Advanced Engineering Systems in Motion: Dynamics of Three Dimensional (3D) Motion
4.8
119 ratings
Advanced Engineering Systems in Motion: Dynamics of Three Dimensional (3D) Motion
Georgia Institute of Technology
About this Course
This course is an advanced study of bodies in motion as applied to engineering systems and structures. We will study the dynamics of rigid bodies in 3D motion. This will consist of both the kinematics and kinetics of motion. Kinematics deals with the geometrical aspects of motion describing position, velocity, and acceleration, all as a function of time. Kinetics is the study of forces acting on these bodies and how it affects their motion.
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Recommended Background:
To be successful in the course you will need to have mastered basic engineering mechanics concepts and to have successfully completed my course entitled Engineering Systems in Motion: Dynamics of Particles and Bodies in 2D Motion.” We will apply many of the engineering fundamentals learned in those classes and you will need those skills before attempting this course.
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Suggested Readings:
While no specific textbook is required, this course is designed to be compatible with any standard engineering dynamics textbook. You will find a book like this useful as a reference and for completing additional practice problems to enhance your learning of the material.
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The copyright of all content and materials in this course are owned by either the Georgia Tech Research Corporation or Dr. Wayne Whiteman. By participating in the course or using the content or materials, whether in whole or in part, you agree that you may download and use any content and/or material in this course for your own personal, non-commercial use only in a manner consistent with a student of any academic course. Any other use of the content and materials, including use by other academic universities or entities, is prohibited without express written permission of the Georgia Tech Research Corporation. Interested parties may contact Dr. Wayne Whiteman directly for information regarding the procedure to obtain a non-exclusive license.
Syllabus - What you will learn from this course
1
Section
Course Introduction; Angular Velocity; Angular Acceleration
In this section students will learn to derive the "derivative formula." We will define angular velocity for 3D motion and learn to determine and solve for the Angular Acceleration for a body.
6 videos (Total 53 min), 13 readings, 1 quiz
6 videos
Module 2: Derive the “Derivative Formula”; Define Angular Velocity for 3D Motion12m
Module 3: Define the Properties of Angular Velocity for 3D Motion5m
Module 4: Solve for the Angular Velocity of a body undergoing 3D Motion10m
Module 5: Determine the Angular Acceleration for a Moving Reference Frame Relative to another Reference Frame8m
Module 6: Solve for the Angular Acceleration for a Body expressed in a Series of Multiple Reference Frames10m
13 readings
Syllabus10m
Consent Form10m
Pdf version of Course Introduction Lecture10m
Pdf version Module 2: Derive the “Derivative Formula”; Define Angular Velocity for 3D Motion Lecture10m
Pdf version of Module 3: Define the Properties of Angular Velocity for 3D Motion Lecture10m
Pdf version of Module 4: Solve for the Angular Velocity of a body undergoing 3D Motion Lecture10m
Worksheet Solutions: Solve for the Angular Velocity of a Body Undergoing 3D Motion10m
Pdf version of Module 5: Determine the Angular Acceleration for a Moving Reference Frame Relative to another Reference Frame Lecture10m
Pdf version of Module 6: Solve for the Angular Acceleration for a Body expressed in a Series of Multiple Reference Frames Lecture10m
Worksheet Solutions: Solve for the Angular Acceleration for a Body Expressed in a Series of Multiple Reference Frames10m
Get More from Georgia Tech10m
Practice Problems10m
Solution of Quiz 110m
1 practice exercises
Course Introduction; Angular Velocity; Angular Acceleration6m
2
Section
Velocities in Moving Reference Frames; Accelerations in Moving Reference Frames; The Earth as a Moving Frame
In this section students will learn about velocities in moving reference frames, accelerations in moving reference frames, and the Earth as a moving frame.
6 videos (Total 64 min), 11 readings, 1 quiz
6 videos
Module 8: Solve for Velocities Expressed in Moving Frames of Reference10m
Module 9: Accelerations expressed in Moving Frames of Reference10m
Module 10: Solve for the Velocity and the Acceleration for Bodies Undergoing 3D Motion and Expressed in Moving Frames of Reference12m
Module 11: Equations of Motion for a Particle Moving Close to the Earth12m
Module 12: Solve a Problem for the Motion of Particles Moving Close to the Earth6m
11 readings
Pdf version of Module 7: Velocities expressed in Moving Frames of Reference Lecture10m
Pdf version of Module 8: Solve for Velocities Expressed in Moving Frames of Reference Lecture10m
Worksheet Solutions: Solve for Velocities Expressed in Moving Frames of Reference10m
Pdf version of Module 9: Accelerations expressed in Moving Frames of Reference Lecture10m
Pdf version of Module 10: Solve for the Velocity and the Acceleration for Bodies Undergoing 3D Motion and Expressed in Moving Frames of Reference Lecture10m
Worksheet Solutions: Solve for the Velocity and the Acceleration for Bodies Undergoing 3D Motion and Expressed in Moving Frames of Reference10m
Pdf version of Module 11: Equations of Motion for a Particle Moving Close to the Earth Lecture10m
Pdf version of Module 12: Solve a Problem for the Motion of Particles Moving Close to the Earth Lecture10m
Earn a Georgia Tech Badge/Certificate/CEUs10m
Practice Problems10m
Solution of Quiz 210m
1 practice exercises
Velocities in Moving Reference Frames; Accelerations in Moving Reference Frames; The Earth as a Moving Frame6m
3
Section
Eulerian Angles; Eulerian Angles Rotation Matrices; Angular Momentum in 3D; Inertial Properties of 3D Bodies
In this section students will learn about Eulerian Angles rotation matrices, angular momentum in 3D, and intertial properties of 3D bodies.
8 videos (Total 70 min), 10 readings, 1 quiz
8 videos
Module 14: Angular Velocity of Bodies in 3D Motion using Eulerian Angles6m
Module 15: Derive Rotational Transformation Matrices6m
Module 16: Solve a Problem Using Rotational Transformation Matrices7m
Module 17: Review Particle Kinetics; Newton’s Laws for Particles; and Euler’s 1st Law for Bodies10m
Module 18: Review the Definition of Angular Momentum; and Euler’s 2nd Law for Bodies7m
Module 19: Angular Momentum for Bodies in 3D Motion12m
Module 20: Review Mass Moments of Inertia and Products of Inertia; Inertial Property Matrix11m
10 readings
Pdf version of Module 13: Eulerian Angles for 3D Rotational Motion Lecture10m
Pdf version of Module 14: Angular Velocity of Bodies in 3D Motion using Eulerian Angles Lecture10m
Pdf version of Module 15: Derive Rotational Transformation Matrices Lecture10m
Pdf version of Module 16: Solve a Problem Using Rotational Transformation Matrices Lecture10m
Pdf version of Module 17: Review Particle Kinetics; Newton’s Laws for Particles; and Euler’s 1st Law for Bodies Lecture10m
Pdf version of Module 18: Review the Definition of Angular Momentum; and Euler’s 2nd Law for Bodies Lecture10m
Pdf version of Module 19: Angular Momentum for Bodies in 3D Motion Lecture10m
Pdf version of Module 20: Review Mass Moments of Inertia and Products of Inertia; Inertial Property Matrix Lecture10m
Practice Problems10m
Solution of Quiz 310m
1 practice exercises
Eulerian Angles; Eulerian Angles Rotation Matrices; Angular Momentum in 3D; Inertial Properties of 3D Bodies6m
4
Section
Translational and Rotational Transformations of Inertial Properties; Principal Axes and Principal Moments of Inertia
In this section students will learn about translational and rotational transformations of inertial properties, and principal axes and principal moments of inertia.
6 videos (Total 47 min), 9 readings, 1 quiz
6 videos
Module 22: Rotational Transformation of Inertial Properties4m
Module 23: Rotational Transformation of Inertial Properties (cont)8m
Module 24: Define Principal Axes and Principal Moments of Inertia4m
Module 25: Determine Principal Axes and Principal Moments of Inertia10m
Module 26: Solve for Principal Axes and Principal Moments of Inertia with an Example11m
9 readings
Pdf version of Module 21: Translational Transformation of Inertial Properties Lecture10m
Pdf Version of Module 22: Rotational Transformation of Inertial Properties Lecture10m
Pdf Version of Module 23: Rotational Transformation of Inertial Properties (cont) Lecture10m
Pdf Version of Module 24: Define Principal Axes and Principal Moments of Inertia Lecture10m
Pdf Version of Module 25 Determine Principal Axes and Principal Moments of Inertia Lecture10m
Pdf Version of Module 26: Solve for Principal Axes and Principal Moments of Inertia Lecture10m
Worksheet Solutions: Solve for Principal Axes and Principal Moments of Inertia with an Example10m
Practice Problems10m
Solution of Quiz 410m
1 practice exercises
Translational and Rotational Transformations of Inertial Properties; Principal Axes and Principal Moments of Inertia.6m
5
Section
Motion Equations Governing 3D Rotational Motion of a Rigid Body (Euler Equations)
In this section students will learn to develop Euler Equations for 3d motion and solve for the motion of a rigid body undergoing 3D rotational motion.
5 videos (Total 60 min), 8 readings, 1 quiz
5 videos
Module 28: Develop Euler Equations for 3D Motion (cont.)5m
Module 29: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion14m
Module 30: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion (cont.)10m
Module 31: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion (cont.)19m
8 readings
Pdf Version of Module 27: Develop Euler Equations for 3D Motion Lecture10m
Pdf Version of Module 28: Develop Euler Equations for 3D Motion (cont.) Lecture10m
Pdf Version of Module 29: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture10m
Pdf Version of Module 30: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture10m
Pdf Version of Module 31: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture10m
Worksheet Solutions: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion10m
Practice Problems10m
Solution of Quiz 510m
1 practice exercises
Motion Equations Governing 3D Rotational Motion of a Rigid Body (Euler Equations)6m
6
Section
3D Impulse-Momentum Principles; 3D Work-Energy Principles
In this section students will learn to develop and apply the principle of impulse-momentum and about 3D work-energy principles.
4 videos (Total 33 min), 8 readings, 1 quiz
4 videos
Module 33: Develop the Principle of Work-Energy for Bodies in 3D Rigid Body Motion8m
Module 34: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion7m
Module 35: Course Conclusion2m
8 readings
Pdf Version of Module 32: Develop and Apply the Principle of Impulse-Momentum to Rigid Bodies Undergoing Motion Lecture10m
Pdf Version of Module 33: Develop the Principle of Work-Energy for Bodies in 3D Rigid Body Motion Lecture10m
Pdf Version of Module 34: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion Lecture10m
Worksheet Solutions: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion10m
Pdf Version of Module 35: Course Conclusion Lecture10m
Where to go from here?10m
Practice Problems10m
Solution of Quiz 610m
1 practice exercises
3D Impulse-Momentum Principles; 3D Work-Energy Principles6m
4.8
Top Reviews
By AC•Nov 24th 2016
The instructor does a fascinating job of structuring and delivering the course material. The concepts are simplified and well explained with the help of practical applications and relevance.
By RA•Feb 13th 2017
It really changed my perception of viewing things around me. Dr. Whiteman is an expert at teaching mechanics. I recommend this course for all the non-circuit branches of engineering.
Instructor
Dr. Wayne Whiteman, PE
Senior Academic ProfessionalAbout Georgia Institute of Technology
The Georgia Institute of Technology is one of the nation's top research universities, distinguished by its commitment to improving the human condition through advanced science and technology.
Georgia Tech's campus occupies 400 acres in the heart of the city of Atlanta, where more than 20,000 undergraduate and graduate students receive a focused, technologically based education.
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