AAE 34000

Dynamics and Vibrations

Credits:     3

Contact hours:     3

Instructor:     Professor Longuski and Professor Howell

Text:     Supplemental notes furnished by instructor.

Course Description:     Kinematics and kinetics of particles and rigid bodies. Topics include a particle in orbit, systems of particles, vibrations, Euler's equations of motion, Eulerian angles, and aerospace vehicle dynamics.

Offered:    Fall and Spring

Pre-requisite:    MA 26600 or MA 36600, MA 30300 or MA 30400, AAE 20300

Co-requisite:    None

Required:    Yes

Student Learning Outcomes:
On completing this course the student shall be able to:

  1. Analyze the free and forced response of a spring/mass/damper
  2. Formulate the EOMs of particles, systems of particles and rigid bodies
  3. Solve the EOMs numerically
  4. Understand the various forms of Euler angles and be able to apply them to rigid body dynamics
  5. Simulate the motion of a spacecraft in MATLAB

Relationship of Course to Program Outcomes

    Program Learning Outcomes Included?
a An ability to apply knowledge of mathematics, science, and engineering Yes
b An ability to design and conduct experiments, as well as to analyze and interpret data No
c An ability to design an aerospace system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health, and safety, manufacturability, and sustainability No
d An ability to function on multidisciplinary teams No
e An ability to identify, formulate, and solve aerospace engineering problems Yes
f An understanding of professional and ethical responsibility No
g An ability to communicate effectively No
h An understanding of the impact of engineering solutions in a global, economic, environmental, and societal context No
i A recognition of the need for, and an ability to engage in life-long learning No
j A knowledge of contemporary issues in aerospace engineering No
k An ability to use the techniques, skills and modern engineering tools necessary for aerospace engineering practice Yes


  1. Mass-Spring-Damper (7 lectures)
    • undamped free vibrations;under-, critically- and over-damped free vibrations;amplification factor and phase angle for forced vibrations;resonance
  2. Review of Kinematics (2 lectures)
    • basic kinematic equation;coordinate systems (cylindrical, spherical, etc.)
  3. Numerical Integration (1 lecture)
    • Euler, Runge-Kutta;MATLAB ode toolbox
  4. Review of Particle Dynamics (8 lectures)
    • free body diagrams; kinematics; Newton's laws; equations of motion;integrals of motion; conservation of linear and angular momentum, conservation of total mechanical energy;principles of linear/angular impulse and momentum;principles of work and kinetic energy;orbital mechanics
  5. Systems of Particles (7 lectures)
    • Newton's and Euler's laws for systems of particles;integrals of motion;rocket problem;collisions
  6. Rigid Body Dynamics (13 lectures)
    • degrees of freedom;moments and products of inertia;inertia matrix and coordinate transformations;principal axes and principal moments of inertia;Euler's theorem;derivation of Euler's equations of motion
  7. Euler Angles (4 lectures)
    • sequences (e.g., 313);angular velocities in terms of Euler angles;free motion of an axisymmetric rigid body; body cone and space cone
  8. Aerospace Applications (1 lecture)

Revision History:
Prepared by: James M. Longuski
Date: September 19, 2000
Revised: March 23, 2006
Updated Pre-Requisites on March 3, 2011
Revised: February 27, 2012