General techniques for constructing variational integrators |
| |
Authors: | Melvin Leok Tatiana Shingel |
| |
Institution: | Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA |
| |
Abstract: | The numerical analysis of variational integrators relies on variational error analysis, which relates the order of accuracy
of a variational integrator with the order of approximation of the exact discrete Lagrangian by a computable discrete Lagrangian.
The exact discrete Lagrangian can either be characterized variationally, or in terms of Jacobi’s solution of the Hamilton-Jacobi
equation. These two characterizations lead to the Galerkin and shooting constructions for discrete Lagrangians, which depend
on a choice of a numerical quadrature formula, together with either a finite-dimensional function space or a one-step method.
We prove that the properties of the quadrature formula, finite-dimensional function space, and underlying one-step method
determine the order of accuracy and momentum-conservation properties of the associated variational integrators. We also illustrate
these systematic methods for constructing variational integrators with numerical examples. |
| |
Keywords: | Geometric numerical integration geometric mechanics symplectic integrator variational integrator Lagrangian mechanics |
本文献已被 SpringerLink 等数据库收录! |
| 点击此处可从《Frontiers of Mathematics in China》浏览原始摘要信息 |
| 点击此处可从《Frontiers of Mathematics in China》下载免费的PDF全文 |