### Abstract

The motion of a spherical pendulum is characterized by the fact that all trajectories are relative periodic orbits with respect to its circle group of symmetry (invariance by rotations around the vertical axis). When the rotational symmetry is broken by some mechanical effect, more complicated, possibly chaotic behavior is expected. When, in particular, the symmetry reduces to the dihedral group D _{n} of symmetries of a regular n-gon, n > 2, the motion itself undergoes dramatic changes even when the amplitude of oscillations is small, which we intend to explain in this paper. Numerical simulations confirm the validity of the theory and show evidence of new interesting effects when the amplitude of the oscillations is larger (symmetric chaos).

Original language | English (US) |
---|---|

Pages (from-to) | 1140-1158 |

Number of pages | 19 |

Journal | SIAM Journal on Applied Dynamical Systems |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2005 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Analysis
- Modeling and Simulation

### Cite this

}

_{n}symmetric perturbation',

*SIAM Journal on Applied Dynamical Systems*, vol. 4, no. 4, pp. 1140-1158. https://doi.org/10.1137/040616681

**The motion of the spherical pendulum subjected to a D _{n} symmetric perturbation.** / Chossat, Pascal; Bou-Rabee, Nawaf.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The motion of the spherical pendulum subjected to a D n symmetric perturbation

AU - Chossat, Pascal

AU - Bou-Rabee, Nawaf

PY - 2005/12/1

Y1 - 2005/12/1

N2 - The motion of a spherical pendulum is characterized by the fact that all trajectories are relative periodic orbits with respect to its circle group of symmetry (invariance by rotations around the vertical axis). When the rotational symmetry is broken by some mechanical effect, more complicated, possibly chaotic behavior is expected. When, in particular, the symmetry reduces to the dihedral group D n of symmetries of a regular n-gon, n > 2, the motion itself undergoes dramatic changes even when the amplitude of oscillations is small, which we intend to explain in this paper. Numerical simulations confirm the validity of the theory and show evidence of new interesting effects when the amplitude of the oscillations is larger (symmetric chaos).

AB - The motion of a spherical pendulum is characterized by the fact that all trajectories are relative periodic orbits with respect to its circle group of symmetry (invariance by rotations around the vertical axis). When the rotational symmetry is broken by some mechanical effect, more complicated, possibly chaotic behavior is expected. When, in particular, the symmetry reduces to the dihedral group D n of symmetries of a regular n-gon, n > 2, the motion itself undergoes dramatic changes even when the amplitude of oscillations is small, which we intend to explain in this paper. Numerical simulations confirm the validity of the theory and show evidence of new interesting effects when the amplitude of the oscillations is larger (symmetric chaos).

UR - http://www.scopus.com/inward/record.url?scp=33644985614&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644985614&partnerID=8YFLogxK

U2 - 10.1137/040616681

DO - 10.1137/040616681

M3 - Article

VL - 4

SP - 1140

EP - 1158

JO - SIAM Journal on Applied Dynamical Systems

JF - SIAM Journal on Applied Dynamical Systems

SN - 1536-0040

IS - 4

ER -

_{n}symmetric perturbation. SIAM Journal on Applied Dynamical Systems. 2005 Dec 1;4(4):1140-1158. https://doi.org/10.1137/040616681