ORBi: Antippa Adel F. - Discrete Harmonic Oscillator: A Short Compendium of Formulas

Reference : Discrete Harmonic Oscillator: A Short Compendium of Formulas


	Document type :	Scientific congresses and symposiums : Paper published in a book
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics Physical, chemical, mathematical & earth Sciences : Physics Engineering, computing & technology : Computer science
	To cite this reference:	http://hdl.handle.net/2268/89001

Title :	Discrete Harmonic Oscillator: A Short Compendium of Formulas
Language :	English
Author, co-author :	Antippa, Adel F. [ > > ]
	Dubois, Daniel [Université de Liège - ULg > HEC-Ecole de gestion de l'ULg : UER > UER Opérations >]
Publication date :	2010
Main document title :	COMPUTING ANTICIPATORY SYSTEMS
Editor :	Dubois, Daniel
Publisher :	American Institute of Physics
Collection and collection volume :	AIP CONFERENCE PROCEEDINGS, VOLUME 1303, Daniel M. Dubois, Editor
Pages :	111-120
On invitation :	Yes
Audience :	International
ISBN :	978-0-7354-0858-6
City :	Melville, New York
Country :	USA
Event name :	CASYS'09 - Ninth International Conference on Computing Anticipatory Systems
Event date :	3-8 August 2009
Event organizer :	CHAOS
Event place (city) :	Liège
Event country :	Belgium
Keywords :	[en] discrete harmonic oscillator ; incursion ; hyperincursion ; synchronization ; orbital stability ; energy conservation
Abstract :	[en] Since 2002, we have, in seven papers, studied the problem of the discrete harmonic oscillator, analytically, numerically, and graphically, and made progress on a number of fronts. We identified the natural frequency of oscillation of the dual incursive oscillators, studied the system bifurcation generated by incursive discretization, and the frequency dependent correlation between the resulting incursive oscillators. We also studied the synchronization of the discretizing time interval with the frequency of oscillation. From this analysis there emerged a nonlinear (or more precisely bilinear) formalism that is perfectly stable at all time scales, and fully conserves the total energy of the system. The formalism is applicable to the discrete harmonic oscillator specifically, and to discrete Hamiltonian systems in general. In retrospect the important themes and crucial steps can more easily be identified, and this is the purpose of this short note. In it we give, in a unified notation, a short compendium of the key formulas. This summary can serve as a guide for navigating through the seven papers, as well as a practical concise manual for using the formalism.
Target :	Researchers ; Professionals ; Students ; General public ; Others
Permalink :	http://hdl.handle.net/2268/89001
DOI :	10.1063/1.3527145
Other URL :	http://link.aip.org/link/?APCPCS/1303/111/1

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