the use of the summation convention. Geodesics can be understood to be the Hamiltonian flows of a special Hamiltonian vector field defined on the cotangent...

regard geodesics as Hamiltonian flows. They are solutions of the associated Hamilton equations, with (pseudo-)Riemannian metric taken as Hamiltonian. A geodesic...

this Hamiltonian are then the same as the geodesics on the manifold. In particular, the Hamiltonian flow in this case is the same thing as the geodesic flow...

be shown that the equations for a geodesic may be formulated as a Hamiltonian flow, see Geodesics as Hamiltonian flows. The symplectomorphisms from a manifold...

Mathematics portal Physics portal Geodesic Geodetic precession Schwarzschild geodesics Geodesics as Hamiltonian flows Synge's world function Steven Weinberg...

derived as conditions of stationary action. Analytical mechanics Configuration space Hamilton–Jacobi equation Phase space Geodesics as Hamiltonian flows Herglotz's...

moment map and geodesic flows, Ann. Global Anal. Geom. 23 (2003) 305; arXiv:math-ph/0109031. Fasso, F., Superintegrable Hamiltonian systems: geometry...

stationarity of the Hamiltonian along the geodesic solution is the integrated running cost reduces to initial cost at t = 0, geodesics of the EL-general...

in the case of autonomous Hamiltonian systems, the energy is generally the only one, and on the energy level sets, the flows are typically chaotic. A key...

examples of vector flows include the geodesic flow, the Hamiltonian flow, the Ricci flow, the mean curvature flow, and Anosov flows. Flows may also be defined...

the last one says that the Hamiltonian vector field H for this mechanical system is a full spray. The constant speed geodesics of the underlying Finsler...

diffeomorphisms is then the shortest length or geodesic flow connecting them. The metric on the space associated to the geodesics is given by ρ ( φ , ψ ) = inf ϕ :...

"Geodesic flows on manifolds of constant negative curvature", Uspekhi Mat. Nauk, vol. 7, no. 1, pp. 118–137. Mautner, F. I. (1957), "Geodesic flows on...

curve-shortening flow can be used to find closed geodesics on Riemannian manifolds, and as a model for the behavior of higher-dimensional flows. A flow is a process...

this is the free-particle Hamiltonian, the solution to the Hamilton-Jacobi equations of motion are simply given by the geodesics on the manifold. In the...

structure of this Hamiltonian, the equations of motion for the particle, the Hamilton–Jacobi equations, are nothing other than the geodesic equations on the...

case of a Hamiltonian is the geodesic Hamiltonian on the cotangent bundle of a compact Riemannian manifold. The quantization of the geodesic flow is given...

Mathematics. His research deals with celestial mechanics, dynamical systems, Hamiltonian dynamics, and ergodic theory. In his dissertation, he solved the Painlevé...

assumed to propagate in a vacuum along a null geodesic in a pseudo-Riemannian manifold. Besides the geodesics principle in a classical field theory there...

Weinstein (1974), both inspired by the work of Smale (1970). Symmetry of a Hamiltonian or Lagrangian system gives rise to conserved quantities, by Noether's...

intrinsic nature of the Gaussian curvature, and studied geodesics, computing the area of a geodesic triangle in various non-Euclidean geometries on surfaces...

the Hamiltonian flow represents the classical trajectory of a mechanical system obeying the Hamilton-Jacobi equations of motion. The Hamiltonian flow is...

flat 3D real space the geodesics are simply straight lines. So for a free particle, Newton's second law coincides with the geodesic equation and states that...

In particular, the geodesics on a Riemannian manifold are given by the solution of the Hamilton–Jacobi equations. The geodesic flow of a flat torus following...

Hamiltonian (system). Study of probability distribution of individual eigenstates (see scars and quantum ergodicity). Semiclassical methods such as periodic-orbit...

physics of system. See Hamiltonian mechanics and the article on geodesic flow for an explicit construction of the Hamiltonian equations of motion. Legendre...

Mesyats Geocentric model Geocentric orbit Geodesic Geodesic deviation equation Geodesics as Hamiltonian flows Geodesics in general relativity Geodetic effect...

Symplectic structure Symplectomorphism Contact structure Contact geometry Hamiltonian system Sasakian manifold Poisson manifold Möbius transformation Conformal...

right-invariance. The lengths of these geodesics give the metric in the metric space structure of human anatomy. Non-geodesic formulations of diffeomorphic mapping...

inverse for the flow given by and the 3 × 3 {\displaystyle 3\times 3} Jacobian matrix for flows in R 3 {\displaystyle \mathbb {R} ^{3}} given as   D φ ≐ ( ∂...