Differential invariants of a class of Lagrangian systems with two degrees of freedom

被引：4

作者：

Bagderina, Yulia Yu. ^{[1
]}

Tarkhanov, Nikolai N. ^{[2
]}

机构：

[1] Russian Acad Sci, Ctr Comp, Inst Math, Ufa 450008, Russia

[2] Univ Potsdam, Inst Math, D-14469 Potsdam, Germany

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 410卷 / 02期

关键词：

Equivalence; Differential invariant; Euler-Lagrange equations; HIGHER-ORDER LAGRANGIANS; EQUIVALENCE PROBLEM; SYMMETRIES; CLASSIFICATION;

D O I：

10.1016/j.jmaa.2013.08.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：733 / 749

页数：17

共 50 条

[31] ON A CLASS OF COUPLED NON-LINEAR SYSTEMS WITH 2 DEGREES OF FREEDOM
DASARATHY, BV
[J]. JOURNAL OF SOUND AND VIBRATION, 1969, 10 (02) : 327 - +
[32] A class of discontinuous dynamical systems III. Degrees of freedom analysis
Moudgalya, KM
[J]. CHEMICAL ENGINEERING SCIENCE, 2001, 56 (18) : 5443 - 5447
[33] AN EFFECTIVE LAGRANGIAN FOR THE LIGHT DEGREES OF FREEDOM IN THE TECHNICOLOR MODELS
KAUL, R
[J]. NUCLEAR PHYSICS B, 1981, 182 (1-2) : 158 - 172
[34] Topology, singularities and integrability in Hamiltonian systems with two degrees of freedom
Bolotin, S. V.
Kozlov, V. V.
[J]. IZVESTIYA MATHEMATICS, 2017, 81 (04) : 671 - 687
[35] On chaotic dynamics in "pseudobilliard" Hamiltonian systems with two degrees of freedom
Eleonsky, VM
Korolev, VG
Kulagin, NE
[J]. CHAOS, 1997, 7 (04) : 710 - 730
[36] Two degrees of freedom quasi-bi-Hamiltonian systems
Brouzet, R
Caboz, R
Rabenivo, J
Ravoson, V
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1996, 29 (09): : 2069 - 2076
[37] The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom
Bibikov, Yu. N.
[J]. PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 2013, 77 (02): : 167 - 171
[38] The invariants of differential systems
Delassus, E
[J]. COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1907, 145 : 617 - 619
[39] Control of underactuated mechanical systems with two degrees of freedom and symmetry
Olfati-Saber, R
[J]. PROCEEDINGS OF THE 2000 AMERICAN CONTROL CONFERENCE, VOLS 1-6, 2000, : 4092 - 4096
[40] Reversible maps in two-degrees of freedom Hamiltonian systems
Zare, K
Tanikawa, K
[J]. CHAOS, 2002, 12 (03) : 699 - 705

← 1 2 3 4 5 →