Alan Adams, Professor Emeritus
States Naval Academy
collection of undergraduate Engineering Dynamics
analyses and solutions constitutes an
Engineering Lecture Complement (ELC).
It is a tool made
possible by Internet technology
and can be used to increase classroom productivity, teaching flexibility
and personalized learning.
computer oriented, WEB
is not an engineering text in the traditional sense. Important fundamental
definitions, concepts, and derivations found in many excellent texts are
not repeated. Here one begins with a problem, or application, and builds
upon the fundamental foundation as needed, just
This simulates the manner in which most engineering problems are addressed
in practice. If this material is used to support an introductory course
in college, the instructor should assure that the student is aware of all
assumptions, limitations, and abstractions inherent in the mathematical
definitions and theory. If this material is used by practicing engineers
or graduate students, they should be aware of suitable references that
can be used as needed to justify the selected approach to a problem.
texts in dynamics begin with the derivation of kinematic relationships.
Dynamics (kinetics) is then applied to particle analysis and finally to
a rigid body dynamic analysis. Many mathematical concepts from vector analysis,
matrix theory, relative kinematics and various coordinate systems are presented
before the dynamic analysis of a practical system is performed. This approach
was developed in the 1960's when national priorities dictated a more scientific
and analytical approach to engineering courses.
material is presented in an order more suitable to a new national priority,
e.g., the computer supported and Internet
based instruction of engineering courses.
Building on an assumed background in calculus and physics, rigid
body analysis occurs early
to make clear the distinction between dynamic analysis and static analysis
for systems in rectilinear or rotational motion. Consideration is given
to the non-linear effects that are necessary to accurately simulate many
real systems. Computer software for equation solving is then utilized to
allow the solution of more realistic mathematical models.
when appropriate, is considered a special
of rigid body analysis. When the basic laws of mechanics are applied to
systems where integration of a known acceleration is used to obtain the
velocity and displacement, complex
such as the kinematics of relative motion, moving coordinates, Coriolis
acceleration, etc., can
until needed in more complex applications. When the kinematic analysis
begins with non-lineardisplacement
equations, numerical techniques are often needed.Computer
supported by animation are then available to produce the continuous
of interest during a specified time interval, rather than an instantaneous
solution for a particular configuration typical of a traditional vector
analysis approach. The ability to animate vectors which represent continuous
kinematic behavior is made possible by the displacement loop equations.
When a complete kinematic analysis is combined with a full dynamic analysis
of a complex system, productivity demands that modern day engineers make
use of available simulation and/or solid modeling software such as ADAMS,
IDEAS, Working Model, ProEngineer, Algor,
of this collection of problem solutions, coupled with formal lecture, is
to create the experience
necessary for the eventual use of such
software for dynamic analysis.
in presenting this material is to use software which allows a "lecture
presentation of the mathematics, solution techniques, and discussions which
are suitable for either a distance
or for a complement to a traditional
collection of problems and solutions which make up this textual material
are generated using the equation solving software Mathcad,
and its symbolic processor which is a subset of MAPLE.
This software is available from MathSoft
chapter contains a small sample of problem solutions which hopefully will
inspire similar effort generated by the user.
gives a short review of vector
concepts that are used throughout. Vectors are used graphically more to
understand resulting kinematic and dynamic behavior rather than to formulate
a solution to the problem. Symbolic mathematics can often be used to actually
obtain the required differentiation and integration as illustrated throughout
first treats 2-D projectile
as particle motion without drag in the classical sense, but then includes
motion with drag which requires a numerical solution to a non-linear differential
equation to obtain velocity and displacement.
to motion of rigid bodies where inertial and/or friction effects are important.
Particle motion is a special case.
deals with linear and angular impluse
as applied to both rigid body motion and particle motion.
methods to both rigid bodies and particles. The use of symbolic mathematics
is predominate in this chapter.
considers 1-D and 2-D elastic, inelastic, real and oblique impact.
gives a full dynamic
supported by graphics and animation for two simple mechanisms. Animation
of the complete solution including kinematic and force vectors is created.
from the vector loop equation point of view. Both analytical and numerical
solutions are used. Animations show the relationship between resulting
vectors during complete cycles of operation. Components of acceleration
vectors include normal, tangential, centripetal and Coriolis. Velocity
vectors include absolute and relative components. In addition, .mpeg files
are available to show further realistic animation of actual mechanisms
if a broad band WEB connection is available to the user.
is normally not part of a first course in dynamics. It deals with the computation
of geometric properties
such as area, weight, centroids and mass moment of inertia for flat parts,
which cannot be
obtained from tables of simple geometric objects. Green's Theorem is used
along with contour integration. These properties are important parameters
in the dynamic equations of motion for planar mechanisms.
suitable for advanced analysis.