### Abstract

In this paper, some analysis techniques for general time-periodic nonlinear Hamiltonian dynamical systems have been presented. First, the well-known Lyapunov-Floquet transformation is utilized to convert the time-periodic dynamical system to a form in which the linear part is time invariant. At this stage two viable alternatives are suggested. In the first approach, the resulting dynamical system is transformed to a Hamiltonian normal form through an application of permutation matrices. In the second approach, the resulting quasilinear time-periodic system is directly analyzed via time-dependent normal form theory.

Original language | English (US) |
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Title of host publication | American Society of Mechanical Engineers, Design Engineering Division (Publication) DE |

Editors | S.C. Sinha, J.P. Cusumano, F. Pfeiffer, A.K. Bajaj, R.A. Ibrahim, al et al |

Pages | 375-386 |

Number of pages | 12 |

Volume | 84 |

Edition | 3 Pt A/1 |

State | Published - 1995 |

Externally published | Yes |

Event | Proceedings of the 1995 ASME Design Engineering Technical Conference. Part A-1 - Boston, MA, USA Duration: Sep 17 1995 → Sep 20 1995 |

### Other

Other | Proceedings of the 1995 ASME Design Engineering Technical Conference. Part A-1 |
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City | Boston, MA, USA |

Period | 9/17/95 → 9/20/95 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*American Society of Mechanical Engineers, Design Engineering Division (Publication) DE*(3 Pt A/1 ed., Vol. 84, pp. 375-386)

**On the analysis of time-periodic nonlinear Hamiltonian dynamical systems.** / Butcher, Eric; Sinha, S. C.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*American Society of Mechanical Engineers, Design Engineering Division (Publication) DE.*3 Pt A/1 edn, vol. 84, pp. 375-386, Proceedings of the 1995 ASME Design Engineering Technical Conference. Part A-1, Boston, MA, USA, 9/17/95.

}

TY - GEN

T1 - On the analysis of time-periodic nonlinear Hamiltonian dynamical systems

AU - Butcher, Eric

AU - Sinha, S. C.

PY - 1995

Y1 - 1995

N2 - In this paper, some analysis techniques for general time-periodic nonlinear Hamiltonian dynamical systems have been presented. First, the well-known Lyapunov-Floquet transformation is utilized to convert the time-periodic dynamical system to a form in which the linear part is time invariant. At this stage two viable alternatives are suggested. In the first approach, the resulting dynamical system is transformed to a Hamiltonian normal form through an application of permutation matrices. In the second approach, the resulting quasilinear time-periodic system is directly analyzed via time-dependent normal form theory.

AB - In this paper, some analysis techniques for general time-periodic nonlinear Hamiltonian dynamical systems have been presented. First, the well-known Lyapunov-Floquet transformation is utilized to convert the time-periodic dynamical system to a form in which the linear part is time invariant. At this stage two viable alternatives are suggested. In the first approach, the resulting dynamical system is transformed to a Hamiltonian normal form through an application of permutation matrices. In the second approach, the resulting quasilinear time-periodic system is directly analyzed via time-dependent normal form theory.

UR - http://www.scopus.com/inward/record.url?scp=0029428928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029428928&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029428928

VL - 84

SP - 375

EP - 386

BT - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE

A2 - Sinha, S.C.

A2 - Cusumano, J.P.

A2 - Pfeiffer, F.

A2 - Bajaj, A.K.

A2 - Ibrahim, R.A.

A2 - et al, al

ER -