Multibody and Non-Linear Dynamics

Uitgebreide vaknaam	Multibody and Non-Linear Dynamics
Leerdoelen	At the end of the course, the student is able to: 1) Apply the concepts of translations and rotations to the modelling of rigid bodies. 2) Formulate a mathematical description of a general motion of a mechanical system in terms of descriptive variables and systems of (differential) equations. 3) Implement the mathematical description in a graphical application to visualize a desired motion of a mechanical system. 4) Distinguish the types of bifurcations for one- and multi-dimensional nonlinear dynamical systems. 5) Analyze the phase plane dynamics of nonlinear systems.
Omschrijving	The course aims at forming a solid background to analyze dynamic problems in mechanics, engineering, and physics. The first part – multi-body dynamics – relies on the concept of problem-based learning allowing to accumulate theoretical knowledge, develop mechanical intuition, and master practical know-how in modeling the motion of systems of rigid bodies. Particular emphasis is placed on developing the ability to implement theoretical concepts in concrete applications and to disseminate results in oral and written forms. The learning objectives are to prepare the students to: • Model the kinematics and dynamics of a multibody mechanism; • Formulate a mathematical description of a general motion of the mechanism in terms of descriptive variables and systems of equations; • Implement this description in a graphical application for visualizing a desired motion of a mechanism. In contrast to traditional courses in mechanics, this course implies active use of computer tools. The assessment relies on a group project, when the students are challenged to model the motion of a real mechanical system. The second part – nonlinear dynamics – is about the dynamics of 1D and 2D dynamical systems. The key idea is to learn how the mathematical apparatus can be used to understand nonlinear world around us. The theoretical treatment is rather informal with the emphasis on analytical methods and geometric intuition. The theory is presented systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, and culminated by limit cycles and their bifurcations. The learning objectives are to prepare the students to: • Describe the dynamics of mechanical and other nonlinear systems; • Identify important dynamic parameters governing the system response; • Analyze stability of the systems with one-, two- and more dimensions. A special attention is paid to applications, including mechanical vibrations, lasers, superconducting circuits.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Opdracht (ASM), Practisch werk (PRC), Werkcollege (T) (32h LC, 32h T, 20h ASM, 16h PRC, 40h self study)
Toetsvorm	Practisch werk (PR), Presentatie (P), Schriftelijk tentamen (WE), Verslag (R) (40% WE, 20% P, 30% R, 10% PR)
Vaksoort	master
Coördinator	dr. A.O. Krushynska
Docent(en)	dr. A.O. Krushynska
Entreevoorwaarden	The course assumes basic knowledge of linear algebra, calculus, kinematics, and elementary mechanics from the bachelor courses.
Opmerkingen	This course was previously registered year with course code WMME19013
Opgenomen in	Opleiding Jaar Periode Type MSc Mechanical Engineering: Advanced Instrumentation  (Electives ) 1 semester I a keuze MSc Mechanical Engineering: Materials for Mechanical Engineering  (Electives ) 1 semester I a keuze MSc Mechanical Engineering: Process Design for Energy Systems  (Electives ) 1 semester I a keuze MSc Mechanical Engineering: Smart Factories  (Electives ) 1 semester I a keuze