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We report relations between invariant manifolds of saddle orbits (Lyapunov family) around a saddle-center equilibrium point and lowest periodic orbits on the two degree of freedom swing equation system. The system consists of two generators operating onto an infinite bus. In this system, a stable equilibrium point represents the normal operation state, and to understand its basin structure is important in connection with practical situations. The Lyapunov families appear under conservative conditions and their invariant manifolds constitute separatrices between trapped and divergent motions. These separatrices continuously deform and become basin boundaries, if changing the system to dissipative one, so that to investigate those manifolds is meaningful. While, in the field of two degree of freedom motions, systems with saddle loops to a saddle-center are well studied, and existence of transverse homoclinic structure of separatrix manifolds is reported. However our investigating system has no such loops. It is interesting what separatrix structure exists without trivial saddle loops. In this report, we focus on above invariant manifolds and lowest periodic orbits which are foliated for the Hamiltonian level.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.9 pp.1692-1700

- Publication Date
- 1999/09/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)

- Category

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Yoshitaka HASEGAWA, Yoshisuke UEDA, "On Trapped Motions and Separatrix Structures of a Two Degree of Freedom Swing Equation System" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 9, pp. 1692-1700, September 1999, doi: .

Abstract: We report relations between invariant manifolds of saddle orbits (Lyapunov family) around a saddle-center equilibrium point and lowest periodic orbits on the two degree of freedom swing equation system. The system consists of two generators operating onto an infinite bus. In this system, a stable equilibrium point represents the normal operation state, and to understand its basin structure is important in connection with practical situations. The Lyapunov families appear under conservative conditions and their invariant manifolds constitute separatrices between trapped and divergent motions. These separatrices continuously deform and become basin boundaries, if changing the system to dissipative one, so that to investigate those manifolds is meaningful. While, in the field of two degree of freedom motions, systems with saddle loops to a saddle-center are well studied, and existence of transverse homoclinic structure of separatrix manifolds is reported. However our investigating system has no such loops. It is interesting what separatrix structure exists without trivial saddle loops. In this report, we focus on above invariant manifolds and lowest periodic orbits which are foliated for the Hamiltonian level.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_9_1692/_p

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@ARTICLE{e82-a_9_1692,

author={Yoshitaka HASEGAWA, Yoshisuke UEDA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={On Trapped Motions and Separatrix Structures of a Two Degree of Freedom Swing Equation System},

year={1999},

volume={E82-A},

number={9},

pages={1692-1700},

abstract={We report relations between invariant manifolds of saddle orbits (Lyapunov family) around a saddle-center equilibrium point and lowest periodic orbits on the two degree of freedom swing equation system. The system consists of two generators operating onto an infinite bus. In this system, a stable equilibrium point represents the normal operation state, and to understand its basin structure is important in connection with practical situations. The Lyapunov families appear under conservative conditions and their invariant manifolds constitute separatrices between trapped and divergent motions. These separatrices continuously deform and become basin boundaries, if changing the system to dissipative one, so that to investigate those manifolds is meaningful. While, in the field of two degree of freedom motions, systems with saddle loops to a saddle-center are well studied, and existence of transverse homoclinic structure of separatrix manifolds is reported. However our investigating system has no such loops. It is interesting what separatrix structure exists without trivial saddle loops. In this report, we focus on above invariant manifolds and lowest periodic orbits which are foliated for the Hamiltonian level.},

keywords={},

doi={},

ISSN={},

month={September},}

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TY - JOUR

TI - On Trapped Motions and Separatrix Structures of a Two Degree of Freedom Swing Equation System

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1692

EP - 1700

AU - Yoshitaka HASEGAWA

AU - Yoshisuke UEDA

PY - 1999

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E82-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 1999

AB - We report relations between invariant manifolds of saddle orbits (Lyapunov family) around a saddle-center equilibrium point and lowest periodic orbits on the two degree of freedom swing equation system. The system consists of two generators operating onto an infinite bus. In this system, a stable equilibrium point represents the normal operation state, and to understand its basin structure is important in connection with practical situations. The Lyapunov families appear under conservative conditions and their invariant manifolds constitute separatrices between trapped and divergent motions. These separatrices continuously deform and become basin boundaries, if changing the system to dissipative one, so that to investigate those manifolds is meaningful. While, in the field of two degree of freedom motions, systems with saddle loops to a saddle-center are well studied, and existence of transverse homoclinic structure of separatrix manifolds is reported. However our investigating system has no such loops. It is interesting what separatrix structure exists without trivial saddle loops. In this report, we focus on above invariant manifolds and lowest periodic orbits which are foliated for the Hamiltonian level.

ER -