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.
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.
What's included
6 videos13 readings1 assignment
Show info about module content
6 videos•Total 53 minutes
Course Introduction•5 minutes
Module 2: Derive the “Derivative Formula”; Define Angular Velocity for 3D Motion•13 minutes
Module 3: Define the Properties of Angular Velocity for 3D Motion•6 minutes
Module 4: Solve for the Angular Velocity of a body undergoing 3D Motion•10 minutes
Module 5: Determine the Angular Acceleration for a Moving Reference Frame Relative to another Reference Frame•8 minutes
Module 6: Solve for the Angular Acceleration for a Body expressed in a Series of Multiple Reference Frames•11 minutes
13 readings•Total 130 minutes
Syllabus•10 minutes
Consent Form•10 minutes
Pdf version of Course Introduction Lecture•10 minutes
Pdf version Module 2: Derive the “Derivative Formula”; Define Angular Velocity for 3D Motion Lecture•10 minutes
Pdf version of Module 3: Define the Properties of Angular Velocity for 3D Motion Lecture•10 minutes
Pdf version of Module 4: Solve for the Angular Velocity of a body undergoing 3D Motion Lecture•10 minutes
Worksheet Solutions: Solve for the Angular Velocity of a Body Undergoing 3D Motion•10 minutes
Pdf version of Module 5: Determine the Angular Acceleration for a Moving Reference Frame Relative to another Reference Frame Lecture•10 minutes
Pdf version of Module 6: Solve for the Angular Acceleration for a Body expressed in a Series of Multiple Reference Frames Lecture•10 minutes
Worksheet Solutions: Solve for the Angular Acceleration for a Body Expressed in a Series of Multiple Reference Frames•10 minutes
Velocities in Moving Reference Frames; Accelerations in Moving Reference Frames; The Earth as a Moving Frame
Module 2•3 hours to complete
Module details
In this section students will learn about velocities in moving reference frames, accelerations in moving reference frames, and the Earth as a moving frame.
What's included
6 videos11 readings1 assignment
Show info about module content
6 videos•Total 64 minutes
Module 7: Velocities expressed in Moving Frames of Reference•11 minutes
Module 8: Solve for Velocities Expressed in Moving Frames of Reference•10 minutes
Module 9: Accelerations expressed in Moving Frames of Reference•10 minutes
Module 10: Solve for the Velocity and the Acceleration for Bodies Undergoing 3D Motion and Expressed in Moving Frames of Reference•13 minutes
Module 11: Equations of Motion for a Particle Moving Close to the Earth•13 minutes
Module 12: Solve a Problem for the Motion of Particles Moving Close to the Earth•7 minutes
11 readings•Total 110 minutes
Pdf version of Module 7: Velocities expressed in Moving Frames of Reference Lecture•10 minutes
Pdf version of Module 8: Solve for Velocities Expressed in Moving Frames of Reference Lecture•10 minutes
Worksheet Solutions: Solve for Velocities Expressed in Moving Frames of Reference•10 minutes
Pdf version of Module 9: Accelerations expressed in Moving Frames of Reference Lecture•10 minutes
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 minutes
Worksheet Solutions: Solve for the Velocity and the Acceleration for Bodies Undergoing 3D Motion and Expressed in Moving Frames of Reference•10 minutes
Pdf version of Module 11: Equations of Motion for a Particle Moving Close to the Earth Lecture•10 minutes
Pdf version of Module 12: Solve a Problem for the Motion of Particles Moving Close to the Earth Lecture•10 minutes
Earn a Georgia Tech Badge/Certificate/CEUs•10 minutes
Practice Problems•10 minutes
Solution of Quiz 2•10 minutes
1 assignment•Total 30 minutes
Velocities in Moving Reference Frames; Accelerations in Moving Reference Frames; The Earth as a Moving Frame•30 minutes
Eulerian Angles; Eulerian Angles Rotation Matrices; Angular Momentum in 3D; Inertial Properties of 3D Bodies
Module 3•3 hours to complete
Module details
In this section students will learn about Eulerian Angles rotation matrices, angular momentum in 3D, and intertial properties of 3D bodies.
What's included
8 videos10 readings1 assignment
Show info about module content
8 videos•Total 70 minutes
Module 13: Eulerian Angles for 3D Rotational Motion•9 minutes
Module 14: Angular Velocity of Bodies in 3D Motion using Eulerian Angles•6 minutes
Module 16: Solve a Problem Using Rotational Transformation Matrices•7 minutes
Module 17: Review Particle Kinetics; Newton’s Laws for Particles; and Euler’s 1st Law for Bodies•10 minutes
Module 18: Review the Definition of Angular Momentum; and Euler’s 2nd Law for Bodies•8 minutes
Module 19: Angular Momentum for Bodies in 3D Motion•12 minutes
Module 20: Review Mass Moments of Inertia and Products of Inertia; Inertial Property Matrix•11 minutes
10 readings•Total 100 minutes
Pdf version of Module 13: Eulerian Angles for 3D Rotational Motion Lecture•10 minutes
Pdf version of Module 14: Angular Velocity of Bodies in 3D Motion using Eulerian Angles Lecture•10 minutes
Pdf version of Module 15: Derive Rotational Transformation Matrices Lecture•10 minutes
Pdf version of Module 16: Solve a Problem Using Rotational Transformation Matrices Lecture•10 minutes
Pdf version of Module 17: Review Particle Kinetics; Newton’s Laws for Particles; and Euler’s 1st Law for Bodies Lecture•10 minutes
Pdf version of Module 18: Review the Definition of Angular Momentum; and Euler’s 2nd Law for Bodies Lecture•10 minutes
Pdf version of Module 19: Angular Momentum for Bodies in 3D Motion Lecture•10 minutes
Pdf version of Module 20: Review Mass Moments of Inertia and Products of Inertia; Inertial Property Matrix Lecture•10 minutes
Practice Problems•10 minutes
Solution of Quiz 3•10 minutes
1 assignment•Total 30 minutes
Eulerian Angles; Eulerian Angles Rotation Matrices; Angular Momentum in 3D; Inertial Properties of 3D Bodies•30 minutes
Translational and Rotational Transformations of Inertial Properties; Principal Axes and Principal Moments of Inertia
Module 4•3 hours to complete
Module details
In this section students will learn about translational and rotational transformations of inertial properties, and principal axes and principal moments of inertia.
What's included
6 videos9 readings1 assignment
Show info about module content
6 videos•Total 47 minutes
Module 21: Translational Transformation of Inertial Properties•8 minutes
Module 22: Rotational Transformation of Inertial Properties•5 minutes
Module 23: Rotational Transformation of Inertial Properties (cont)•8 minutes
Module 24: Define Principal Axes and Principal Moments of Inertia•4 minutes
Module 25: Determine Principal Axes and Principal Moments of Inertia•11 minutes
Module 26: Solve for Principal Axes and Principal Moments of Inertia with an Example•11 minutes
9 readings•Total 90 minutes
Pdf version of Module 21: Translational Transformation of Inertial Properties Lecture•10 minutes
Pdf Version of Module 22: Rotational Transformation of Inertial Properties Lecture•10 minutes
Pdf Version of Module 23: Rotational Transformation of Inertial Properties (cont) Lecture•10 minutes
Pdf Version of Module 24: Define Principal Axes and Principal Moments of Inertia Lecture•10 minutes
Pdf Version of Module 25 Determine Principal Axes and Principal Moments of Inertia Lecture•10 minutes
Pdf Version of Module 26: Solve for Principal Axes and Principal Moments of Inertia Lecture•10 minutes
Worksheet Solutions: Solve for Principal Axes and Principal Moments of Inertia with an Example•10 minutes
Practice Problems•10 minutes
Solution of Quiz 4•10 minutes
1 assignment•Total 30 minutes
Translational and Rotational Transformations of Inertial Properties; Principal Axes and Principal Moments of Inertia.•30 minutes
Motion Equations Governing 3D Rotational Motion of a Rigid Body (Euler Equations)
Module 5•3 hours to complete
Module details
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.
What's included
5 videos8 readings1 assignment
Show info about module content
5 videos•Total 60 minutes
Module 27: Develop Euler Equations for 3D Motion•9 minutes
Module 28: Develop Euler Equations for 3D Motion (cont.)•5 minutes
Module 29: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion•15 minutes
Module 30: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion (cont.)•11 minutes
Module 31: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion (cont.)•20 minutes
8 readings•Total 80 minutes
Pdf Version of Module 27: Develop Euler Equations for 3D Motion Lecture•10 minutes
Pdf Version of Module 28: Develop Euler Equations for 3D Motion (cont.) Lecture•10 minutes
Pdf Version of Module 29: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture•10 minutes
Pdf Version of Module 30: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture•10 minutes
Pdf Version of Module 31: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion Lecture•10 minutes
Worksheet Solutions: Solve for the Motion of a Rigid Body Undergoing 3D Rotational Motion•10 minutes
Practice Problems•10 minutes
Solution of Quiz 5•10 minutes
1 assignment•Total 30 minutes
Motion Equations Governing 3D Rotational Motion of a Rigid Body (Euler Equations)•30 minutes
3D Impulse-Momentum Principles; 3D Work-Energy Principles
Module 6•2 hours to complete
Module details
In this section students will learn to develop and apply the principle of impulse-momentum and about 3D work-energy principles.
What's included
4 videos8 readings1 assignment
Show info about module content
4 videos•Total 33 minutes
Module 32: Develop and Apply the Principle of Impulse-Momentum to Rigid Bodies Undergoing Motion•15 minutes
Module 33: Develop the Principle of Work-Energy for Bodies in 3D Rigid Body Motion•8 minutes
Module 34: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion•8 minutes
Module 35: Course Conclusion•3 minutes
8 readings•Total 80 minutes
Pdf Version of Module 32: Develop and Apply the Principle of Impulse-Momentum to Rigid Bodies Undergoing Motion Lecture•10 minutes
Pdf Version of Module 33: Develop the Principle of Work-Energy for Bodies in 3D Rigid Body Motion Lecture•10 minutes
Pdf Version of Module 34: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion Lecture•10 minutes
Worksheet Solutions: Apply the Principle of Work-Energy for Bodies in 3D Rigid Body Motion•10 minutes
Pdf Version of Module 35: Course Conclusion Lecture•10 minutes
Where to go from here?•10 minutes
Practice Problems•10 minutes
Solution of Quiz 6•10 minutes
1 assignment•Total 30 minutes
3D Impulse-Momentum Principles; 3D Work-Energy Principles•30 minutes
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