Reduction, Symmetry, and Phases in Mechanics.
Montgomery, Douglas C.
Reduction, Symmetry, and Phases in Mechanics. - 1st ed. - 1 online resource (118 pages) - Memoirs of the American Mathematical Society ; v.88 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Introduction -- 1 Some Examples -- 2 Reconstruction of dynamics for Hamiltonian systems -- 3 Reconstruction of dynamics for Lagrangian systems -- 4 Ehresmann connections and holonomy -- 5 Reconstruction phases -- 6 Averaging connections -- 7 Existence, uniqueness and curvature of the Hannay-Berry connections -- 8 The Hannay-Berry connection in the presence of additional symmetry -- 9 The Hannay-Berry connection on level sets of the momentum map -- 10 Case I: Bundles of symplectic manifolds with the canonical connection -- integrable systems -- 11 Case II: Cartan connections -- moving systems -- 12 The Cartan angles -- the ball in the hoop and the Foucault pendulum -- 13 Induced connections on the tower of bundles -- 14 The Hannay-Berry connection for general systems -- References.
9781470408596
Mechanics, Analytic.
Symmetry groups.
Holonomy groups.
Electronic books.
QA3 -- .M377 1990eb
531
Reduction, Symmetry, and Phases in Mechanics. - 1st ed. - 1 online resource (118 pages) - Memoirs of the American Mathematical Society ; v.88 . - Memoirs of the American Mathematical Society .
Intro -- Contents -- Introduction -- 1 Some Examples -- 2 Reconstruction of dynamics for Hamiltonian systems -- 3 Reconstruction of dynamics for Lagrangian systems -- 4 Ehresmann connections and holonomy -- 5 Reconstruction phases -- 6 Averaging connections -- 7 Existence, uniqueness and curvature of the Hannay-Berry connections -- 8 The Hannay-Berry connection in the presence of additional symmetry -- 9 The Hannay-Berry connection on level sets of the momentum map -- 10 Case I: Bundles of symplectic manifolds with the canonical connection -- integrable systems -- 11 Case II: Cartan connections -- moving systems -- 12 The Cartan angles -- the ball in the hoop and the Foucault pendulum -- 13 Induced connections on the tower of bundles -- 14 The Hannay-Berry connection for general systems -- References.
9781470408596
Mechanics, Analytic.
Symmetry groups.
Holonomy groups.
Electronic books.
QA3 -- .M377 1990eb
531