Results 251 to 260 of about 293,764 (287)

Linearization of Hamiltonian and Gradient Systems

IMA Journal of Mathematical Control and Information, 1984
Necessary and sufficient conditions are derived in order to transform a nonlinear Hamiltonian or gradient system by a change of coordinates of its state space into a linear Hamiltonian or gradient system. It is shown that such a transformaion necessarily respects the symplectic or metrical structure. The conditions are given in terms of the observation
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Linear Hamiltonian Systems

1990
Consider a system of m linear equations with continuous T -periodic coefficients: $$ \dot x = M\left( t \right)x $$ (1) where M (t) is a real m × m matrix, depending continuously on t ∈ ℝ such that: $$ M\left( {t + T} \right) = M\left( t \right) $$ (2) .
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Theorem on linearized Hamiltonian systems

Journal of Mathematical Physics, 1985
Many nonlinear field equations can be written in Hamiltonian form. Thus the equation ∂tu=K(u) can be written ∂tu =[u, H], where H is an appropriate functional and [ , ] is a Poisson bracket. Frequently one is interested in the solution of the equation linearized about a given solution, i.e., the equation ∂t τ=K′(τ), where K′(τ)=(d/dε) K(u+ετ)‖ε=0.
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Regular Linear Hamiltonian Systems

2002
Examination of systems of differential equations began in the early 1900’s with the work of G. D. Birkhoff and R. E. Langer (see [2] for example.), R. L. Wilder and L. Schlesinger. G. A. Bliss [3] in 1926 seems to have been the first to discuss regular, self-adjoint differential systems.
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Point Spectrum: Linear Hamiltonian Systems

2013
Hamiltonian systems are about balance, with the energy and other invariants preserved under the flow. For a spatially localized critical point of a Hamiltonian system, the balance is reflected in the symmetry of the spectrum, which typically pins the essential spectrum to the imaginary axis in unweighted spaces.
Todd Kapitula, Keith Promislow
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General moment invariants for linear Hamiltonian systems

Physical Review A, 1992
This paper studies the behavior of the moments of a particle distribution as it is transported through a Hamiltonian system. Functions of moments that remain invariant for an arbitrary linear Hamiltonian system are constructed. These functions remain approximately invariant for Hamiltonian systems that are not strongly nonlinear. Consequently, they can
, Dragt, , Neri, , Rangarajan
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Block Boundary Value Methods for linear Hamiltonian systems

Applied Mathematics and Computation, 1997
The article continues the work of the authors on boundary value methods for the numerical integration of ordinary differential equations. Here they study the application of these methods to the symplectic integration of linear Hamiltonian systems. Compared with the standard approach to linear multistep methods [see e.g. \textit{T. Eirola} and \textit{J.
BRUGNANO, LUIGI, TRIGIANTE, DONATO
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Stability of linear almost-Hamiltonian periodic systems

Journal of Applied Mathematics and Mechanics, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Linearized structures of lagrangian, hamiltonian, and quasi-hamiltonian systems

Physics Letters A, 1986
Abstract Linearized structures are found for general lagrangian, hamiltonian, and quasi-hamiltonian systems, as well as for Lax and zero-curvature representations.
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Linear Versus Nonlinear Stability in Hamiltonian Systems

2017
The stability of periodic solutions of time-independent Hamiltonian systems is often studied by linearization techniques. In the case of two degrees of freedom near stable equilibrium this is a correct procedure, in the case of three or more degrees of freedom we present some counterexamples.
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