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.
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.
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.
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.
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.
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.
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.
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.
