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Numerical Analysis of the Spring Pendulum System using MATLAB

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003890/00001

Material Information

Title: Numerical Analysis of the Spring Pendulum System using MATLAB
Physical Description: Book
Language: English
Creator: Brannock, Matthew
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2008
Publication Date: 2008

Subjects

Subjects / Keywords: Classical Mechanics
Numerical Analysis
Chaos
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The spring pendulum is a physical system which exhibits chaotic behavior; the motion is sensitive to initial conditions. The ordinary differential equations of this system can be derived using Lagrangian formalism, but cannot be solved analytically. Using computer software such as MATLAB allows for the numerical simulation of the spring pendulum system for any set of initial conditions. The Lyapunov Exponent is a measure of the chaotic nature of a system, and can be computed numerically. Primarily, the relationship between the Lyapunov exponent of the spring pendulum system as a function of the spring constant and the motion of the spring pendulum system was studied. Particular attention was paid to the local minima and maxima and resulting motion. No consistent correlation was found between the Lyapunov exponent as a function of the spring constant and the resulting motion. Further analysis of other relationships between the Lyapunov exponent and the motion is necessary, preferably in an automated fashion.
Statement of Responsibility: by Matthew Brannock
Thesis: Thesis (B.A.) -- New College of Florida, 2008
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Colladay, Don

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2008 B8
System ID: NCFE003890:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE003890/00001

Material Information

Title: Numerical Analysis of the Spring Pendulum System using MATLAB
Physical Description: Book
Language: English
Creator: Brannock, Matthew
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2008
Publication Date: 2008

Subjects

Subjects / Keywords: Classical Mechanics
Numerical Analysis
Chaos
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The spring pendulum is a physical system which exhibits chaotic behavior; the motion is sensitive to initial conditions. The ordinary differential equations of this system can be derived using Lagrangian formalism, but cannot be solved analytically. Using computer software such as MATLAB allows for the numerical simulation of the spring pendulum system for any set of initial conditions. The Lyapunov Exponent is a measure of the chaotic nature of a system, and can be computed numerically. Primarily, the relationship between the Lyapunov exponent of the spring pendulum system as a function of the spring constant and the motion of the spring pendulum system was studied. Particular attention was paid to the local minima and maxima and resulting motion. No consistent correlation was found between the Lyapunov exponent as a function of the spring constant and the resulting motion. Further analysis of other relationships between the Lyapunov exponent and the motion is necessary, preferably in an automated fashion.
Statement of Responsibility: by Matthew Brannock
Thesis: Thesis (B.A.) -- New College of Florida, 2008
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Colladay, Don

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2008 B8
System ID: NCFE003890:00001

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