Lagrangian and hamiltonian formulation with fractional derivatives
Other Title(s)
المشتقة الكسرية و معادلات لاجرانج و هاميلتون
Dissertant
Thesis advisor
Comitee Members
al-Rusan, Akram A.
al-Umari, Husayn Yusuf
Masaifah, Yaqub
University
Mutah University
Faculty
Faculty of Science
Department
Department of physics
University Country
Jordan
Degree
Master
Degree Date
2003
English Abstract
The present work is divided in two parts: the First part is to study the effect of per fluorination on keto-enol tautomer's of 2-butanone and enol counterparts, and also the effect of inserting one and two fluorine atoms at different positions on the 2-butanone and enol counterparts.
The second Part is to study the effect of other substituents such as CF3, N02, CN, NC, CH3, NH2, O" at (a-position) on the 2-butanone and enol counterparts.
MINDO- Forces method was used to calculate heats of formation, electron densities and charge distributions with complete optimization of geometry of all compounds.
MNDO method was used to calculate the entropies of all compounds.
The substituents affect the geometrical parameters (bond lengths and angles) especially at the position where the substituent is attached.
The stabilizing effects of substituents on 2-butanone and enol counterparts were determine by thermodynamic calculations (Gibbs free energy) and isoseismic reactions.
First part: The calculated heats of formation (AHF) of 2-butanone I and 2-buten-2-ol 2 are -58.151 kcal / mol and -58.529 kcal / mol, respectively, i.e.
2-butanone i is less stable than its enol counterpart by 0.378 kcal / mol.
While the calculated heat of formation (AHF) of 1-buten-2-ol 3 is -53.677 kcal / mol i.e.
2-butanone 1 is more stable than its enol counterpart by 4.474 kcal / mol.
This is supported by calculation of Gibbs free energy (AG) between ketone 1 and enol 2 which was found to be -0.779 kcal/mol i.e.
reaction is spontaneous which means enol 2 is slightly stable than Ketone This is in agreement with published experimental results.
In the case of per fluorination of keto-enol system, per fluorination destabilized ketone greater than enol, this is supported by isoseismic reaction and Gibbs free energy Value.
For stepwise fluorination of keto-enol system, it was found that as the number of fluorine atoms increases the stability of the enol form increases relative to the keto form.
Second part: The effect of substituents such as N02, CF3, CN, NC, NH2, CH3, O" have been studied on 2-butanone.
Two enol counterparts are formed.
The first enol (la) has the substituent attached to the double bond and the second enol (lb) has the substituent attached to carbon adjacent to the double bond
Main Subjects
No. of Pages
53
Table of Contents
Table of contents.
Abstract.
Chapter one : Introduction.
Chapter two : Introduction to fractional calculus.
Chapter three : Lagrangian and hamiltonian mechanics with fractional derivatives.
Chapter four : Non-conservative lagrangian mechanics.
Chapter five : Conclusion.
References.
American Psychological Association (APA)
al-Halhuli, Tariq Sulayman M.. (2003). Lagrangian and hamiltonian formulation with fractional derivatives. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-303558
Modern Language Association (MLA)
al-Halhuli, Tariq Sulayman M.. Lagrangian and hamiltonian formulation with fractional derivatives. (Master's theses Theses and Dissertations Master). Mutah University. (2003).
https://search.emarefa.net/detail/BIM-303558
American Medical Association (AMA)
al-Halhuli, Tariq Sulayman M.. (2003). Lagrangian and hamiltonian formulation with fractional derivatives. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-303558
Language
English
Data Type
Arab Theses
Record ID
BIM-303558
