A Modern Approach to Classical MechanicsWorld Scientific, 2002 - 442 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 H non-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. |
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Inhalt
Introduction | 1 |
The foundations of mechanics | 11 |
Onedimensional motion of a particle | 27 |
Encountering peculiar motion in two dimensions | 59 |
Motion in a central force field | 85 |
The gravitational interaction of two bodies | 119 |
Collisions of particles Scattering | 145 |
Changing the frame of reference | 167 |
The rigid body | 249 |
Small oscillations | 291 |
Hamiltons canonical formulation of mechanics | 317 |
HamiltonJacobi theory | 347 |
From integrable to nonintegrable systems | 381 |
In retrospect | 411 |
B Rotations and tensors | 421 |
437 | |
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Häufige Begriffe und Wortgruppen
1/r potential angular momentum angular velocity axis canonical equations canonical transformation Cartesian center of mass central force field chaotic behavior classical mechanics components conservation law conserved quantities consider const constant constraint coordinate system curve degrees of freedom depends derivative determined differential equations dynamical eigenvalues eigenvectors ellipse equation of motion Euler-Lagrange equation example Əqi frequency function given in Eq Hamiltonian harmonic oscillator Hence inertial frame infinitesimal initial values integral interaction invariant L₂ Lagrange's equations Lagrangian linear matrix momenta obtain orbit P₁ parameters particle pendulum phase space plane Poincaré section point masses problem r₁ radius vector relation relative motion respect rigid body rotating frame sin² solution spherical Subsection surface symmetry tensor three body problem torus trajectory turning point two-dimensional vanishes variables w₁ ән дак