This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange's equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLAB® to solve dynamics and vibrations problems.
This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the approach presented in Spring 2007. Our notation was adapted from that of Professor Kane of Stanford University.
Overview
Syllabus
- Lecture 1: Course information; Begin kinematics
- Lecture 2: The "spider on a Frisbee" problem
- Lecture 3: Pulley problem, angular velocity, magic formula
- Lecture 4: Magic and super-magic formulae
- Lecture 5: Super-magic formula, degrees of freedom, non-standard coordinates, kinematic constraints
- Lecture 7: Impulse, skier separation problem
- Lecture 8: Single particle; Two particles
- Lecture 9: Dumbbell problem, multiple particle systems, rigid bodies, derivation of torque
- Lecture 10: Three cases, rolling disc problem
Taught by
Prof. Nicholas Makris, Dr. Yahya Modarres-Sadeghi, Prof. Sanjay Sarma, and Prof. Peter So
