scholarly journals Not-so-classical mechanics: unexpected symmetries of classical motion

2005 ◽  
Vol 83 (2) ◽  
pp. 91-138 ◽  
Author(s):  
James T Wheeler
Keyword(s):  
Gauge Theories ◽  
Vries Equation ◽  
Classical Mechanics ◽  
Logistic Equation ◽  
Central Force ◽  
Newtonian Mechanics ◽  
Classical Motion ◽  
Recent Interest ◽  
Bohmian Quantum Mechanics ◽  
Force Problem

A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central-force problem; inequivalent Lagrangians and Hamiltonians; constants of central-force motion; a general discussion of higher order Lagrangians and Hamiltonians, with examples from Bohmian quantum mechanics, the Korteweg–de Vries equation, and the logistic equation; gauge theories of Newtonian mechanics; and classical spin, Grassmann numbers, and pseudomechanics. PACS No.: 45.25.Jj

scholarly journals From the Universe to Subsystems: Why Quantum Mechanics Appears More Stochastic than Classical Mechanics

2016 ◽  
Vol 15 (03) ◽  
pp. 1640002 ◽  
Author(s):  
Andrea Oldofredi ◽  
Dustin Lazarovici ◽  
Dirk-André Deckert ◽  
Michael Esfeld
Keyword(s):  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Bohmian Quantum Mechanics ◽  
The Universe

By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole the dynamical relations describing the evolution of subsystems. We explain how probabilities enter into this process, what quantum and classical probabilities have in common and where exactly their difference lies.

Genericity of the non-periodic solutions of the central force problem

1990 ◽  
Vol 165 (1) ◽  
pp. 95-99
Author(s):  
Ana Nunes ◽  
Josefina Casasayas
Keyword(s):  
Periodic Solutions ◽  
Central Force ◽  
Force Problem

scholarly journals Symmetries in central-force problems

2003 ◽  
pp. 47-52 ◽  
Author(s):  
V. Mioc ◽  
M. Barbosu
Keyword(s):  
Vector Fields ◽  
Body Problem ◽  
Blow Up ◽  
Central Force ◽  
Polar Coordinates ◽  
Global Flow ◽  
Two Body Problem ◽  
Concrete Problem ◽  
Central Force Problems ◽  
Force Problem

The two-body problem in central fields (reducible to a central-force problem) models a lot of concrete astronomical situations. The corresponding vector fields (in Cartesian and polar coordinates, extended via collision-blow-up and infinity-blow-up transformations) exhibit nice symmetries that form eight-element Abelian groups endowed with an idempotent structure. All these groups are isomorphic, which is not a trivial result, given the different structures of the corresponding phase spaces. Each of these groups contains seven four-element subgroups isomorphic to Klein?s group. These symmetries are of much help in understanding various characteristics of the global flow of the general problem or of a concrete problem at hand, and are essential in searching for periodic orbits.

scholarly journals Exponential Stability in the Perturbed Central Force Problem

2018 ◽  
Vol 23 (7-8) ◽  
pp. 821-841
Author(s):  
Dario Bambusi ◽  
Alessandra Fusè ◽  
Marco Sansottera
Keyword(s):  
Exponential Stability ◽  
Central Force ◽  
Force Problem

scholarly journals THEORETICAL MECHANICS OF 6-DIMENSIONAL (6D) CENTRAL-FORCE MOTION WITH TANGENTIAL OSCILLATIONS.

2014 ◽  
Vol 1 (1) ◽  
pp. 22-33
Author(s):  
Edison A. Enaibe ◽  
Akpata Erhieyovwe ◽  
Osafile E. Omosede
Keyword(s):  
Force Field ◽  
The Body ◽  
Central Force ◽  
Polar Coordinates ◽  
Theoretical Knowledge ◽  
Newtonian Mechanics ◽  
Central Force Field ◽  
Axis Of Rotation ◽  
Angular Velocities ◽  
Theoretical Mechanics

The relevance of the Central - force motion in the macroscopic and microscopic frames warrants a detailed study of the theoretical mechanics associated with it. So far, researchers have only considered central - force motion, as motion only in the translational and rotational elliptical plane with polar coordinates. However, the theoretical knowledge advanced by these researchers in line with this type of motion is scientifically restricted as several possibilities are equally applicable. In order to make the mechanics of a Central - force motion sufficiently meaningful, we have in this work extended the theory which has only been that of translational and rotational in the elliptical plane, by including fictitious radii and spin oscillations of the body about the axis of rotation. In this work, we used the methods of Newtonian mechanics to establish the new central-force field obeyed by the motion of a body, when the effect of spin oscillation is added. The new central-force field comprises of the radial accelerations, translational orbital angular velocity and the oscillating spin angular velocities. The energy conveyed in the spin oscillating phase increases as the orbital oscillating angles above or below the horizon of the elliptical plane is increased.

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