scholarly journals CANONICALIZATION OF CONSTRAINED HAMILTONIAN EQUATIONS IN A SINGULAR SYSTEM

2020 ◽  
Vol 4 (12) ◽  
pp. 107-117
Author(s):  
Shan Cao ◽  
Jing-Li Fu ◽  
Hua-Shu Dou
Keyword(s):  
Hamiltonian System ◽  
Singular System ◽  
Canonical Equation ◽  
Variable Transformation ◽  
Hamiltonian Equations ◽  
Constrained Hamiltonian System ◽  
New Variables

In this paper, the canonicalization of constrained Hamiltonian system is discussed. Because the constrained Hamiltonian equations are non-canonical, they lead to many limitations in the research. For this purpose, variable transformation is constructed that satisfies the condition of canonical equation, and the new variables can be obtained by a series of derivations. Finally, two examples are given to illustrate the applications of the result.

scholarly journals Canonical Variables of The Second Kind and The Reduction of The N-Body Problem

1999 ◽  
Vol 172 ◽  
pp. 269-280
Author(s):  
John G. Bryant
Keyword(s):  
Hamiltonian System ◽  
Body Problem ◽  
Blow Up ◽  
Kepler Problem ◽  
Geometrical Optics ◽  
Canonical Variables ◽  
N Body Problem ◽  
Homogeneous Reduction ◽  
New Variables

AbstractWe introduce a new kind of canonical variables that prove very useful when the order of a Hamiltonian system can be reduced by one, as in the case of isoenergetic reduction, and of what we call homogeneous reduction. The Kepler Problem, Geometrical Optics and McGehee Blow-up are discussed as examples. Finally we carry out the isoenergetic reduction of the general N-Body Problem using the new variables, and briefly discuss its application to the problem of collision.

scholarly journals On the quest for generalized Hamiltonian descriptions of 3D-flows generated by the curl of a vector potential

2020 ◽  
Vol 17 (03) ◽  
pp. 2050042
Author(s):  
Oğul Esen ◽  
Partha Guha
Keyword(s):  
Hamiltonian System ◽  
Vector Potential ◽  
Three Dimensional ◽  
Hamiltonian Equations ◽  
3D Flows ◽  
Hamiltonian Analysis

We examine Hamiltonian analysis of three-dimensional advection flow [Formula: see text] of incompressible nature [Formula: see text] assuming that the dynamics is generated by the curl of a vector potential [Formula: see text]. More concretely, we elaborate Nambu–Hamiltonian and bi-Hamiltonian characters of such systems under the light of vanishing or non-vanishing of the quantity [Formula: see text]. We present an example (satisfying [Formula: see text]) which can be written as in the form of Nambu–Hamiltonian and bi-Hamiltonian formulations. We present another example (satisfying [Formula: see text]) which we cannot able to write it in the form of a Nambu–Hamiltonian or bi-Hamiltonian system while it can be manifested in terms of Hamiltonian one-form and yields generalized or vector Hamiltonian equations [Formula: see text].

scholarly journals REMARKS ON GENERALIZED UNCERTAINTY PRINCIPLE INDUCED FROM CONSTRAINT SYSTEM

2014 ◽  
Vol 29 (01) ◽  
pp. 1450002 ◽  
Author(s):  
MYUNGSEOK EUNE ◽  
WONTAE KIM
Keyword(s):  
Hamiltonian System ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Poisson Algebra ◽  
Minimal Length ◽  
Constraint System ◽  
Commutation Relations ◽  
Constrained Hamiltonian System ◽  
Dirac Brackets

The extended commutation relations for generalized uncertainty principle (GUP) have been based on the assumption of the minimal length in position. Instead of this assumption, we start with a constrained Hamiltonian system described by the conventional Poisson algebra and then impose appropriate second class constraints to this system. Consequently, we can show that the consistent Dirac brackets for this system are nothing, but the extended commutation relations describing the GUP.

scholarly journals Comment on “Hyperchaos in constrained Hamiltonian system and its control” by J. Li, H. Wu and F. Mei

2020 ◽  
Vol 101 (1) ◽  
pp. 639-654
Author(s):  
Wojciech Szumiński ◽  
Maria Przybylska ◽  
Andrzej J. Maciejewski
Keyword(s):  
Hamiltonian System ◽  
Constrained Hamiltonian System
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