New Mechanical Engineering
Graduate Dynamics Sequence
starting in the academic year 2012-2013

Two courses are cancelled

TAM 5700          Intermediate Dynamics (Fall)            and
MAE 4770/5770 Vibrations                     (Spring)
      are cancelled.

They are replaced by two new re-organized courses.

The new courses

Together, the two new courses will cover about 2/3 of the vibrations material from the former MAE 4770/5770, all of the core dynamics material from the former TAM 5700, some of the material from previous robotics and modeling courses, and a bit more multi-object dynamics than has been taught before. Here are the official descriptions of the new courses.

1) MAE 4730/5730: Intermediate Dynamics and Vibrations (called 4735/5735 in fall 2013)

Fall, MWF 10:10-11, Instructor for fall 2012: Ruina

The course emphasizes the dynamics and vibrations of multi-degree-of-freedom systems including particles, rigid-objects and structures. Introduction to Lagrange's equations. Finding equations of motion, solving analytically and numerically; graphical presentation of solutions. Conservation laws. Modal analysis of discrete and continuous systems. Damped and undamped systems. Vibration absorbers and vibration control for discrete systems.

Prerequisites: Math 2940, MAE 3260 or equivalents, or permission of the instructor.

For more details see this the MAE 5730 www page.

2) MAE 6700: Advanced Dynamics (anticipated, not yet officially listed)

 Spring. 3 credits. Instructor for Spring 2013: Ruina

Advanced dynamics of particles and rigid objects with emphasis on 3 dimensions and complex multi-object systems. Topics include: Hamilton's principle, Lagrange equations, dynamics of mixed lumped and discrete systems. Raliegh-Ritz method, stability theory, and approaches to multi-object systems. Examples will come from celestial mechanics, machines, robotics and vehicle dynamics.

Prerequisites: MAE 5735, or equivalent, or permission of the instructor.

What should you take?

If you had been planning to take 4770/5770 Vibrations in the Spring (now cancelled), the new fall 4730/5730 is the closest approximation. If you had planned to take TAM 5700 (now cancelled) in the fall, the closest approximation to the lower level parts of the former 5700 is the new 4730/5730 and the closest approximation to the higher level level aspects of the former 5700 is the new 6700. MAE 4730/5730 is a pre-requisite for MAE 6700.

In any case you should check with your advisor. Here are some guidelines.

You are a PhD student with a major interest in Dynamics:
    You should take both of these classes (unless you already know the material).

You are a PhD student with a minor interest in Dynamics:
You should take at least one of these classes.

You are an M-Eng student with a major interest in Dynamics:
  You should take at least one of these classes.

You are an M-Eng student with a minor interest in Dynamics:
  You should take at least one of these classes.

You are an undergraduate:
If you like and are good at dynamics, and have place in your schedule, you should take  the first of these courses (4735). Then consider continueing on (6700) if you are somewhat advanced.


Because of retirements, changes of faculty and departments merging, the dynamics course offerings have evolved without restructuring for several years. Here are some of the issues that the new course sequence is intended to address while also making a coherent 2-course sequence.

* The Modeling and Simulation course had good material that should be taught, but the course is no longer being taught.

* The only dynamics course now between TAM/ENGRD 2030, Sophomore Intro to Dynamics, and TAM 5700, Intermediate Dynamics, is MAE 3260 System Dynamics which is largely about linear systems rather than (F=ma) mechanics.

* Undergraduates with machines/mechanisms/robotics/bio-dynamics interests could use and enjoy a more advanced dynamics course than TAM 2030 but not so advanced as TAM 5700 has sometimes been.

* MAE 4170/5170, Introduction to Robotics Dynamics, Control, Design, is no longer being taught, but has some material that should be taught.

* For graduate students in Dynamics there is a need for multi-object dynamics that goes past the usual coverage of TAM 5700.

* Some entering students M-Eng students have found that TAM 5700 has started at too high a level, while some entering PhD students have found that it starts at too low a level.

* There seems not to be a need for a full semester on Vibrations.

* There has been some overlap between Vibrations (MAE 4700) and Intermediate Dynamics (TAM 5700).

email to Andy Ruina <>