Comparative Review. Classical Dynamics of Particles and Systems, 4th ed.

2000 ◽  
Vol 68 (4) ◽  
pp. 390-393 ◽  
Author(s):  
Jerry Marion ◽  
Stephen Thornton ◽  
R. W. Robinett
Keyword(s):  
Classical Dynamics ◽  
Comparative Review ◽  
Dynamics Of Particles

Anatomy of the canonical transformation

1993 ◽  
Vol 345 (1677) ◽  
pp. 577-598 ◽  
Keyword(s):  
Fluid Dynamics ◽  
Canonical Transformation ◽  
Generating Functions ◽  
Hamiltonian Structure ◽  
Rigid Bodies ◽  
Symplectic Integrators ◽  
Classical Dynamics ◽  
Canonical Transformations ◽  
Geophysical Fluid Dynamics ◽  
Dynamics Of Particles

A concise account of the structure of the canonical transformation is given, in the lowest dimensional case. This case is chosen because it offers a special clarity in several respects. In particular, the diversity of possible generating functions is illustrated by m any examples which are not available elsewhere. Many of these are of physical interest, and some of them are multivalued. These examples are used to inform a comparative study of the several different definitions of a canonical transformation to be found in the literature. The paper is pertinent to all those branches of mechanics which can be given a hamiltonian representation. These include not only the classical dynamics of particles and rigid bodies, but also some more recent studies in continuum mechanics, including geophysical fluid dynamics. An area of particular modern interest is that of symplectic integrators. These are numerical integrating algorithms which generate a solution to Hamilton’s equations via a sequence of canonical transformations, which preserve the hamiltonian structure in the numerical solution.

The Classical Dynamics of Particles

Physics Today ◽  
1975 ◽  
Vol 28 (12) ◽  
pp. 56-57
Author(s):  
R. A. Mann ◽  
A. O. Barut
Keyword(s):  
Classical Dynamics ◽  
Dynamics Of Particles

Classical dynamics of particles and waves

2012 ◽  
pp. 310-337
Author(s):  
Vladimir V. Mitin ◽  
Dmitry I. Sementsov ◽  
Nizami Z. Vagidov
Keyword(s):  
Classical Dynamics ◽  
Dynamics Of Particles

scholarly journals A quantum route to the classical Lagrangian formalism

2021 ◽  
pp. 2150091
Author(s):  
F. M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort ◽  
G. Marmo ◽  
L. Schiavone ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Smooth Manifold ◽  
Von Neumann Algebra ◽  
Fundamental Question ◽  
Lagrangian Formalism ◽  
Classical Dynamics ◽  
New Approach ◽  
Von Neumann ◽  
Dynamics Of Particles

Using the recently developed groupoidal description of Schwinger’s picture of Quantum Mechanics, a new approach to Dirac’s fundamental question on the role of the Lagrangian in Quantum Mechanics is provided. It is shown that a function [Formula: see text] on the groupoid of configurations (or kinematical groupoid) of a quantum system determines a state on the von Neumann algebra of the histories of the system. This function, which we call q-Lagrangian, can be described in terms of a new function [Formula: see text] on the Lie algebroid of the theory. When the kinematical groupoid is the pair groupoid of a smooth manifold M, the quadratic expansion of [Formula: see text] will reproduce the standard Lagrangians on TM used to describe the classical dynamics of particles.

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