E-Book Overview
A supplement to accompany Engineering Mechanics: Dynamics, 6th Edition by J.L. Meriam and L.G. Kraige. — 2nd Ed. — John Wiley, 2007. — 145 p.
Introduction An Introduction to MATLAB Kinematics of Particles Kinetics of Particles Kinetics of Systems of Particles Plane Kinematics of Rigid Bodies Plane Kinetics of Rigid Bodies Introduction to Three-Dimensional Vibration and Time Response
E-Book Content
Solving Dynamics Problems in MATLAB Brian D. Harper Mechanical Engineering The Ohio State University
A supplement to accompany Engineering Mechanics: Dynamics, 6th Edition by J.L. Meriam and L.G. Kraige
JOHN WILEY & SONS, INC. New York • Chichester • Brisbane • Toronto • Singapore
CONTENTS
Introduction Chapter 1
5 An Introduction to MATLAB
7
Numerical Calculations Writing Scripts (m-files) Defining Functions Graphics Symbolic Calculations Differentiation and Integration
7 10 12 13 21 24
Solving Equations
26
Chapter 2
37
Kinematics of Particles
2.1 Sample Problem 2/4 (Rectilinear Motion) 2.2 Problem 2/87 (Rectangular Coordinates) 2.3 Problem 2/126 (n-t Coordinates) 2.4 Sample Problem 2/9 (Polar Coordinates) 2.5 Sample Problem 2/10 (Polar Coordinates) 2.6 Problem 2/183 (Space Curvilinear Motion) 2.7 Sample Problem 2/16 (Constrained Motion of Connected Particles)
38 41 46 48 52 55
Chapter 3
61
Kinetics of Particles
3.1 Sample Problem 3/3 (Rectilinear Motion) 3.2 Problem 3/98 (Curvilinear Motion) 3.3 Sample Problem 3/17 (Potential Energy) 3.4 Problem 3/218 (Linear Impulse/Momentum) 3.5 Problem 3/250 (Angular Impulse/Momentum) 3.6 Problem 3/365 (Curvilinear Motion)
57
62 65 67 70 72 73
Chapter 4
Kinetics of Systems of Particles
77
4.1 Problem 4/26 (Conservation of Momentum) 4.2 Problem 4/62 (Steady Mass Flow) 4.3 Problem 4/86 (Variable Mass)
78 80 83
Chapter 5
87
Plane Kinematics of Rigid Bodies
5.1 Problem 5/3 (Rotation) 5.2 Problem 5/44 (Absolute Motion) 5.3 Sample Problem 5/9 (Relative Velocity) 5.4 Problem 5/123 (Relative Acceleration) 5.5 Sample Problem 5/15 (Absolute Motion)
88 93 95 99 100
Chapter 6
107
Plane Kinetics of Rigid Bodies
6.1 Sample Problem 6/2 (Translation) 6.2 Sample Problem 6/4 (Fixed-Axis Rotation) 6.3 Problem 6/98 (General Plane Motion) 6.4 Problem 6/104 (General Plane Motion) 6.5 Sample Problem 6/10 (Work and Energy) 6.6 Problem 6/206 (Impulse/Momentum)
Chapter 7
Introduction to Three-Dimensional Dynamics of Rigid Bodies
108 113 115 118 120 125
129
7.1 Sample Problem 7/3 (General Motion) 7.2 Sample Problem 7/6 (Kinetic Energy)
130 132
Chapter 8
137
Vibration and Time Response
8.1 Sample Problem 8/2 (Free Vibration of Particles) 8.2 Problem 8/139 (Damped Free Vibrations) 8.3 Sample Problem 8/6 (Forced Vibration of Particles)
138 140 143
INTRODUCTION
Computers and software have had a tremendous impact upon engineering education over the past several years and most engineering schools now incorporate computational software such as MATLAB in their curriculum. Since you have this supplement the chances are pretty good that you are already aware of this and will have to learn to use MATLAB as part of a Dynamics course. The purpose of this supplement is to help you do just that. There seems to be some disagreement among engineering educators regarding how computers should be used in an engineering course such as Dynamics. I will use this as an opportunity to give my own philosophy along with a little advice. In trying to master the fundamentals of Dyna