Dynamics and Control I

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.

• 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