Introduction to Mechanics
A modern introduction to Newtonian dynamics and the basics of special relativity, this book discusses standard topics such as Newton’s laws of motion, energy, linear and angular momentum, rigid body dynamics, and oscillations, then goes on to introduce modern topics such as symmetries, phase space, nonlinear dynamics and chaos. The author presents Newton’s equation of motion as a differential equation, bringing out key issues such as phase space and determinism in mechanical systems and helps introduce modern research topics such as chaos theory in a natural way. He highlights key assumptions of Newtonian mechanics and incorporates numerical solutions of many mechanical systems using MATLAB®.
Table of Contents
History of Mechanics. Newton’s Laws of Motion. Forces. Kinematics vs. Dynamics. Motion in One Dimension. Phase Space Description of Mechanical Systems. Symmetry Properties of Newton’s Equation. Two-Dimensional Motion; Central Force Problem. Three-Dimensional Mtion. Motion in a Nninertial Reference Frame. Energy. Conservation of Linear Momentum and Centre of Mass. Collisions. Simple Harmonic Motion. Nonlinear Oscillations and Chaos. Waves: Oscillations in Continuous Media. Angular Momentum. Rigid Body Dynamics. Special Theory of Relativity: Kinematics. Relativistic Dynamics. Epilogue. Appendix A: Present Paradigm of Physics and Science. Appendix B: Dimensional Analysis and Estimation. Appendix C: Numerical Solution of Differential Equations. Appendix D: Matlab and Octave. Appendix E: Vectors and Tensors. Appendix F: Vector Operations on Vector and Scalar Fields. Appendix G: Important Astronomical Data. Appendix H: Important Physical Constants. References. Index.
Dr Mahendra Verma is of the Indian Institute of Technology, India.
… as an introduction to the subject, undergraduates at all levels of study could benefit from leafing through its pages. Indeed I suspect many graduate students and even professors could gain fresh insight into concepts and problems. I certainly did, and have benefitted in my own teaching by reviewing this book. … Verma’s work covers a broad range of subject matter, managing to go into quite some depth in some areas … That it manages to do this without seeming crammed or cluttered says much about the excellent setting out and organisation of the sections. … it is probably the range of this book that sets it apart from others. As well as all the standard mechanics topics that could and should be encountered in such a volume, Verma manages to include fascinating and detailed analysis of phase space, tensors, special relativity, non-linear dynamics and solutions of differential equations (not to mention interludes on scientific history) all without loss of detail and this is highly commendable. There is even a short appendix on the use of MATLAB … this mechanics textbook will be of use to physicists at all stages of their development, from undergraduate right through to professorial level. I will indeed be recommending it to my students … .
—Vijay Tymms, Reviews, Volume 11, Issue 2, 2010