Mechanics, second course

Aim

To develop a broader and deeper knovledge of classical mechanics through the study of particle mechanics relative to rotating references, rigid body dynamics and oscillations with several degrees of freedom. After the course, the student should be able to:

• Select a coordinate system for a specific dynamics problem with insight into the consequences of different choices.
• Analyze dynamics problems using numerical solution of systems of ordinary differential equations.
• Use vector algebraic methods to analyze dynamics problems, including eigenvalue analysis and coordinate transformations. Course content Newton's equations of motion. The concept of an inertial system. Relative motion in the plane. Angular velocity and acceleration as vectors. The Coriolis equation. Dynamics of paricles in rotating coordinate systems. The equations of motion for systems of particles and for rigid bodies.Calculation of the moment of momentum for a rigid body.The inertia tensor and its representation in different coordinate systems. Oscillations with several degrees of freedom. Interpretation of the eigenvectors as eigenmodes. Teaching and working methods The course is given as a series of lectures and computer sessions. Mor emphasis than typical for a course at this level is given to computer sessions where the students implement mechanical models in MATLAB. Examination LAB1Computer assignments2 creditsU, 3, 4, 5TEN1Written examination2 creditsU, 3, 4, 5 Grades Four-grade scale, LiU, U, 3, 4, 5 Other information Supplementary courses: Courses in Physics, Applied mechanics, Mechatronics Vehicle dynamics and Solid mechanics. About teaching and examination languageThe teaching language is presented in the Overview tab for each course. The examination language relates to the teaching language as follows: If teaching language is “Swedish”, the course as a whole could be given in Swedish, or partly in English. Examination language is Swedish, but parts of the examination can be in English.If teaching language is “English”, the course as a whole is taught in English. Examination language is English.If teaching language is “Swedish/English”, the course as a whole will be taught in English if students without prior knowledge of the Swedish language participate. Examination language is Swedish or English depending on teaching language.OtherThe course is conducted in a manner where both men's and women's experience and knowledge are made visible and developed. The planning and implementation of a course should correspond to the course syllabus. The course evaluation should therefore be conducted with the course syllabus as a starting point. The course is campus-based at the location specified for the course, unless otherwise stated under “Teaching and working methods”. Please note, in a campus-based course occasional remote sessions could be included. If special circumstances prevail, the vice-chancellor may in a special decision specify the preconditions for temporary deviations from this course syllabus, and delegate the right to take such decisions. Department Institutionen för ekonomisk och industriell utveckling Course literature CompendiaLars Johansson, Exempelsamling för mekanik YiLars Johansson, Föreläsningsanteckningar för mekanik Yi

Content

Newton's equations of motion. The concept of an inertial system. Relative motion in the plane. Angular velocity and acceleration as vectors. The Coriolis equation. Dynamics of paricles in rotating coordinate systems. The equations of motion for systems of particles and for rigid bodies.Calculation of the moment of momentum for a rigid body.The inertia tensor and its representation in different coordinate systems. Oscillations with several degrees of freedom. Interpretation of the eigenvectors as eigenmodes.