Hamel’s Formalism for Infinite-Dimensional Mechanical Systems

Donghua Shi; Yakov Berchenko-Kogan; Dmitry V. Zenkov; Anthony M. Bloch

doi:10.1007/s00332-016-9332-7

Hamel’s Formalism for Infinite-Dimensional Mechanical Systems

Donghua Shi^*, Yakov Berchenko-Kogan, Dmitry V. Zenkov, Anthony M. Bloch

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

In this paper, we introduce Hamel’s formalism for infinite-dimensional mechanical systems and in particular consider its applications to the dynamics of nonholonomically constrained systems. This development is a nontrivial extension of its finite-dimensional counterpart. The analysis is applied to several continuum mechanical systems of interest, including coupled systems and systems with infinitely many constraints.

Original language	English
Pages (from-to)	241-283
Number of pages	43
Journal	Journal of Nonlinear Science
Volume	27
Issue number	1
DOIs	https://doi.org/10.1007/s00332-016-9332-7
Publication status	Published - 1 Feb 2017

Keywords

Hamel equations
Momentum
Nonholonomic constraints
Symmetry

Access to Document

10.1007/s00332-016-9332-7

Cite this

Shi, D., Berchenko-Kogan, Y., Zenkov, D. V., & Bloch, A. M. (2017). Hamel’s Formalism for Infinite-Dimensional Mechanical Systems. Journal of Nonlinear Science, 27(1), 241-283. https://doi.org/10.1007/s00332-016-9332-7

@article{33d954091b7649c1b10ff57cf4ccc917,

title = "Hamel{\textquoteright}s Formalism for Infinite-Dimensional Mechanical Systems",

abstract = "In this paper, we introduce Hamel{\textquoteright}s formalism for infinite-dimensional mechanical systems and in particular consider its applications to the dynamics of nonholonomically constrained systems. This development is a nontrivial extension of its finite-dimensional counterpart. The analysis is applied to several continuum mechanical systems of interest, including coupled systems and systems with infinitely many constraints.",

keywords = "Hamel equations, Momentum, Nonholonomic constraints, Symmetry",

author = "Donghua Shi and Yakov Berchenko-Kogan and Zenkov, {Dmitry V.} and Bloch, {Anthony M.}",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2017",

month = feb,

day = "1",

doi = "10.1007/s00332-016-9332-7",

language = "English",

volume = "27",

pages = "241--283",

journal = "Journal of Nonlinear Science",

issn = "0938-8974",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Hamel’s Formalism for Infinite-Dimensional Mechanical Systems

AU - Shi, Donghua

AU - Berchenko-Kogan, Yakov

AU - Zenkov, Dmitry V.

AU - Bloch, Anthony M.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - In this paper, we introduce Hamel’s formalism for infinite-dimensional mechanical systems and in particular consider its applications to the dynamics of nonholonomically constrained systems. This development is a nontrivial extension of its finite-dimensional counterpart. The analysis is applied to several continuum mechanical systems of interest, including coupled systems and systems with infinitely many constraints.

AB - In this paper, we introduce Hamel’s formalism for infinite-dimensional mechanical systems and in particular consider its applications to the dynamics of nonholonomically constrained systems. This development is a nontrivial extension of its finite-dimensional counterpart. The analysis is applied to several continuum mechanical systems of interest, including coupled systems and systems with infinitely many constraints.

KW - Hamel equations

KW - Momentum

KW - Nonholonomic constraints

KW - Symmetry

UR - http://www.scopus.com/inward/record.url?scp=84984817894&partnerID=8YFLogxK

U2 - 10.1007/s00332-016-9332-7

DO - 10.1007/s00332-016-9332-7

M3 - Article

AN - SCOPUS:84984817894

SN - 0938-8974

VL - 27

SP - 241

EP - 283

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

IS - 1

ER -

Hamel’s Formalism for Infinite-Dimensional Mechanical Systems

Abstract

Keywords

Access to Document

Other files and links

Cite this