Classical mechanics illustrated by modern physics : 42 problems with solutions

In many fields of modern physics, classical mechanics plays a key role. However, the teaching of mechanics at the undergraduate level often confines the applications to old-fashioned devices such as combinations of springs and masses, pendulums, or rolling cylinders.This book provides an illustration of classical mechanics in the form of problems (at undergraduate level) inspired -- for the most part -- by contemporary research in physics, and resulting from the teaching and research experience of the authors. A noticeable feature of this book is that it emphasizes the experimental aspects of a large majority of problems. All problems are accompanied by detailed solutions: the calculations are clarified and their physical significance commented on in-depth. Within the solutions, the basic concepts from undergraduate lectures in classical mechanics, necessary to solve the problems, are recalled when needed. The authors systematically mention recent bibliographical references (most of them freely accessible via the Internet) allowing the reader to deepen their understanding of the subject, and thus contributing to the building of a general culture in physics.

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The foundations of physics lie in classical mechanics, the subject matter of this course resource. Guery-Odelin and Lahaye (both, Paul Sabatier Univ., France) inform the fundamental concepts of the subject with their own research. The unique aspect of this challenging text lies in the inclusion of special topics such as friction, movement of charged particles, and manipulation of atoms by using lasers. The book also covers traditional topics from classical mechanics that are connected to advanced topics such as superfluidity. The text is divided into 11 chapters, and the material in each chapter is graded into three levels of difficulty to give the instructor a choice in making appropriate selections for consideration in a course. Each chapter has solved examples, but a major drawback is the absence of end-of-chapter problems. The authors provide good suggestions for additional reading, citing many primary sources, and include a serviceable index. The book would best serve as a supplement to a more traditional classical mechanics book. Summing Up: Recommended. Academic audiences, upper-division undergraduate and above. N. Sadanand Central Connecticut State University

Foreword	p. v
Preface	p. vii
Acknowledgments	p. ix
Notations	p. xv
1 Orders of Magnitude and Dimensional Analysis	p. 1
1.1 A few orders of magnitude*	p. 1
1.2 Dimensional analysis*	p. 6
2 Motion in the Gravity Field	p. 13
2.1 Safety parabola*	p. 13
2.2 Shape of a liquid jet*	p. 15
2.3 The tautochrone curve**	p. 18
2.4 Gravitational cavity**	p. 22
3 Friction	p. 29
3.1 Energy balance for forced oscillations*	p. 29
3.2 Solid friction versus fluid friction*	p. 32
3.3 Fluid friction and delayed response**	p. 37
3.4 Absence of dissipation in a system with friction**	p. 40
4 Rotating Frames	p. 45
4.1 The rotating saddle*	p. 45
4.2 When Coriolis enters the game*	p. 49
5 Oscillators	p. 57
5.1 Oscillation period**	p. 57
5.2 Optimal transport of a bunch of atoms**	p. 63
5.3 Trajectory in a curved guide**	p. 69
5.4 Role of non-linearities***	p. 72
6 A Few Theorems in Mechanics	p. 81
6.1 The virial theorem**	p. 81
6.2 Adiabatic invariants***	p. 85
6.3 Lax form and constants of motion***	p. 91
7 Collisions	p. 101
7.1 Collisions and thermalization*	p. 101
7.2 Minimum distance of approach*	p. 105
7.3 Landau's criterion of superfluidity**	p. 106
7.4 Collision cross section**	p. 110
7.5 Slowing atoms with a moving wall**	p. 125
8 Manipulation of Charged Particles	p. 135
8.1 Coulomb crystal*	p. 135
8.2 Normal modes of a one-dimensional ion chain**	p. 138
8.3 Monopole mode for interacting particles**	p. 146
8.4 Mass spectrometry**	p. 149
8.5 Ponderomotive force**	p. 161
8.6 Effective potential and phase jump**	p. 167
9 ôColdö Atoms	p. 173
9.1 Effusive atomic beam**	p. 174
9.2 Zeeman slower**	p. 180
9.3 Doppler cooling**	p. 188
9.4 Time-of-flight thermometry**	p. 197
9.5 Linear and parametric heating***	p. 200
9.6 Evaporative cooling*	p. 207
10 Celestial Mechanics	p. 213
10.1 Closed trajectories in a central field*	p. 213
10.2 Lagrange points***	p. 215
11 Relativistic Mechanics	p. 229
11.1 On the other side of the Galaxy*	p. 229
11.2 Relativistic oscillator**	p. 232
11.3 Perihelion precession of Mercury**	p. 235
11.4 Electron motion in a plane wave***	p. 239
Index	p. 247

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