Discrete variational Hamiltonian mechanics

被引：72

作者：

Lall, S. ^{[1
]}

West, M. ^{[1
]}

机构：

[1] Stanford Univ, Stanford, CA 94305 USA

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2006年 / 39卷 / 19期

关键词：

D O I：

10.1088/0305-4470/39/19/S11

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms.

引用

页码：5509 / 5519

页数：11

共 23 条

[1]

[Anonymous], J COMPUT MATH

[2]

Bertsekas D. P., 2005, DYNAMIC PROGRAMMING, VI

[3]

Boyd S., 2004, CONVEX OPTIMIZATION

[4] SYMPLECTIC INTEGRATION OF HAMILTONIAN-SYSTEMS [J].

CHANNELL, PJ ;

SCOVEL, C .

NONLINEARITY, 1990, 3 (02) :231-259

[5]

Clarke F.H., 1990, OPTIMIZATION NONSMOO

[6]

DELEON M, 2003, MATH0311169

[7]

FENG K, 1986, J COMPUT MATH, V4, P279

[8]

Goldstein H, 1980, CLASSICAL MECH

[9] Time integration and discrete Hamiltonian systems [J].

Gonzalez, O .

JOURNAL OF NONLINEAR SCIENCE, 1996, 6 (05) :449-467

[10]

Hairer E., 2010, Springer Series in Computational Mathematics, V31

← 1 2 3 →