Discrete variational Lie group formulation of geometrically exact beam dynamics

被引：42

作者：

Demoures, F. ^{[1
]}

Gay-Balmaz, F. ^{[2
]}

Leyendecker, S. ^{[3
]}

Ober-Bloebaum, S. ^{[4
]}

Ratiu, T. S. ^{[1
]}

Weinand, Y. ^{[5
]}

机构：

[1] Ecole Polytech Fed Lausanne, Sect Math, CH-1015 Lausanne, Switzerland

[2] Ecole Normale Super, CNRS, Lab Meteorol Dynam, F-75005 Paris, France

[3] Univ Erlangen Nurnberg, Dept Mech Engn, D-91058 Erlangen, Germany

[4] Univ Paderborn, Dept Math, D-33098 Paderborn, Germany

[5] Ecole Polytech Fed Lausanne, Civil Engn Inst, CH-1015 Lausanne, Switzerland

来源：

NUMERISCHE MATHEMATIK | 2015年 / 130卷 / 01期

基金：

瑞士国家科学基金会;

关键词：

FINITE-ELEMENT; CONSTRAINED DYNAMICS; LAGRANGIAN MECHANICS; EULER-POINCARE; SYSTEMS; INTEGRATORS; ENERGY; ROTATIONS; RODS; PARAMETRIZATION;

D O I：

10.1007/s00211-014-0659-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resulting scheme preserves both the discrete momentum maps and symplectic structures, and exhibits almost-perfect energy conservation. Comparisons with existing numerical schemes are provided and the convergence behavior is analyzed numerically.

引用

页码：73 / 123

页数：51

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