Description

A discussion of means to analyze kinematics and ways to develop equations of motion. It is essentially an introduction to Lagrangian mechanics with applications to systems of particles and rigid bodies. The course first reviews basic concepts on kinematics, dynamics, and relative motion. It discusses the concepts of constraints, degrees of freedom, and generalized coordinates, before setting up the stage for the principle of virtual work, and D'Alembert's principle that lead to Lagrange equations. The dynamics of particle systems are analyzed first and then the approach is extended to rigid bodies.

(Suggested) Prerequisites

• Basic calculus
• Vector analysis,
• Calculus of variations.

Course Aims

Introduction to

• Kinematics and dynamics of systems of particles and rigid bodies
• Analytical mechanics
• Lagrangian approach

By the end of the course students should be able to develop the equations of motion for systems of particles and rigid bodies using the Lagrangian formalism.

Time & location	Tuesday/Thursday 1230-1345 Dane Smith Hall Room 134
Instructor	Bert Tanner Mechanical Engineering Bldg, Room 422 Tel: 277-1493 e-mail:
Office hours	Wednesday 1100-1400
Text	Haim Baruh, Analytical Dynamics, McGraw-Hill. 1999 Further reading: Goldstein, Poole, and Safko, Classical Mechanics, 3rd edition, Addison Wesley, 2002 L. Meirovitch, Methods of Analytical Dynamics, Dover, 2003
Grading policy	20% Weekly assignments 30% Midterm examination (take home) 50% Final examination (in class) - 5/15, 1000-1200
Topics	Units and coordinate frames Basic Vector Analysis Newtonian mechanics Degrees of freedom, constraints Momentum and energy Integrals of motion Moving coordinate frames Coordinate transformation and frame rotations Angular velocity and acceleration Relative velocity and acceleration Equations of motion for systems of particles Mementum and Energy of system of particles Generalized coordinates & constraints Virtual work and generalized forces D'Alembert's & Hamilton's principles Lagrange equations The case of constrained systems Moments of inertia Transformation properties of rigid bodies Rigid body kinematics Euler's theorem Euler angles and parameters Constrained motion of rigid bodies Momentum of rigid bodies Work and energy for rigid bodies Lagrange equations for rigid bodies D'Alembert's principle for rigid bodies Kane's equations
Homework	Homework Out Due 1.15 1/24 1/31   2.2, 2.4 2/7 2/14   2.13, 2.28 2/14 2/28 2.31, 2.32 2/28 3/6 3.1, 3.4 3/6 3/13 3.29, 3.32 3/13 3/27   4.1, 4.4 4/3 4/10   4.7, 4.8 4/10 4/17   4.11, 4.14, 4.16 4/17 5/1