In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical...
44 KB (8,124 words) - 20:29, 13 May 2024
The Hamilton-Jacobi-Bellman (HJB) equation is a nonlinear partial differential equation that provides necessary and sufficient conditions for optimality...
14 KB (2,050 words) - 17:50, 26 April 2024
general relativity, the Hamilton–Jacobi–Einstein equation (HJEE) or Einstein–Hamilton–Jacobi equation (EHJE) is an equation in the Hamiltonian formulation...
16 KB (1,959 words) - 00:11, 15 June 2023
Action (physics) (redirect from Hamilton's Principal Function)
classical mechanics. Due to a similarity with the Schrödinger equation, the Hamilton–Jacobi equation provides, arguably, the most direct link with quantum mechanics...
24 KB (3,074 words) - 22:32, 19 April 2024
Hamiltonian mechanics (redirect from Hamilton's equation)
theory Hamiltonian system Hamilton–Jacobi equation Hamilton–Jacobi–Einstein equation Lagrangian mechanics Maxwell's equations Hamiltonian (quantum mechanics)...
52 KB (9,275 words) - 00:18, 4 March 2024
Newton's laws of motion (category Equations of physics)
{\displaystyle t} . The Hamiltonian is incorporated into the Hamilton–Jacobi equation, a differential equation for S {\displaystyle S} . Bodies move over time in...
121 KB (15,329 words) - 14:55, 27 May 2024
the Hamilton–Jacobi equation; conversely the analogy provides an alternative and more accessible path for introducing the Hamilton–Jacobi equation approach...
14 KB (1,851 words) - 00:36, 4 December 2023
contributions to elliptic functions, dynamics, differential equations, determinants, and number theory. Jacobi was born of Ashkenazi Jewish parentage in Potsdam...
20 KB (2,058 words) - 04:43, 3 June 2024
{L^{2}}{m^{2}r^{3}}}+{\frac {1}{m}}F(r)} The orbital equation can be derived directly from the Hamilton–Jacobi equation. Adopting the radial distance r and the azimuthal...
53 KB (8,196 words) - 09:31, 4 May 2024
Stationary-action principle (redirect from Hamilton's principal of least action)
William Rowan Hamilton and in tandem Carl Gustav Jacobi developed a variational form for classical mechanics known as the Hamilton–Jacobi equation.: 201 In...
19 KB (2,083 words) - 18:40, 22 May 2024
Four-gradient (section As a component of the SR Hamilton–Jacobi equation in relativistic analytic mechanics)
dt)(dx\,dy\,dz)} is the 4D differential volume element The Hamilton–Jacobi equation (HJE) is a formulation of classical mechanics, equivalent to other...
48 KB (8,619 words) - 16:27, 8 May 2024
of motion (Newton's law, Euler–Lagrange equation, Hamilton–Jacobi equation, etc.) is the Schrödinger equation in its most general form: i ℏ ∂ Ψ ∂ t =...
55 KB (7,476 words) - 00:15, 29 March 2024
Hamilton's principle, Hamilton's principal function, the Hamilton–Jacobi equation, Cayley-Hamilton theorem are named after Hamilton. The Hamiltonian is...
42 KB (4,620 words) - 08:22, 4 June 2024
can also be derived from the Hamilton–Jacobi equation in parabolic coordinates (ξ, η), which are defined by the equations ξ = r + x , η = r − x , {\displaystyle...
79 KB (10,213 words) - 23:48, 10 May 2024
guidance equation to be the fundamental law, and sees the Born rule as a derived concept. The second equation is a modified Hamilton–Jacobi equation for the...
27 KB (3,433 words) - 14:26, 4 June 2024
two equations: from the imaginary and real part of the Schrödinger equation follow the continuity equation and the quantum Hamilton–Jacobi equation respectively...
57 KB (7,744 words) - 19:13, 1 May 2024
differential equations Broer–Kaup equations Burgers' equation Euler equations Fokker–Planck equation Hamilton–Jacobi equation, Hamilton–Jacobi–Bellman equation Heat...
2 KB (157 words) - 18:19, 14 March 2022
The same equation can also be derived using a Lagrangian approach or the Hamilton–Jacobi equation (see below). The solution of the orbit equation is φ =...
65 KB (12,016 words) - 04:02, 23 May 2024
represents the Schrödinger equation as a quantum Hamilton–Jacobi equation. The Madelung equations are quantum Euler equations: ∂ t ρ m + ∇ ⋅ ( ρ m u ) =...
7 KB (946 words) - 08:02, 28 April 2023
binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical...
23 KB (3,771 words) - 15:52, 19 May 2024
Maxwell's equations can be derived as conditions of stationary action. Analytical mechanics Configuration space Hamilton–Jacobi equation Phase space...
16 KB (2,268 words) - 03:46, 19 November 2023
Maupertuis's principle (section Jacobi's formulation)
mechanics Hamilton's principle Gauss's principle of least constraint (also describes Hertz's principle of least curvature) Hamilton–Jacobi equation Jahnke...
13 KB (1,725 words) - 15:10, 11 March 2024
Liouville's theorem (Hamiltonian) (redirect from Liouville's Equation)
are denoted by dots, and are evaluated according to Hamilton's equations for the system. This equation demonstrates the conservation of density in phase...
24 KB (3,836 words) - 23:50, 24 May 2024
Viscosity solution (category Partial differential equations)
order equations arising in dynamic programming (the Hamilton–Jacobi–Bellman equation), differential games (the Hamilton–Jacobi–Isaacs equation) or front...
16 KB (2,597 words) - 16:44, 8 September 2023
coordinates are related to the canonical coordinates by means of the Hamilton–Jacobi equations. Linear discriminant analysis Symplectic manifold Symplectic vector...
6 KB (872 words) - 00:34, 31 October 2023
compact. This is usually of practical calculational value when the Hamilton–Jacobi equation is completely separable, and the separation constants can be solved...
9 KB (1,511 words) - 00:00, 25 April 2024
analytic mechanics (the Levi-Civita separability conditions in the Hamilton–Jacobi equation) and hydrodynamics. Born into an Italian Jewish family in Padua...
21 KB (1,947 words) - 06:41, 27 April 2024
characterisation of the additive separation of variables in the Hamilton–Jacobi equation Web, a linear system of divisors of dimension 3 Web Entertainment...
4 KB (528 words) - 10:53, 5 February 2024
it derives the Schrödinger equation from the postulated stochastic process. In this derivation, the Hamilton-Jacobi equations { ∂ ∂ x i S ± ( x , t ) =...
38 KB (7,097 words) - 18:54, 18 April 2024
in Evanston, Wyoming, USA Hamiltonian mechanics Hamilton–Jacobi equation, a set of physical equations in Hamiltonian mechanics Hamiltonian (quantum mechanics)...
8 KB (869 words) - 10:52, 16 May 2024