Advanced Engineering Systems in Motion: Dynamics of Three Dimensional (3D) Motion

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Advanced Engineering Systems in Motion: Dynamics of Three Dimensional (3D) Motion

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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. --------------------------- 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 Mot…

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When you enroll for courses through Coursera you get to choose for a paid plan or for a free plan

  • Free plan: No certicification and/or audit only. You will have access to all course materials except graded items.
  • Paid plan: Commit to earning a Certificate—it's a trusted, shareable way to showcase your new skills.

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. --------------------------- 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. --------------------------- 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. --------------------------- 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.

Created by:  Georgia Institute of Technology
  • Taught by:  Dr. Wayne Whiteman, PE, Senior Academic Professional

    Woodruff School of Mechanical Engineering
Commitment 6 weeks of material; 5 to 7 hours per week work for students Language English How To Pass Pass all graded assignments to complete the course. User Ratings 4.8 stars Average User Rating 4.8See what learners said Coursework

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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.

Syllabus


WEEK 1


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, 13 readings expand


  1. Reading: Syllabus
  2. Reading: Consent Form
  3. Video: Course Introduction
  4. Reading: Pdf version of Course Introduction Lecture
  5. Video: Module 2: Derive the “Derivative Formula”; Define Angular Velocity for 3D Motion
  6. Reading: Pdf version Module 2: Derive the “Derivative Formula”; Define Angular Velocity for 3D Motion Lecture
  7. Video: Module 3: Define the Properties of Angular Velocity for 3D Motion
  8. Reading: Pdf version of Module 3: Define the Properties of Angular Velocity for 3D Motion Lecture
  9. Video: Module 4: Solve for the Angular Velocity of a body undergoing 3D Motion
  10. Reading: Pdf version of Module 4: Solve for the Angular Velocity of a body undergoing 3D Motion Lecture
  11. Reading: Worksheet Solutions: Solve for the Angular Velocity of a Body Undergoing 3D Motion
  12. Video: Module 5: Determine the Angular Acceleration for a Moving Reference Frame Relative to another Reference Frame
  13. Reading: Pdf version of Module 5: Determine the Angular Acceleration for a Moving Reference Frame Relative to another Reference Frame Lecture
  14. Video: Module 6: Solve for the Angular Acceleration for a Body expressed in a Series of Multiple Reference Frames
  15. Reading: Pdf version of Module 6: Solve for the Angular Acceleration for a Body expressed in a Series of Multiple Reference Frames Lecture
  16. Reading: Worksheet Solutions: Solve for the Angular Acceleration for a Body Expressed in a Series of Multiple Reference Frames
  17. Reading: Get from Georgia Tech
  18. Reading: Practice Problems
  19. Reading: Solution of Quiz 1

Graded: Course Introduction; Angular Velocity; Angular Acceleration

WEEK 2


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, 11 readings expand


  1. Video: Module 7: Velocities expressed in Moving Frames of Reference
  2. Reading: Pdf version of Module 7: Velocities expressed in Moving Frames of Reference Lecture
  3. Video: Module 8: Solve for Velocities Expressed in Moving Frames of Reference
  4. Reading: Pdf version of Module 8: Solve for Velocities Expressed in Moving Frames of Reference Lecture
  5. Reading: Worksheet Solutions: Solve for Velocities Expressed in Moving Frames of Reference
  6. Video: Module 9: Accelerations expressed in Moving Frames of Reference
  7. Reading: Pdf version of Module 9: Accelerations expressed in Moving Frames of Reference Lecture
  8. Video: Module 10: Solve for the Velocity and the Acceleration for Bodies Undergoing 3D Motion and Expressed in Moving Frames of Reference
  9. Reading: Pdf version of Module 10: Solve for the Velocity and the Acceleration for Bodies Undergoing 3D Motion and Expressed in Moving Frames of Reference Lecture
  10. Reading: Worksheet Solutions: Solve for the Velocity and the Acceleration for Bodies Undergoing 3D Motion and Expressed in Moving Frames of Reference
  11. Video: Module 11: Equations of Motion for a Particle Moving Close to the Earth
  12. Reading: Pdf version of Module 11: Equations of Motion for a Particle Moving Close to the Earth Lecture
  13. Video: Module 12: Solve a Problem for the Motion of Particles Moving Close to the Earth
  14. Reading: Pdf version of Module 12: Solve a Problem for the Motion of Particles Moving Close to the Earth Lecture
  15. Reading: Earn a Georgia Tech Badge/Certificate/CEUs
  16. Reading: Practice Problems
  17. Reading: Solution of Quiz 2

Graded: Velocities in Moving Reference Frames; Accelerations in Moving Reference Frames; The Earth as a Moving Frame

WEEK 3


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, 10 readings expand


  1. Video: Module 13: Eulerian Angles for 3D Rotational Motion
  2. Reading: Pdf version of Module 13: Eulerian Angles for 3D Rotational Motion Lecture
  3. Video: Module 14: Angular Velocity of Bodies in 3D Motion using Eulerian Angles
  4. Reading: Pdf version of Module 14: Angular Velocity of Bodies in 3D Motion using Eulerian Angles Lecture
  5. Video: Module 15: Derive Rotational Transformation Matrices
  6. Reading: Pdf version of Module 15: Derive Rotational Transformation Matrices Lecture
  7. Video: Module 16: Solve a Problem Using Rotational Transformation Matrices
  8. Reading: Pdf version of Module 16: Solve a Problem Using Rotational Transformation Matrices Lecture
  9. Video: Module 17: Review Particle Kinetics; Newton’s Laws for Particles; and Euler’s 1st Law for Bodies
  10. Reading: Pdf version of Module 17: Review Particle Kinetics; Newton’s Laws for Particles; and Euler’s 1st Law for Bodies Lecture
  11. Video: Module 18: Review the Definition of Angular Momentum; and Euler’s 2nd Law for Bodies
  12. Reading: Pdf version of Module 18: Review the Definition of Angular Momentum; and Euler’s 2nd Law for Bodies Lecture
  13. Video: Module 19: Angular Momentum for Bodies in 3D Motion
  14. Reading: Pdf version of Module 19: Angular Momentum for Bodies in 3D Motion Lecture
  15. Video: Module 20: Review Mass Moments of Inertia and Products of Inertia; Inertial Property Matrix
  16. Reading: Pdf version of Module 20: Review Mass Moments of Inertia and Products of Inertia; Inertial Property Matrix Lecture
  17. Reading: Practice Problems
  18. Reading: Solution of Quiz 3

Graded: Eulerian Angles; Eulerian Angles Rotation Matrices; Angular Momentum in 3D; Inertial Properties of 3D Bodies

WEEK 4


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, 9 readings expand


  1. Video: Module 21: Translational Transformation of Inertial Properties
  2. Reading: Pdf version of Module 21: Translational Transformation of Inertial Properties Lecture
  3. Video: Module 22: Rotational Transformation of Inertial Properties
  4. Reading: Pdf Version of Module 22: Rotational Transformation of Inertial Properties Lecture
  5. Video: Module 23: Rotational Transformation of Inertial Properties (cont)
  6. Reading: Pdf Version of Module 23: Rotational Transformation of Inertial Properties (cont) Lecture
  7. Video: Module 24: Define Principal Axes and Principal Moments of Inertia
  8. Reading: Pdf Version of Module 24: Define Principal Axes and Principal Moments of Inertia Lecture
  9. Video: Module 25: Determine Principal Axes and Principal Moments of Inertia
  10. Reading: Pdf Version of Module 25 Determine Principal Axes and Principal Moments of Inertia Lecture
  11. Video: Module 26: Solve for Principal Axes and Principal Moments of Inertia with an Example
  12. Reading: Pdf Version of Module 26: Solve for Principal Axes and Principal Moments of Inertia Lecture
  13. Reading: Worksheet Solutions: Solve for Principal Axes and Principal Moments of Inertia with an Example
  14. Reading: Practice Problems
  15. Reading: Solution of Quiz 4

Graded: Translational and Rotational Transformations of Inertial Properties; Principal Axes and Principal Moments of Inertia.

WEEK 5


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, 8 readings expand


  1. Video: Module 27: Develop Euler Equations for 3D Motion
  2. Reading: Pdf Version of Module 27: Develop Euler Equations for 3D Motion Lecture
  3. Video: Module 28: Develop Euler Equations for 3D Motion (cont.)
  4. Reading: Pdf Version of Module 28: Develop Euler Equations for 3D Motion (cont.) Lecture
  5. Video: Module 29: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion
  6. Reading: Pdf Version of Module 29: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture
  7. Video: Module 30: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion (cont.)
  8. Reading: Pdf Version of Module 30: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture
  9. Video: Module 31: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion (cont.)
  10. Reading: Pdf Version of Module 31: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture
  11. Reading: Worksheet Solutions: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion
  12. Reading: Practice Problems
  13. Reading: Solution of Quiz 5

Graded: Motion Equations Governing 3D Rotational Motion of a Rigid Body (Euler Equations)

WEEK 6


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, 8 readings expand


  1. Video: Module 32: Develop and Apply the Principle of Impulse-Momentum to Rigid Bodies Undergoing Motion
  2. Reading: Pdf Version of Module 32: Develop and Apply the Principle of Impulse-Momentum to Rigid Bodies Undergoing Motion Lecture
  3. Video: Module 33: Develop the Principle of Work-Energy for Bodies in 3D Rigid Body Motion
  4. Reading: Pdf Version of Module 33: Develop the Principle of Work-Energy for Bodies in 3D Rigid Body Motion Lecture
  5. Video: Module 34: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion
  6. Reading: Pdf Version of Module 34: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion Lecture
  7. Reading: Worksheet Solutions: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion
  8. Video: Module 35: Course Conclusion
  9. Reading: Pdf Version of Module 35: Course Conclusion Lecture
  10. Reading: Where to go from here?
  11. Reading: Practice Problems
  12. Reading: Solution of Quiz 6

Graded: 3D Impulse-Momentum Principles; 3D Work-Energy Principles
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