### Mathematical models of thermal drift of gyroscopic sensors of inertial systems

V.E. Dzhashitov, V.M. Pankratov / Under the general editorship of the RAS Academician
V.G. Peshekhonov

150 p.

St. Petersburg: SRC of Russia - CSRI "Elektropribor", 2001

ISBN 5-900780-30-9

Mathematical models of classical and promising gyroscopic inertial data sensors of various physical principles and laws of operation have been considered. Principles of operation and dynamics fundamentals of thermally disturbed inertial gyroscopic sensors, devices and systems based on them are stated. Mathematical models of thermal drift of float, dynamically tuned, electrostatic non-contact, wave solid-state, micromechanical and fiber-optic gyros have been constructed and investigated. Particular attention has been given to the new mathematical models of thermal drift making it possible to investigate the phenomenon of deterministic chaos in non-linear thermally disturbed dynamic systems with inertial sensors.

The book is intended for scientists, engineers and technicians. Also it can be useful for post-graduates and students of higher education institutes.

Bibliography: 16 references. 34 illustrations. 1 table.

Introduction | 5 |

Chapter 1. Models of bound physical processes of mechanical motion, heat-mass exchange,
thermoelasticity, hydromechanics and optics for sensors of various principles of operation | 10 |

1.1. Problems of mathematical models construction and their solution strategy | - |

1.2. Mathematical models and investigation methods for thermal processes in gyroscopic sensors of inertial systems | 15 |

1.3. Mathematical models and investigation methods for mechanical motion processes in gyroscopic sensors of inertial systems | 24 |

1.4. Mathematical models and thermoelasticity theory methods in investigation of stressed and deformed state of gyroscopic sensors of inertial systems | 27 |

1.5. Mathematical models and investigation methods for hydromechanical processes in gyroscopic sensors of inertial systems | 30 |

1.6. Mathematical models and investigation methods for optic processes in fiber paths of gyroscopic sensors of inertial systems | 33 |

Chapter 2. Inertial data sensors of various physical principles of operation | 38 |

2.1. Float inertial sensors - principle of operation, mathematical models, investigation problems | - |

2.2. Rotor vibratory dynamically tuned inertial sensors - principle of operation, mathematical models, investigation problems | 48 |

2.3. Electrostatic spherical inertial sensors - principle of operation, mathematical models, investigation problems | 57 |

2.4. Wave solid-state inertial sensors - principle of operation, mathematical models, investigation problems | 63 |

2.5. Micromechanical inertial sensors - principle of operation, mathematical models, investigation problems | 74 |

2.6. Fiber-optic inertial sensors - principle of operation, mathematical models, investigation problems | 108 |

2.7. Systematization of mathematical models of thermally disturbed inertial sensors | 118 |

Chapter 3. Special construction and investigation problems of mathematical models of thermally
disturbed inertial data sensors | 128 |

3.1. Deterministic chaos in disturbed non-linear gyroscopic systems - general approach | - |

3.2. Deterministic chaos in thermally disturbed fiber-optic inertial sensors | 139 |

Conclusions | 148 |

References | 149 |