Classical
Mechanics| Classical
Mechanics |
In General > s.a. history
of physics; state.
* Idea: The class of
physical theories in which the system has a well-defined history, with dynamics
described by (differential or functional) equations
of motion on a configuration space C (infinite-dimensional in field
theory); The logical
structure is that of a Boolean lattice.
* History: Since the
1970's, when it was realized that chaos arises even with few degrees of freedom
in non-linear systems,
the perspective in the field has changed.
* And quantum theory:
In classical mechanics, a Hamiltonian or a Lagrangian is useful in practice,
but conceptually by no means necessary; In quantum theory, the
situation
is different.
* Subjects of interest: Various general aspects of non-linear dynamical
systems, like chaos and turbulence.
* Important recent applications: Galaxy formation; Saturn ring structure.
Concepts, Phenomena, and Results > s.a. approaches
and formalisms; field theory.
* Work-energy theorem:
The net work done on an object under a displacement equals the object's change
in KE.
> Concepts: see
energy; entropy; force;
inertia; information;
statistical mechanics; time; Trajectory.
> Phenomena: see
chaos;
Friction; systems.
> Results: see Bertrand's
Theorem; Noether
Theorem.
Variations and Generalizations > s.a. hilbert
space; higher-order lagrangians; MOND.
* Standard ones: Special
and general relativistic dynamics; Quantum dynamics.
* Barbour-Bertotti: Classical,
without the ideal elements of inertial frames and external time (> see parametrized
theories).
* Super classical quantum
mechanics:
A proposed theory which is equivalent to the Heisenberg, Schrödinger,
and Dirac non-relativistic quantum mechanics, with the addition of Born's probabilistic
interpretation of the wave function built in from the start.
@ Relationship with special and general relativity: Havas RMP(64); NCB 102(88)495
[Newton's third law].
@ Relationship with quantum mechanics:
Dittrich & Reuter 01; Savickas AJP(02)
[and general relativity]; Valentini qp/03 [non-quantum
systems].
@ Quantum correction: Bouda & Djama PLA(01)
[second law]; Ward MPLA(02).
@ Post-Newtonian: Chicone gq/01-in
[equations of motion are functional differential equations].
@ Nambu mechanics: Lassig & Joshi LMP(97)
[constrained systems]; > s.a. poisson structure.
@ Supermechanics: Cariñena & Figueroa JPA(97)
[Hamiltonian and Lagrangian].
@ Other examples: Salesi IJMPA(02)qp/01 [spinning
particles].
@ Stochastic: Guerra PRP(81);
Streater RPMP(93)
[and Markov chains]; > s.a. stochastic processes.
@ Other generalizations: Lamb AJP(01)
[super-classical quantm mechanics]; Kisil JPA(04)qp/02,
Brodlie & Kisil in(03)qp,
Brodlie JMP(04)
[p-mechanics]; Khrennikov & Nilsson 04 [p-adic; r BAMS(06)];
Kisil RPMP(05)
[p-mechanics and field theory].
References > s.a. BRST transformations; parametrized
systems [including
relationalism]; spacetime; topological
field theories.
@ Resources: issue AJP(00)#4
[reviews].
@ Texts: Hertz re-56 [classic]; Mercier 59; Bergmann 62 [I]; Pars 65;
Aharoni 72; Desloge 82; Raychaudhuri 83; Griffiths 85; Fowles 86; Kibble 86;
Reichert
90;
Matzner & Shepley 91; Marsden 92; Barger & Olsson 95; Marion & Thornton
95; Hestenes 99; Teodorescu 07.
@ Texts, II: Kleppner & Kolenkow 73 [IIa advanced]; Chow 95; Iro 03;
Kibble & Berkshire
04;
Taylor 05.
@ Texts, III: Synge & Griffith 59; Saletan & Cromer 71; Sudarshan & Mukunda
75; Abraham & Marsden
78; Goldstein 80; Gallavotti 83; Woodhouse 87; Arnold 89; Calkin 96; Thirring
97; Corinaldesi 99; Greiner 02; Fasano
& Marmi 06.
@ Texts, problems:
Tonti 77 [method]; Lim 94 [and
solutions].
@ Texts, geometrical emphasis:
Marmo
et al 85; Holm 08.
@ Other emphasis: Lanczos 49 [variational methods]; Rasband 83, Abraham & Ratiu
94 [symmetries]; Katok & Hasselblatt
95, Scheck 97 [non-linear/chaos]; José & Saletan 98; Sussman & Wisdom
01 [conceptual-computational]; Johns 05 [relativity and quantum mechanics].
@ Foundations: Hesse AJP(64)
[philosophical]; Desloge AJP(89);
Gallavotti mp/05;
Darrigol SHPMP(07)
[necessary nature]; Prestron SHPSA(08) [Mach and Hertz].
> Online resources:
Internet
Encyclopedia of Science pages.
Main page – Abbreviations – Journals – Comments – Other
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
3 jul 2008