Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanic.pdf

下载文档 降价啦

6
0
约 40页
2017-04-06 发布于江苏
举报
版权申诉
保障服务

Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanic.pdf

1、本文档共40页，可阅读全部内容。
2、有哪些信誉好的足球投注网站（book118）网站文档一经付费（服务费），不意味着购买了该文档的版权，仅供个人/单位学习、研究之用，不得用于商业用途，未经授权，严禁复制、发行、汇编、翻译或者网络传播等，侵权必究。
3、本站所有内容均由合作方或网友上传，本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺！文档内容仅供研究参考，付费前请自行鉴别。如您付费，意味着您自己接受本站规则且自行承担风险，本站不退款、不进行额外附加服务；查看《如何避免下载的几个坑》。如果您已付费下载过本站文档，您可以点击这里二次下载。
4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等，请点击“版权申诉”（推荐），也可以打举报电话：400-050-0827(电话支持时间：9:00-18:30)。

Variational Integrators and the Newmark Algorithm for Conservative and Dissipative Mechanic

Variational Integrators and the NewmarkAlgorithm for Conservative and DissipativeMechanical SystemsC. KaneGraduate Aeronautical Laboratories and CDSCalifornia Institute of TechnologyPasadena, CA 91125kane@cds.caltech.eduJ. E. MarsdenCDS 107-81California Institute of TechnologyPasadena, CA 91125marsden@cds.caltech.eduM. OrtizGraduate Aeronautical LaboratoriesCalifornia Institute of TechnologyPasadena, CA 91125ortiz@madrid.caltech.eduM. WestCDS 107-81California Institute of TechnologyPasadena, CA 91125mwest@cds.caltech.eduMarch, 1999, This version: November 25, 1999 1 AbstractThe purpose of this work is twofold. First, we demonstrate analyt-ically that the classical Newmark family as well as related integrationalgorithms are variational in the sense of the Veselov formulation ofdiscrete mechanics. Such variational algorithms are well known to besymplectic and momentum preserving and to often have excellent globalenergy behavior. This analytical result is veried through numerical ex-amples and is believed to be one of the primary reasons that this classof algorithms performs so well.Second, we develop algorithms for mechanical systems with forcing,and in particular, for dissipative systems. In this case, we develop inte-grators that are based on a discretization of the Lagrange dAlembertprinciple as well as on a variational formulation of dissipation. It isdemonstrated that these types of structured integrators have good nu-merical behavior in terms of obtaining the correct amounts by whichthe energy changes over the integration run.Contents1 Introduction and Background 31.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Background on Geometric Integrators . . . . . . . . . . . . . . 42 Variational Integrators 62.1 A Review of Variational Integrators . . . . . . . . . . . . . . . 62.2 Construction of Mechanical Integrators . . . . . . . . . . . . . 102.3 Representations of Variational Integrators . . . . . . . . . . . 113 The Newmark Algorit