# 151-0503-00L Mechanics III

Semester | Autumn Semester 2014 |

Lecturers | G. Haller |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | Kinematics, dynamics and oscillations: Motion of a single particle - Motion of systems of particles - 2D motion of rigid bodies - 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, or forces and torques. Advanced topics include 3d rigid body motion and vibrations. Numerous 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; state space formulation; numerical integration - Examples (e.g.: skier fly-off, roller coaster, race car rollover) 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 - Examples (e.g.: planar collisions, coupled pendulum systems) 3. 2D motion of rigid bodies || Kinematics and Kinetics: 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 - Examples (e.g.: falling stick, center of percussion of a baseball bat, break-point of an imploded chimney) 4. 3D motion of rigid bodies || Kinematics and Kinetics: basic concepts, 3D rotations, angular velocity of 3D rotations, Examples (rolling cone, Cardan drive) - Linear momentum principle, angular momentum principle, work-energy principle - moment of inertia tensor, Parallel axis theorem, Differentiation in a rotating frame, Gyroscopes, Euler's equations. 5. Vibrations || 1-DOF oscillations: natural frequencies, free-, damped-, and forced response - Examples (e.g., vibration absorbers, ship oscillations) - 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 | Engineering Mechanics: Dynamics (13th Edition), R. C. Hibbeler, Pearson |

Prerequisites / Notice | Please log in to moodle ( https://moodle-app2.let.ethz.ch/auth/shibboleth/login.php ), search for "Mechanics III", and join the course there. All exercises sheets, lecture materials etc. will be uploaded there. There will be two practice exams in moodle. They will not be graded, and can be solved from home on your own computer. |