Search results
Results from the WOW.Com Content Network
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
The Hamilton Institute is an applied mathematics research institute at Maynooth University and the Royal Irish Academy holds an annual public Hamilton lecture at which Murray Gell-Mann, Frank Wilczek, Andrew Wiles and Timothy Gowers have all spoken. 2005 was the 200th anniversary of Hamilton's birth and the Irish government designated that the ...
Suppose that M is a compact smooth manifold, and let g t be a Ricci flow for t in the interval (a, b).Define Ψ: (a, b) → (0, ∞) so that each of the Riemannian metrics Ψ(t)g t has volume 1; this is possible since M is compact.
By a limiting procedure, Richard Schoen and Shing-Tung Yau used Hamilton's theorem to prove that any finite-energy map from a complete Riemannian manifold to a closed Riemannian manifold of nonpositive curvature can be deformed into a finite-energy harmonic map. [29]
Hamilton's equations give the time evolution of coordinates and conjugate momenta in four first-order differential equations, ˙ = ˙ = ˙ = ˙ = Momentum , which corresponds to the vertical component of angular momentum = ˙ , is a constant of motion. That is a consequence of the rotational symmetry of the ...
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can be studied in both Hamiltonian mechanics and dynamical systems theory.
[1] [2] The qualitative form of this connection is called Hamilton's optico-mechanical analogy. In mathematics, the Hamilton–Jacobi equation is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations .
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics.It asserts that the phase-space distribution function is constant along the trajectories of the system—that is that the density of system points in the vicinity of a given system point traveling through phase-space is constant with time.