Chaotic system?
I'm currently working on an individual project. In which I have created a program to simulate a particle bouncing around a finite bordered region.
Where I need help in understanding how I might show chaos in a finite region. For example, one region I am working with is the region left by inscribing a circle in a square. I know this region to be chaotic but I don't know how to show that through some form of data analysis. The data I have is the position and velocity, but due to the elastic nature of the system, the velocity only changes direction.
I started to create phase-plane diagrams for the system but didn't think that truly showed chaos and from there I do not know how to approach this problem.
chaos-theory billiards
edited Dec 12 '18 at 22:34
caverac
14k21130
asked Dec 12 '18 at 21:36
data_is_fundata_is_fun
83
add a comment |
I'm currently working on an individual project. In which I have created a program to simulate a particle bouncing around a finite bordered region.
Where I need help in understanding how I might show chaos in a finite region. For example, one region I am working with is the region left by inscribing a circle in a square. I know this region to be chaotic but I don't know how to show that through some form of data analysis. The data I have is the position and velocity, but due to the elastic nature of the system, the velocity only changes direction.
I started to create phase-plane diagrams for the system but didn't think that truly showed chaos and from there I do not know how to approach this problem.
chaos-theory billiards
edited Dec 12 '18 at 22:34
caverac
14k21130
asked Dec 12 '18 at 21:36
data_is_fundata_is_fun
83
add a comment |
I'm currently working on an individual project. In which I have created a program to simulate a particle bouncing around a finite bordered region.
Where I need help in understanding how I might show chaos in a finite region. For example, one region I am working with is the region left by inscribing a circle in a square. I know this region to be chaotic but I don't know how to show that through some form of data analysis. The data I have is the position and velocity, but due to the elastic nature of the system, the velocity only changes direction.
I started to create phase-plane diagrams for the system but didn't think that truly showed chaos and from there I do not know how to approach this problem.
chaos-theory billiards
edited Dec 12 '18 at 22:34
caverac
14k21130
asked Dec 12 '18 at 21:36
data_is_fundata_is_fun
83
I'm currently working on an individual project. In which I have created a program to simulate a particle bouncing around a finite bordered region.
Where I need help in understanding how I might show chaos in a finite region. For example, one region I am working with is the region left by inscribing a circle in a square. I know this region to be chaotic but I don't know how to show that through some form of data analysis. The data I have is the position and velocity, but due to the elastic nature of the system, the velocity only changes direction.
I started to create phase-plane diagrams for the system but didn't think that truly showed chaos and from there I do not know how to approach this problem.
chaos-theory billiards
chaos-theory billiards
edited Dec 12 '18 at 22:34
caverac
14k21130
asked Dec 12 '18 at 21:36
data_is_fundata_is_fun
83
edited Dec 12 '18 at 22:34
caverac
14k21130
asked Dec 12 '18 at 21:36
data_is_fundata_is_fun
83
edited Dec 12 '18 at 22:34
caverac
14k21130
edited Dec 12 '18 at 22:34
caverac
14k21130
edited Dec 12 '18 at 22:34
caverac
14k21130
14k21130
asked Dec 12 '18 at 21:36
data_is_fundata_is_fun
83
asked Dec 12 '18 at 21:36
data_is_fundata_is_fun
83
asked Dec 12 '18 at 21:36
data_is_fundata_is_fun
83
83
add a comment |
add a comment |
1 Answer
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Go to the section Billiards of this book: http://chaosbook.org/
The idea is to define a Poincare map, with the coordinates $s_n$ (the arc-length position along the boundary for the $n$-th bouncing) and $p_n$ (the momentum component parallel to the boundary). Based on this map you can study the stability of the problem and, therefore, whether it exhibits chaos
answered Dec 12 '18 at 22:05
caveraccaverac
14k21130
Thank you for directing me to the book it was very informative!
– data_is_fun
Dec 12 '18 at 22:26
@data_is_fun It is a great resource! I'm glad you found it useful
– caverac
Dec 12 '18 at 22:27
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Go to the section Billiards of this book: http://chaosbook.org/
The idea is to define a Poincare map, with the coordinates $s_n$ (the arc-length position along the boundary for the $n$-th bouncing) and $p_n$ (the momentum component parallel to the boundary). Based on this map you can study the stability of the problem and, therefore, whether it exhibits chaos
answered Dec 12 '18 at 22:05
caveraccaverac
14k21130
Thank you for directing me to the book it was very informative!
– data_is_fun
Dec 12 '18 at 22:26
@data_is_fun It is a great resource! I'm glad you found it useful
– caverac
Dec 12 '18 at 22:27
add a comment |
Go to the section Billiards of this book: http://chaosbook.org/
The idea is to define a Poincare map, with the coordinates $s_n$ (the arc-length position along the boundary for the $n$-th bouncing) and $p_n$ (the momentum component parallel to the boundary). Based on this map you can study the stability of the problem and, therefore, whether it exhibits chaos
answered Dec 12 '18 at 22:05
caveraccaverac
14k21130
Thank you for directing me to the book it was very informative!
– data_is_fun
Dec 12 '18 at 22:26
@data_is_fun It is a great resource! I'm glad you found it useful
– caverac
Dec 12 '18 at 22:27
add a comment |
Go to the section Billiards of this book: http://chaosbook.org/
The idea is to define a Poincare map, with the coordinates $s_n$ (the arc-length position along the boundary for the $n$-th bouncing) and $p_n$ (the momentum component parallel to the boundary). Based on this map you can study the stability of the problem and, therefore, whether it exhibits chaos
answered Dec 12 '18 at 22:05
caveraccaverac
14k21130
Go to the section Billiards of this book: http://chaosbook.org/
The idea is to define a Poincare map, with the coordinates $s_n$ (the arc-length position along the boundary for the $n$-th bouncing) and $p_n$ (the momentum component parallel to the boundary). Based on this map you can study the stability of the problem and, therefore, whether it exhibits chaos
answered Dec 12 '18 at 22:05
caveraccaverac
14k21130
answered Dec 12 '18 at 22:05
caveraccaverac
14k21130
answered Dec 12 '18 at 22:05
caveraccaverac
14k21130
answered Dec 12 '18 at 22:05
caveraccaverac
14k21130
14k21130
Thank you for directing me to the book it was very informative!
– data_is_fun
Dec 12 '18 at 22:26
@data_is_fun It is a great resource! I'm glad you found it useful
– caverac
Dec 12 '18 at 22:27
add a comment |
Thank you for directing me to the book it was very informative!
– data_is_fun
Dec 12 '18 at 22:26
@data_is_fun It is a great resource! I'm glad you found it useful
– caverac
Dec 12 '18 at 22:27
Thank you for directing me to the book it was very informative!
– data_is_fun
Dec 12 '18 at 22:26
Thank you for directing me to the book it was very informative!
– data_is_fun
Dec 12 '18 at 22:26
@data_is_fun It is a great resource! I'm glad you found it useful
– caverac
Dec 12 '18 at 22:27
@data_is_fun It is a great resource! I'm glad you found it useful
– caverac
Dec 12 '18 at 22:27
add a comment |
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