## Abstract

The Toda Chain is a nonlinear mass-spring chain which can in principle be integrated analytically by the action-angle theory of classical mechanics. We show that the transformation from physical variables to action variables can be implemented very simply on a computer. We study the correspondence between action variables and the motions of the chain, and find the role of the action variables to be very similar to the role of normal-mode amplitudes in the harmonic chain. This similarity leads to a partly rigorous, partly heuristic normal-mode analysis for the Toda chain. New results are obtained when this normal-mode analysis is applied to certain perturbations of the Toda chain such as the Fermi-Pasta-Ulam chain or the Toda chain with a mass impurity.

Original language | English (US) |
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Pages (from-to) | 157-209 |

Number of pages | 53 |

Journal | Journal of Computational Physics |

Volume | 45 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1982 |

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics