# George Haller: Catalogue data in Autumn Semester 2016

Name | Prof. Dr. George Haller |

Field | Nonlinear Dynamics |

Address | Chair in Nonlinear Dynamics ETH Zürich, LEE M 210 Leonhardstrasse 21 8092 Zürich SWITZERLAND |

Telephone | +41 44 633 82 50 |

georgehaller@ethz.ch | |

URL | http://georgehaller.com |

Department | Mechanical and Process Engineering |

Relationship | Full Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

151-0503-00L | Dynamics | 6 credits | 4V + 2U | G. Haller, P. Tiso | |

Abstract | Kinematics, dynamics and oscillations: Motion of a single particle - Motion of systems of particles - 2D and 3D motion of rigid bodies Vibrations | ||||

Objective | This course provides Bachelor students of mechanical engineering with fundamental knowledge of kinematics and dynamics of mechanical systems. By studying motion of a single particle, systems of particles and rigid bodies, we introduce essential concepts such as work and energy, equations of motion, and forces and torques. Further topics include stability of equilibria and vibrations. Examples presented in the lectures and weekly exercise lessons help students learn basic techniques that are necessary for advanced courses and work on engineering applications. | ||||

Content | 1. Motion of a single particle || Kinematics: trajectory, velocity, acceleration, inertial frame, moving frames - Forces and torques. Active- and reaction forces. - Linear momentum principle, angular momentum principle, work-energy principle - Equations of motion; 2. Motion of systems of particles || Internal and external forces - Linear momentum principle, angular momentum principle, work-energy principle - Rigid body systems of particles; conservative systems 3. 3D motion of rigid bodies || Kinematics: angular velocity, velocity transport formula, instantaneous center of rotation - Linear momentum principle, angular momentum principle, work-energy principle - Parallel axis theorem. Angular momentum transport formula 4. Vibrations || 1-DOF oscillations: natural frequencies, free-, damped-, and forced response - Multi-DOF oscillations: natural frequencies, normal modes, free-, damped-, and forced response - Estimating natural frequencies and mode shapes - Examples | ||||

Lecture notes | Hand-written slides will be downloadable after each lecture. | ||||

Literature | Typed course notes from the previous year | ||||

Prerequisites / Notice | Please log in to moodle ( https://moodle-app2.let.ethz.ch/auth/shibboleth/login.php ), search for "Dynamics", and join the course there. All exercises sheets, lecture materials etc. will be uploaded there. | ||||

151-0532-00L | Nonlinear Dynamics and Chaos I | 4 credits | 2V + 2U | G. Haller, F. Kogelbauer | |

Abstract | Basic facts about nonlinear systems; stability and near-equilibrium dynamics; bifurcations; dynamical systems on the plane; non-autonomous dynamical systems; chaotic dynamics. | ||||

Objective | This course is intended for Masters and Ph.D. students in engineering sciences, physics and applied mathematics who are interested in the behavior of nonlinear dynamical systems. It offers an introduction to the qualitative study of nonlinear physical phenomena modeled by differential equations or discrete maps. We discuss applications in classical mechanics, electrical engineering, fluid mechanics, and biology. A more advanced Part II of this class is offered every other year. | ||||

Content | (1) Basic facts about nonlinear systems: Existence, uniqueness, and dependence on initial data. (2) Near equilibrium dynamics: Linear and Lyapunov stability (3) Bifurcations of equilibria: Center manifolds, normal forms, and elementary bifurcations (4) Nonlinear dynamical systems on the plane: Phase plane techniques, limit sets, and limit cycles. (5) Time-dependent dynamical systems: Floquet theory, Poincare maps, averaging methods, resonance | ||||

Lecture notes | The class lecture notes will be posted electronically after each lecture. Students should not rely on these but prepare their own notes during the lecture. | ||||

Prerequisites / Notice | - Prerequisites: Analysis, linear algebra and a basic course in differential equations. - Exam: two-hour written exam in English. - Homework: A homework assignment will be due roughly every other week. Hints to solutions will be posted after the homework due dates. |