Classical Mechanics: with MATLAB Applications

✍ Scribed by Javier E Hasbun PhD

• Publisher: CreateSpace Independent Publishing Platform
• Year: 2018
• Tongue: English
• Leaves: 443
• Edition: 2
• Category: Library

✦ Synopsis

This is a textbook that deals with the subject of classical Mechanics. It is intended for students at the undergraduate level. The subject is considered essential for the advanced study of physics and engineering.

Students enrolled in undergraduate classical mechanics are assumed to have taken a year of calculus based physics. While students who have taken differential equations and mathematical physics will perform better in understanding the underlying concepts, such courses can easily be a co-requisite. The text makes use of traditional concepts in analytical mechanics such as Newton's laws of motion, harmonic motion, vector calculus, systems of coordinates, central forces, gravitation, systems of particles, rigid body rotation, Lagrangian dynamics, and non-linear dynamics. However, due to the large emphasis placed on computational physics in many departments, this text incorporates numerical methods using MATLAB. Scripts written in MATLAB are compatible with the open source OCTAVE platform.

The various concepts developed in the text are backed by MATLAB scripts, which are included within the text for easy comprehension. The accompanying compact disk contains the scripts' source code as well as the figures generated by the scripts. MATLAB is a popular computational tool that's available from http:///www.mathworks.com in a student or professional version and the open source OCTAVE is available form https://www.gnu.org/software/octave/. The scripts incorporated to carry out the multitude of calculations presented in the textbook are self-contained and should easily run on MATLAB versions 5.3 and above or OCTAVE. The scripts are fully commented so that students with little computational skills could easily modify them to make their own investigations of the various physics concepts and formulae.

The textbook contains a MATLAB tutorial in appendix A. Appendix B contains useful mathematical formulas employed in the text. Appendix C contains useful geometry formulas. Appendix D contains important line, area, and volume elements. For easy reference, needed physical constants often needed in computations are provided on the back and front covers.

✦ Table of Contents

Chapter 1 Review of Newtons Laws 1
Chapter 2 Application of Newtons Second Law of Motion in One Dimension 25
Chapter 3 Harmonic Motion in One Dimension 45
Chapter 4 Examples of Harmonic Motion 75
Chapter 5 Vectors and Differential Calculus 119
Chapter 6 Motion in Two and Three Dimensions 149
Chapter 7 Systems of Coordinates 181
Chapter 8 Central Forces 215
Chapter 9 Gravitation 253
Chapter 10 Rutherford Scattering 291
Chapter 11 System of Particles 319
Chapter 12 Motion of Rigid Bodies 391
Chapter 13 Lagrangian Dynamics 465
Appendix A MATLAB Tutorial 507
Appendix B Useful Mathematical Formulas Used in the Text 521
Appendix C Plane Geometry 523
Appendix D One Two and ThreeDimensional Elements 527
Answers to Selected Problems 529
References 537
Index 539