finding the above biharmonic map equation as the corresponding Euler-Lagrange equation. Harmonic maps correspond to critical points for which the bioenergy

Hamiltonian constraint (3,310 words) [view diff] exact match in snippet view article find links to article

our Hamiltonian constraint! It could also be obtained from the Euler–Lagrange equation of motion, noting that the action depends on λ{\displaystyle \lambda

Klein–Gordon equation (6,536 words) [view diff] exact match in snippet view article find links to article

equation can also be derived by a variational method, arising as the Euler–Lagrange equation of the action S = ∫ ( − ℏ 2 η μ ν ∂ μ ψ ¯ ∂ ν ψ − M 2 c 2 ψ ¯ ψ

Relativistic quantum mechanics (10,055 words) [view diff] exact match in snippet view article find links to article

then generate the differential equation by the field-theoretic Euler–Lagrange equation: ∂ μ ( ∂ L ∂ ( ∂ μ ψ ) ) − ∂ L ∂ ψ = 0 {\displaystyle \partial

Bayesian model of computational anatomy (3,931 words) [view diff] exact match in snippet view article find links to article

Riemannian metric of Computational anatomy solves for the flow of the Euler-Lagrange equation. Solving the geodesic from the initial condition v 0 {\displaystyle