Implicit Hamiltonian systems with symmetry

Arjan van der Schaft

doi:10.1016/S0034-4877(98)80176-6

Implicit Hamiltonian systems with symmetry

Arjan van der Schaft

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

48 Citations (Scopus)

5 Downloads (Pure)

Abstract

Implicit Hamiltonian systems with symmetry are treated by exploiting the notion of symmetry of Dirac structures. It is shown how Dirac structures can be reduced to Dirac structures on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system. The approach is specialized to nonholonomic mechanical systems with symmetry.

Original language	Undefined
Pages (from-to)	203-221
Number of pages	19
Journal	Reports on mathematical physics
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/S0034-4877(98)80176-6
Publication status	Published - 1998

Keywords

Hamiltonian systems
Dirac structures
Reduction
METIS-140316
nonholonomic constraints
implicit systems
IR-73839
Symmetry

Access to Document

10.1016/S0034-4877(98)80176-6

Cite this

@article{9cc60dbdc42d4579bc4fb5d355f1f594,

title = "Implicit Hamiltonian systems with symmetry",

abstract = "Implicit Hamiltonian systems with symmetry are treated by exploiting the notion of symmetry of Dirac structures. It is shown how Dirac structures can be reduced to Dirac structures on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system. The approach is specialized to nonholonomic mechanical systems with symmetry.",

keywords = "Hamiltonian systems, Dirac structures, Reduction, METIS-140316, nonholonomic constraints, implicit systems, IR-73839, Symmetry",

author = "{van der Schaft}, Arjan",

year = "1998",

doi = "10.1016/S0034-4877(98)80176-6",

language = "Undefined",

volume = "41",

pages = "203--221",

journal = "Reports on mathematical physics",

issn = "0034-4877",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Implicit Hamiltonian systems with symmetry

AU - van der Schaft, Arjan

PY - 1998

Y1 - 1998

N2 - Implicit Hamiltonian systems with symmetry are treated by exploiting the notion of symmetry of Dirac structures. It is shown how Dirac structures can be reduced to Dirac structures on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system. The approach is specialized to nonholonomic mechanical systems with symmetry.

AB - Implicit Hamiltonian systems with symmetry are treated by exploiting the notion of symmetry of Dirac structures. It is shown how Dirac structures can be reduced to Dirac structures on the orbit space of the symmetry group, leading to a reduced implicit (generalized) Hamiltonian system. The approach is specialized to nonholonomic mechanical systems with symmetry.

KW - Hamiltonian systems

KW - Dirac structures

KW - Reduction

KW - METIS-140316

KW - nonholonomic constraints

KW - implicit systems

KW - IR-73839

KW - Symmetry

U2 - 10.1016/S0034-4877(98)80176-6

DO - 10.1016/S0034-4877(98)80176-6

M3 - Article

SN - 0034-4877

VL - 41

SP - 203

EP - 221

JO - Reports on mathematical physics

JF - Reports on mathematical physics

IS - 2

ER -