### Abstract

This work considers classical problem of motion in systems with dry friction, known as the Painleve problem. This problem takes place in the presence of collisions of a rod with a at surface, and the use of the classical mechanics method runs into difficulties due to the impulsive nature of the interaction force that does not lend itself to exact calculations. The methodology suggested by the authors in recent years permits approximating a family of solutions corresponding to a large value of the stiffness coefficient of the obstacle.

Original language | English (US) |
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Title of host publication | Proceedings of the 18th IFAC World Congress |

Publisher | IFAC Secretariat |

Pages | 3463-3473 |

Number of pages | 11 |

Edition | 1 PART 1 |

ISBN (Print) | 9783902661937 |

DOIs | |

State | Published - Jan 1 2011 |

### Publication series

Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
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Number | 1 PART 1 |

Volume | 44 |

ISSN (Print) | 1474-6670 |

### Keywords

- Autonomous vehicles
- Control
- Guidance systems

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

Miller, B. M., Rubinovich, E. Y., & Bentsman, J. (2011). Spatiotemporal singular transformation in dynamical systems with impacts and its use in obtaning generalized solution of Painleve problem. In

*Proceedings of the 18th IFAC World Congress*(1 PART 1 ed., pp. 3463-3473). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 44, No. 1 PART 1). IFAC Secretariat. https://doi.org/10.3182/20110828-6-IT-1002.01314