Hamiltonian system

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• ID : Q2072471

말뭉치

1. In mechanics, a Hamiltonian system describes a motion involving holonomic constraints and forces which have a potential (cf.
2. Another general concept which sometimes makes it possible to integrate a Hamiltonian system involves passing to an auxiliary partial differential equation — the so-called Hamilton–Jacobi equation (cf.
3. A Hamiltonian system is a dynamical system governed by Hamilton's equations.
4. Informally, a Hamiltonian system is a mathematical formalism developed by Hamilton to describe the evolution equations of a physical system.
5. One of the stronger constraints imposed by Hamiltonian structure relates to stability: it is impossible for a trajectory to be asymptotically stable in a Hamiltonian system.
6. Kolmogorov, Arnold and Moser proved that a sufficiently smooth, nearly-integrable Hamiltonian system still has many such invariant tori (see KAM theory).
7. In the autonomous case, a Hamiltonian system conserves energy, however, it is easy to construct nonHamiltonian systems that also conserve an energy-like quantity.
8. A Hamiltonian system may be understood as a fiber bundle E over time R, with the fibers E t , t ∈ R, being the position space.
9. Any smooth real-valued function H on a symplectic manifold can be used to define a Hamiltonian system.
10. Firstly, finding a nonconstant particular solution of the considered Hamiltonian system.
11. Its associated Hamiltonian system is This differential system is known as the Hamiltonian system with Nelson potential.
12. This paper aims for a fractional Hamiltonian system of variable order.
13. Furthermore, the equilibrium points of the Hamiltonian system occur at the critical points of \(H\) (where the partials of \(H\) vanish).
14. Let us examine the possible types of equilibrium solutions for a Hamiltonian system.
15. *} Show that this system is a Hamiltonian system.
16. The Hamiltonian system plays a vital part in describing the evolution of a physical system.
17. Then (i) with and symplectic manifolds is called a full Hamiltonian system if is a Lagrangian submanifold of where is derived from the local coordinates.
18. (ii) is called degenerate Hamiltonian system if there exists a full Hamiltonian system such that is a submanifold of .
19. The Linear system in state form given by (11) is a linear Hamiltonian system if and are symplectic linear spaces.
20. After feedback, this system will again be an affine Hamiltonian system.

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위키데이터

• ID : Q2072471