AAE 50700: Principles of Dynamics

Description:

Kinematics, fundamental laws of mechanics, constraints, and generalized coordinates. Lagrange's equations, virtual work. Application to particle dynamics, rigid body motion, and spacecraft dynamics. Professor Longuski.

Format: 3 hrs lecture per week

Credit hours: 3

Status: Elective, Dynamics and Controls

Offered: Fall

Pre-requisite: AAE 340 or equivalent

Co-requisite: None

Course Instructor: Professor Longuski

Text: Greenwood, D. T., Principles of Dynamics, Second Edition, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1988

Assessment Method: Grading is weighted 20% on homework, 20% on a project, 40% on two in-class exams, and 20% on a final exam

Course Objective: The senior or graduate student will benefit from this more mathematical viewpoint of dynamics, which begins with Lagrange's equations. Analytic solutions for rigid body dynamics reveal the behavior of the system to the student and clarify the meaning of the equations of motion. Finally, the student is introduced to the elegant and powerful concepts of the variational principles of dynamics.

Necessary Background: A solid foundation in vectorical mechanics (Newton's laws) and rigid body dynamics (Euler's equations of motion, Euler angles) is required.

Topics (number of Lectures):

  1. Lagrange's Equations (10 lectures)

· Degrees of freedom

· Generalized Coordinates and Quasi-coordinates

· Holonomic and Nonholonomic Constraints

· Virtual Work

· Integrals of the Motion

2. Rigid Body Dynamics and Analytic Solutions (18 lectures)

· Euler's Equations of Motion

· Free Motion

· The Poinsot Method

· Motion of a Top

· Motion with Body-Fixed Torques

3. Spacecraft Dynamics (8 lectures)

· Analytic Solutions for the Thrusting-Spinning Rocket

· Two-Burn Scheme for Angular Momentum Vector Control

· Special Project

  1. Introduction to Variational Principles of Mechanics (8 lectures)

· The Calculus of Variations

· The Brachistochrone Problem

· Euler-Lagrange Equations

· Hamilton's Principle for Holonomic Systems

Relationship of course to program objectives:

This course provides the essential technical components of (1) Lagrangian Dynamics. Students develop basic engineering skills in formulating and solving open-ended problems (2a) and in writing a project report. (2c) Some students have turned their projects into directed studies (AAE 590), conference papers, journal articles and a patent application (3).

Prepared by: James M. Longuski

Date: March 19, 2001