Mechanics: From Newton's Laws to Deterministic ChaosWorld Publishing Corporation, 1990 - 431 páginas A course in mechanics is of primary importance in any physics teaching program. Scheck's book integrates the various aspects of classical mechanics, relativistic mechanics, and modern topics such as deterministic chaos. Both the physical approach to mechanics and its mathematical foundations are emphasised. With elementary Newtonian mechanics as a starting point, the principles of canonical mechanics in Hamiltonian and Lagrangian formulations are outlined. Rigid bodies are treated in detail, and the basic concepts of special relativity are given. Particular emphasis is put on the geometrical aspects of mechanics, such as geometrical objects on manifolds. A chapter on stability and chaos concludes the book, introducing topics such as the long-time behavior of dynamical flows, deterministic chaos, and chaotic motion in celestial mechanics. |
Contenido
Elementary Newtonian Mechanics | 1 |
The Mechanics of Rigid Bodies | 3 |
Relativistic Mechanics | 4 |
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angle angular momentum angular velocity apocenter attractor axis calculate canonical equations canonical transformations center of mass charts conserved const coordinates defined degrees of freedom denotes derivative described differential equation dimension dynamical equations of motion Euler-Lagrange equations example Əqi finite fixed flow force field given Hamiltonian function harmonic oscillator I₁ inertia tensor inertial system initial conditions integral curve invariant kinetic energy Lagrangian function Legendre transformation linear Lorentz m₁ manifold mapping mass points matrix means mechanics momenta n-particle system neighborhood obtain one-form orbit p₁ parameter particle pendulum pericenter perturbation phase space physical plane Poincaré mapping Poisson bracket potential energy r₁ relative motion respect rigid body rotation scattering Sect shown in Fig shows sin² smooth solution symmetric symplectic theorem vanishes variables vector field