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
1970s, when it was realized that chaos arises even with few degrees of freedom
in non-linear systems, the perspective in the field has changed.

* __Subjects of interest__:
Various general aspects of non-linear dynamical systems, like chaos and turbulence.

* __Important recent applications__:
Galaxy formation; Saturn ring structure.

**Related Topics**

> __Approaches__: see formulations [including
dynamical systems]; hamiltonian dynamics; lagrangian dynamics.

> __Concepts__: see Degrees of Freedom;
energy; entropy; force;
inertia; information; statistical
mechanics; time; Trajectory.

> __Systems__: see classical systems;
field theory.

> __Phenomena__: see chaos;
Friction.

> __Results__: see Bertrand's Theorem;
noether theorem; Work-Energy Theorem.

**Variations and Generalizations** > s.a. hilbert space;
higher-order lagrangians; MOND.

* __Standard ones__: Special
and general relativistic dynamics; Quantum dynamics.

* __And quantum theory__:
Quantum corrections, if taken into account, introduce modifications to classical 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)aug [and general relativity];
Valentini PLA(04)qp/03 [non-quantum systems];
Bojowald et al PRD(12)-a1208 [higher time derivatives in effective dynamics];
Kurihara et al JTAP(14)-a1312 [classical mechanics as an equilibrium state of statistical mechanics].

@ __Quantum corrections__:
Bouda & Djama PLA(01) [second law];
Ward MPLA(02);
Vachaspati PRD(17)-a1704 [coherent state coupled to a quantum bath].

@ __Post-Newtonian__: Chicone gq/01-conf
[equations of motion are functional differential equations].

@ __Nambu mechanics__:
Lassig & Joshi LMP(97) [constrained systems];
> s.a. poisson structure.

@ __Supermechanics, anticommuting degrees of freedom__:
Cariñena & Figueroa JPA(97) [Hamiltonian and Lagrangian];
Bruce et al JGM(17)-a1606 [geometric].

@ __Other examples__: Salesi IJMPA(02)qp/01 [spinning particles].

@ __Stochastic__: Guerra PRP(81);
Streater RPMP(93) [and Markov chains];
Zambrini a1212
[path-integral inspired stochastic deformation of Lagrangian and Hamiltonian approaches];
> s.a. stochastic processes.

@ __Other generalizations__: Lamb AJP(01)apr [super-classical quantum 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];
Lämmerzahl & Rademaker PRD(12)-a0904 [higher-order equations of motion];
García-Morales CNSNS(16)-a1507 [semipredictable];
Chashchina a1902 [Planck-scale modification];
> s.a. conformal invariance.

**References** > s.a. BRST transformations;
parametrized systems [including relationalism];
spacetime; topological field theories.

@ __Resources__: issue AJP(00)apr [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,
08,
09 [comprehensive].

@ __Texts, II__: Chow 95;
Kibble & Berkshire 04;
Taylor 05;
Morin 08;
Verma 09;
Johnson 10;
Kleppner & Kolenkow 10 [II advanced];
Chaichian et al 12;
Chow 13;
Rajeev 13;
Englert 15;
Iro 15;
Nolte 15 [geometry, non-linear dynamics, complex systems, networks, relativity;
r PT(15)];
Bettini 16;
Nolting 16.

@ __Texts, III__: Synge & Griffith 59;
Saletan & Cromer 71;
Sudarshan & Mukunda 75;
Abraham & Marsden 78;
Goldstein 80;
Gallavotti 83;
Woodhouse 87;
Arnold 89;
Calkin 96 [Lagrangian and Hamiltonian];
Thirring 97;
Hand & Finch 98;
Corinaldesi 99;
Greiner 02;
Fasano & Marmi 06;
DiBenedetto 10;
Shapiro & de Berredo-Peixoto 13;
Lemos 18;
Leinaas 19.

@ __Geometrical emphasis__: Marmo et al 85;
Giachetta et al 10;
Holm 11;
Lessig a1206 [primer].

@ __Problems and solutions__:
Tonti 77 [method];
Lim 94;
de Lange & Pierrus 10.

@ __Other emphasis__: Lanczos 49 [variational methods];
Rasband 83,
Abraham & Ratiu 94 [symmetries];
Katok & Hasselblatt 95,
Scheck 10 [non-linear/chaos];
José & Saletan 98;
Johns 05 [relativity and quantum mechanics];
Müller-Kirsten 08 [relativity];
Thorne & Blandford 15 [applications];
Sussman & Wisdom 15 [conceptual-computational];
Hentschke 17
[numerical, theory of elasticity, engineering applications];
> s.a. computational physics.

@ __Foundations__: Hesse AJP(64)dec [philosophical];
Desloge AJP(89)aug;
Gallavotti in(06)mp/05;
Darrigol SHPMP(07) [necessary nature];
Preston SHPSA(08) [Mach and Hertz];
Sklar 13;
Hartmann a1307-PhD;
Alonso-Blanco & Muñoz-Díaz a1404,
a1411;
Lubashevsky a1603 [from "microlevel reducibility"].

> __Online resources__:
Internet Encyclopedia of Science pages.

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send feedback and suggestions to bombelli at olemiss.edu – modified 24 aug 2019