A Modern Approach To Classical MechanicsWorld Scientific Publishing Company, 30.12.2002 - 456 Seiten The approach to classical mechanics adopted in this book includes and stresses recent developments in nonlinear dynamical systems. The concepts necessary to formulate and understand chaotic behavior are presented. Besides the conventional topics (such as oscillators, the Kepler problem, spinning tops and the two centers problem) studied in the frame of Newtonian, Lagrangian, and Hamiltonian mechanics, nonintegrable systems (the Hénon-Heiles system, motion in a Coulomb force field together with a homogeneous magnetic field, the restricted three-body problem) are also discussed. The question of the integrability (of planetary motion, for example) leads finally to the KAM-theorem.This book is the result of lectures on 'Classical Mechanics' as the first part of a basic course in Theoretical Physics. These lectures were given by the author to undergraduate students in their second year at the Johannes Kepler University Linz, Austria. The book is also addressed to lecturers in this field and to physicists who want to obtain a new perspective on classical mechanics. |
Inhalt
| 1 | |
| 11 | |
3 Onedimensional motion of a particle | 27 |
4 Encountering peculiar motion in two dimensions | 59 |
5 Motion in a central force field | 85 |
6 The gravitational interaction of two bodies | 119 |
7 Collisions of particles Scattering | 145 |
8 Changing the frame of reference | 167 |
11 The rigid body | 249 |
12 Small oscillations | 291 |
13 Hamiltons canonical formulation of mechanics | 317 |
14 HamiltonJacobi theory | 347 |
15 Prom integrable to nonintegrable systems | 381 |
In retrospect | 411 |
Appendix | 413 |
Bibliography | 433 |
9 Lagrangian mechanics | 191 |
10 Conservation laws and symmetries in many particle systems | 225 |
| 437 | |
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according angle angular momentum angular velocity appear applied axis behavior body calculated called canonical center of mass chaotic Chapter closed components Consequently conserved quantities consider const constant constraint coordinate system coordinates corresponding cost curve defined depends derivative determined differential direction distance dynamical energy equal equation of motion equilibrium example exists expressed field Figure fixed force frame frequency function given gives gravitational Hamiltonian harmonic Hence independent inertial initial values integral interaction invariant Lagrangian matrix mechanics move obtain orbit origin oscillator parameters particle particular pendulum period phase space physical plane point masses position potential problem radius reduced reference relation relative remains respect rotation scattering shown shows solution solved surface symmetry takes theory tion trajectory transformation turning values vanishes variables vector yields