Topic
Variational integrator
About: Variational integrator is a research topic. Over the lifetime, 1391 publications have been published within this topic receiving 40421 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
2 Sep 2009
TL;DR: In this article, the authors present a model for symmetric integration of non-Canonical Hamiltonian systems and a model of symmetric Hamiltonian integration with symmetric integrators.
Abstract: Examples and Numerical Experiments.- Numerical Integrators.- Order Conditions, Trees and B-Series.- Conservation of First Integrals and Methods on Manifolds.- Symmetric Integration and Reversibility.- Symplectic Integration of Hamiltonian Systems.- Non-Canonical Hamiltonian Systems.- Structure-Preserving Implementation.- Backward Error Analysis and Structure Preservation.- Hamiltonian Perturbation Theory and Symplectic Integrators.- Reversible Perturbation Theory and Symmetric Integrators.- Dissipatively Perturbed Hamiltonian and Reversible Systems.- Oscillatory Differential Equations with Constant High Frequencies.- Oscillatory Differential Equations with Varying High Frequencies.- Dynamics of Multistep Methods.
4,232 citations
TL;DR: For Hamiltonian systems of the form H = T(p)+V(q) a method was shown to construct explicit and time reversible symplectic integrators of higher order as discussed by the authors.
2,516 citations
TL;DR: In this paper, a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles is presented, including the Verlet, SHAKE, RATTLE, Newmark, and the symplectic partitioned Runge-Kutta schemes.
Abstract: 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 in a natural way. Amongst the many specific schemes treated as examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplectic partitioned Runge–Kutta schemes are presented.
1,911 citations
Book•
1 Jan 2002
TL;DR: In this paper, the authors present a review of the work, energy, and variational calculus of solid mechanics and their application in the analysis of plate models. But their focus is on the theory and analysis of plates.
Abstract: Preface xv 1 Introduction 1 2 Mathematical Preliminaries 8 3 Review Of Equations Of Solid Mechanics 48 4 Work, Energy, And Variational Calculus 79 5 Energy Principles Of Structural 133 6 Dynamical Systems: Hamilton's Principle 177 7 Direct Variational Methods 204 8 Theory And Analysis Of Plates 299 9 The Finite Element Method 433 10 Mixed Variational Formulations 502 Answers / Solutions to Selected Problems 544 Index 583 About the Author 591
1,233 citations
1,203 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 19 |
| 2023 | 25 |
| 2022 | 94 |
| 2021 | 42 |
| 2020 | 30 |