Discrete Hamiltonian variational integrators
نویسندگان
چکیده
منابع مشابه
Discrete Hamiltonian variational integrators
We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system, by considering a Legendre transformation of Jacobi’s solution of the Hamilton–Jacobi equation. This provides an exact correspondence between continuous and discrete Hamiltonian mechanics, which arise from the continuousand discrete-time H...
متن کاملSpectral variational integrators for semi-discrete Hamiltonian wave equations
In this paper, we present a highly accurate Hamiltonian structure-preserving numerical method for simulating Hamiltonian wave equations. This method is obtained by applying spectral variational integrators (SVI) to the system of Hamiltonian ODEs which are derived from the spatial semi-discretization of the Hamiltonian PDE. The spatial variable is discretized by using high-order symmetric finite...
متن کاملProperties of Hamiltonian Variational Integrators
The field of geometric numerical integration(GNI) seeks to exploit the underlying (geometric)structure of a dynamical system in order to construct numerical methods that exhibit desirable properties of stability and/or preservation of invariants of the flow. Variational Integrators are built for Hamiltonian systems by discretizing the generating function of the symplectic flow, rather than disc...
متن کاملDiscrete mechanics and variational integrators
This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints ...
متن کاملLagrangian and Hamiltonian Taylor variational integrators
In this paper, we present a variational integrator that is based on an approximation of the Euler–Lagrange boundary-value problem via Taylor’s method. This can be viewed as a special case of the shooting-based variational integrator. The Taylor variational integrator exploits the structure of the Taylor method, which results in a shooting method that is one order higher compared to other shooti...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2011
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drq027