Thad Morton

Dynamics (ENGR 2030)

Class Time:   MWF 1:00 - 1:50 p.m. (Spring)

Prerequisites:  ENGR 2010 Statics

Textbook:   Engineering Mechanics: Dynamics, by Gray, Costanzo, & Plesha, 2nd ed., McGraw-Hill (2013).   ISBN:  978-0-07-338030-8

When people think of engineering, they think of how to design, analyze, or repair machines, structures, or systems. But all of these tasks are founded on mathematics, and without mathematics, none of these can be done proficiently. Dynamics is about analyzing the motion of bodies or components of devices. This analysis encompasses the position of an object or mechanism (kinematics) and the forces it experiences (kinetics). So dynamics is important in the analysis and design of, for example, robots, satellites, household appliances, hand tools, machine tools, cranes, computer disk drives, engines, motors, brakes, door locks, and turbomachinery, such as compressors, fans, gas or steam turbines, automotive turbochargers, and torque converters.

My aim for this dynamics class is to equip students with some of the most powerful techniques for solving complex three-dimensional dynamics problems. These 3-D problems are made much easier by using tensor* methods. These methods allow the engineer to take a step back and spend his/her mental efforts most effectively. Students who have been trained in my class will be able to look at a mechanism (such as the figures below) and readily identify the relevant coordinate systems needed to analyze its motion. When faced with complex problems, these methods save time and are more reliable (less error-prone) than the usual vector component methods. If a design problem is set up with clarity, often the mathematics itself will show the engineer pieces of the puzzle that might be missing or what opportunities in the design lie unseized.

* The name “tensor” was originally derived from the “tension” experienced by a deformed solid. So the stress tensor was the first tensor so named. Since then, tensor analysis has been developed by numerous researchers. The power of tensor methods can be exploited in dynamics, fluid mechanics, general relativity, and nearly every other field of engineering.


                                       Spin testing of a gas turbine rotor.



                 Motion of a projectile above a rotating earth.


The methods I teach are those I have used while working in industry. I later realized that engineering students should get this kind of education; this is one of the reasons I decided to teach. SUU is one of only three state universities in Utah that offer an accredited B.S. degree in engineering, and after seeing some students' homework and their work in this course, I think their abilities in the topic are probably second to none.

Undergraduate dynamics courses usually follow a gradual building of complexity from 1-D, to 2-D, and finally, if time permits, to 3-D dynamics problems. Too often, the analysis of many real-world 3-D problems is not treated adequately expect in some graduate courses. But many engineering students do not go on to graduate school, and so will not learn how to solve complex 3-D problems efficiently and systematically. To help remedy this problem, in my undergraduate dynamics class last semester, after the standard 1-D introduction, I invested a couple of weeks teaching these three-dimensional methods, so that students from my class could solve complex 3-dimensional rigid-body dynamics problems systematically. Most gained valuable confidence in their abilities. The methods students learn in class are rarely, if ever, taught in an undergraduate dynamics course, but they help students in the work field and prepare them well for advanced graduate courses in robotics, dynamics, and controls. It is always helpful for students to have extra reliable tools to design or analyze products.


Teaching Journal

The purpose of the following teaching journal is to explain to those who will be hiring my engineering students what they learn in my dynamics class. Employers may not have a clear understanding of what was actually learned and accomplished in courses listed on students’ resumes, so in the following teaching journal, I will tell you myself what my students have learned and what types of problems they have solved. Students with good grades in this course have the problem solving skills employers are looking for.

Jan. 9, 2012


Jan. 11, 2012

       Rectangular Kinematics

Jan. 13, 2012

       Curvilinear Kinematics

Jan. 18, 2012

       Graphical Kinematics (2D Vectors)

Jan. 20, 2012

       Graphical Kinematics (2D Vectors),  Quiz 1

Jan. 23, 2012

       Graphical Kinematics (Design Synthesis)

Jan. 25, 2012

       Curvilinear Motion: Normal & Tangential Components

       (Projectile motion problems. Determining proper highway banking for automobile traffic.)

Jan. 27, 2012

       Curvilinear Motion: Cylindrical Components; Dependent Motion Analysis,  Quiz 2

       (Slotted arm problem. Rope & pulley problems.)

Jan. 30 2012

       Dependent Motion Analysis (Rope & pulleys); Equations of Motion (Momentum)

       (Dynamics of rope & pulley, block & tackle problems.)

Feb. 1, 2012

       Equations of Motion (Momentum); Normal & Tangential; Cylindrical Coordinates,  Quiz 3

       (Dynamics of airplane maneuvers, slotted arm devices.)

Feb. 3, 2012

       Work, Energy, and Power

       (Roller coaster dynamics problems, etc.)

Feb. 6, 2012

       Conservation of Energy,  Quiz 4

       (Dynamics of roller coasters with non-circular loops, bungee jumping problems.)

Feb. 8, 2012

       Impulse and Momentum

       (Ballistics problems. Analysis of ammunition performance and comparison with reported data.

       Dynamic analysis of rope & pulley devices using impulse and momentum.)

Feb. 10, 2012

       Conservation of Momentum;   Impact

       (Gun recoil problems. Oblique projectile impact problems.)

Feb. 13, 2012

       Tensors and Indicial Notation

Feb. 15, 2012

       Tensors and Indicial Notation

Feb. 17, 2012

       Exam 1

Feb. 20, 2012


Feb. 22, 2012

       Tensors and Indicial Notation

Feb. 24, 2012

       Exam 2


Three-Dimensional Kinematics of a Rigid Body

Feb. 27, 2012

       Time Derivatives in Rotating Systems; Relative Motion Analysis using Rotating Frames

Feb. 29, 2012

       Exam 3

Mar. 2, 2012

       Time Derivatives in Rotating Systems; Relative Motion Analysis using Rotating Frames

       (Determine velocity & acceleration of devices undergoing complex nested rotations.)

Mar. 5, 2012

       Relative Motion Analysis using Rotating Frames,  Quiz 1

       (Determine velocity & acceleration of devices undergoing complex nested rotations.)

Mar. 7, 2012

       Relative Motion Analysis using Rotating Frames

       (Determine velocity & acceleration of components attached to rotating motors on spinning platforms.)

Mar. 9, 2012

       Relative Motion Analysis using Rotating Frames

       (Determine velocity & acceleration of devices undergoing complex nested rotations.)

Mar. 12, 2012  ~ Mar. 16, 2012

       Spring Break

Mar. 19, 2012

       Relative Motion Analysis using Rotating Frames

       (Crane dynamics problem)

Mar. 21, 2012

       Relative Motion Analysis

       (Engine piston dynamics)

Mar. 23, 2012

       General Motion  (Gears)

Mar. 26, 2012

       General Motion  (Rotating fan blades)

Mar. 28, 2012

       General Motion   (Nested motions)


Three-Dimensional Kinetics of a Rigid Body

Mar. 30, 2012

       The Inertia Tensor – Derivation

Apr. 2, 2012

       The Inertia Tensor

       (Determine the inertia tensor of a pipe with arbitrary bends.)

Apr. 4, 2012

       The Inertia Tensor

Apr. 6, 2012

       Exam 4

Apr. 9, 2012

       Angular Momentum;    Kinetic Energy

       (Determine the kinetic energy of a satellite that is translating and rotating about 3 arbitrary axes.

       Determine the angular velocity of a suspended plate and the axis of its rotation after projectile impact.)

Apr. 11, 2012

       Angular Momentum;    Kinetic Energy

       (Determine the angular momentum vector and kinetic energy of a pipe with arbitrary bends upon rotation about a specified axis.)

Apr. 13, 2012

       Equations of Motion

       (Rope & pulley problem with inertial wheel)

Apr. 16, 2012

       Equations of Motion

       (Find bearing reaction forces on an unbalance rotating shaft.)

Apr. 18, 2012

       Work and Energy

       (Rope & pulley problem with inertial wheels and inertial pulleys)

Apr. 20, 2012

       Vibrations:    Forced, Viscous, Damped

       (Derivation of equations governing vibration.)

Apr. 23, 2012

       Vibrations:    Forced, Viscous, Damped

       (Determine equations governing vibration of a body suspended with springs and dashpots.

       Determine the angular velocity at which resonance will occur for a rotating unbalanced wheel. Determine its amplitude of vibration.)

Apr. 25, 2012

       Vibrations:    Forced, Viscous, Damped

May 2, 2012

                Comprehensive Final Exam

| Thad Morton |

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Last Update: Saturday, December 07, 2013