Advanced Dynamics

Overview

A study of dynamics is useful not only in determining dynamic forces for design (such as in automotive and aerospace systems, machine tools etc.), but also in understanding the phenomena of tides, cyclonic circulation, precession of tops, flight of boomerangs etc. This course will cover the fundamental topics in dynamics of particles and rigid bodies using the approaches of Newtonian and analytical dynamics. The coverage will start with kinematics in inertial and non-inertial (rotating) frames, discuss the different approaches to study the dynamics of a single particle, system of particles, rigid bodies in two and three dimensions, and finally introduce the approach of analytical dynamics. The course will have a strong emphasis on problem solving, and is expected to build a strong foundation in dynamics.INTENDED AUDIENCE :Mechanical Engineering,Aerospace Engineering,PhysicsPRE-REQUISITES : Undergraduate Mechanics, Dynamics, and Engineering MathematicsINDUSTRY SUPPORT : Automotive, Railway, and Aerospace industry

Syllabus

Week 1:Coordinate systems, Kinematics of particles, rotating frames, relative motion
Week 2:Kinetics of particles, cyclonic circulation, Foucault pendulum Week 3:Integrals of Newton’s second law, angular momentum, conservation laws
Week 4:Impact, Newton’s law of gravitation and tidal dynamics Week 5:Systems with variable mass, systems with flow Week 6:Dynamics of rigid bodies, Newton-Euler equations
Week 7:Dynamics of tops, gyroscopes and boomerangs
Week 8:Rotation matrix and its parametrization, geometry of rotation
Week 9:Introduction to analytical dynamics, configuration space, constraints, generalized coordinates and forces
Week 10:Hamilton’s principle, Lagrange’s equation of motion, constraint forces
Week 11:Generalized momentum, cyclic coordinates and conservation laws
Week 12:Symmetry and Noether’s theorem, Hamiltonian and its conservation