On the Dynamics of Systems with Two Degrees of Freedom

被引：0

作者：

Denisova, N., V ^{[1
,2
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow 119991, Russia

[2] Demidov Yaroslavl State Univ, Yaroslavl 150000, Russia

来源：

DOKLADY MATHEMATICS | 2022年 / 105卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

conformal coordinates; conditional integrals; invariant tori;

D O I：

10.1134/S1064562422010021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The dynamics of systems in a potential field is considered in the case where kinetic energy can be represented in conformal form. In the case of two degrees of freedom, conformal coordinates always exist. It is assumed that the system can additionally experience gyroscopic forces. For a fixed value of the total energy, the equations of motion are reduced to a simple "universal" form by changing time. A case of integrability of the equations of motion at fixed total energy is indicated.

引用

页码：1 / 5

页数：5

共 50 条

[1] On the Dynamics of Systems with Two Degrees of Freedom
N. V. Denisova
[J]. Doklady Mathematics, 2022, 105 : 1 - 5
[2] 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
[3] ON DYNAMICS OF SEVERAL DEGREES OF FREEDOM SYSTEMS
SIKORA, J
BOGACZ, R
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1993, 73 (4-5): : T118 - T122
[4] Dynamics of singularly perturbed nonlinear systems with two degrees-of-freedom
Bajaj, AK
Georgiou, IT
Corless, M
[J]. IUTAM SYMPOSIUM ON INTERACTION BETWEEN DYNAMICS AND CONTROL IN ADVANCED MECHANICAL SYSTEMS, 1997, 52 : 9 - 16
[5] Dynamical systems with two degrees of freedom
Birkhoff, GD
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1917, 3 : 314 - 316
[6] Dynamical systems with two degrees of freedom
Birkhoff, George D.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1917, 18 (1-4) : 199 - 300
[7] On dynamics of an aeroelastic system with two degrees of freedom
Selyutskiy, Y. D.
[J]. APPLIED MATHEMATICAL MODELLING, 2019, 67 : 449 - 455
[8] ON THE METRIPLECTIC DYNAMICS FOR SYSTEMS WITH INTERNAL DEGREES OF FREEDOM
TURSKI, LA
[J]. PHYSICS LETTERS A, 1987, 125 (09) : 461 - 464
[9] Vibrational Dissipative Systems with Two Degrees of Freedom
Petrov, A. G.
[J]. DOKLADY PHYSICS, 2021, 66 (09) : 264 - 268
[10] On stability in Hamiltonian systems with two degrees of freedom
Yu. N. Bibikov
[J]. Mathematical Notes, 2014, 95 : 174 - 179

← 1 2 3 4 5 →