Ebook: The Hamilton-Type Principle in Fluid Dynamics: Fundamentals and Applications to Magnetohydrodynamics, Thermodynamics, and Astrophysics

The objective of this book is to contribute to specialized literature with the most significant results obtained by the author in Continuous Mechanics and Astrophysics. The nature of the book is largely determined by the fact that it describes Fluid Dynamics,Magnetohydrodynamics,and Classical Thermodynamics as branches of Lagrange’s Analytical Mechanics; and in that sense, the approach presented in it is markedly different from the treatment given to them in traditional text books. In order to reach that goal, a Hamilton-Type Variational Principle, as the proper mathermatical technique for the theoretical description of the dy- mic state of any fluid is formulated. The scheme is completed proposing a new group of variations regarding the evolution parameter which is time; and with the demonstration of a theorem concerning the invariance of the action integral under continuous and infinitesimal temporary transfor- tions. With all that has been mentioned before and taking into account the methodsof thecalculusof variationsandtheadequateboundaryconditions, a general methodology for the mathematical treatment of fluid flows characteristic of Fluid Dynamics, Magnetohydrodynamics, and also fluids at rest proper of Classical Thermodynamics is presented.

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The content of this book summarizes the basic re-search work accomplished by the author on the field of Fluid Dynamics, Magnetohydrodynaics (MHD), Classical Thermodynamics, and Astrophy-sics.

There is also a section attached to each chapter with the title of Selected Topics. In these sections fine theoretical points are cleared up and a large number of illustrative problems are solved.

The book is for those interested in the analytical treatment of perfect and real fluids, and in the dynamic state of fluids electrically charged which flow in magnetic fields.

With this material the authors hope to facilitate access to fundamental aspects of Fluid Dynamics, MHD, and Thermodynamics, and the application of these disciplines to Astrophysics.

The reader will need to be acquainted with Maxwell?s equations of Classical Electrodyna-mics, those of Hydrodynamics balance equations, and the fundamental postulates of Thermodynamics. But from the view point of the required mathematics, the book is self-contained with everything that is needed clearly stated within the text.

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The content of this book summarizes the basic re-search work accomplished by the author on the field of Fluid Dynamics, Magnetohydrodynaics (MHD), Classical Thermodynamics, and Astrophy-sics.

There is also a section attached to each chapter with the title of Selected Topics. In these sections fine theoretical points are cleared up and a large number of illustrative problems are solved.

The book is for those interested in the analytical treatment of perfect and real fluids, and in the dynamic state of fluids electrically charged which flow in magnetic fields.

With this material the authors hope to facilitate access to fundamental aspects of Fluid Dynamics, MHD, and Thermodynamics, and the application of these disciplines to Astrophysics.

The reader will need to be acquainted with Maxwell?s equations of Classical Electrodyna-mics, those of Hydrodynamics balance equations, and the fundamental postulates of Thermodynamics. But from the view point of the required mathematics, the book is self-contained with everything that is needed clearly stated within the text.

Content:
Front Matter....Pages i-xxv
General Principles....Pages 1-18
Mass Density....Pages 19-38
Analytical Mechanics....Pages 39-60
Ideal Fluids....Pages 61-94
Potential Flow....Pages 95-126
Viscous Fluids....Pages 127-156
Free Convection....Pages 157-184
Magnetohydrodynamics....Pages 185-206
Potential Flow in a Magnetic Field....Pages 207-222
Magnetohydrodynamic Waves....Pages 223-238
The Sunspots....Pages 239-266
The Hamilton Equations of Motion....Pages 267-292
Thermodynamics....Pages 293-332
The Magnetic Field in the Stability of the Stars....Pages 333-402
Back Matter....Pages 403-404

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The content of this book summarizes the basic re-search work accomplished by the author on the field of Fluid Dynamics, Magnetohydrodynaics (MHD), Classical Thermodynamics, and Astrophy-sics.

There is also a section attached to each chapter with the title of Selected Topics. In these sections fine theoretical points are cleared up and a large number of illustrative problems are solved.

The book is for those interested in the analytical treatment of perfect and real fluids, and in the dynamic state of fluids electrically charged which flow in magnetic fields.

With this material the authors hope to facilitate access to fundamental aspects of Fluid Dynamics, MHD, and Thermodynamics, and the application of these disciplines to Astrophysics.

The reader will need to be acquainted with Maxwell?s equations of Classical Electrodyna-mics, those of Hydrodynamics balance equations, and the fundamental postulates of Thermodynamics. But from the view point of the required mathematics, the book is self-contained with everything that is needed clearly stated within the text.

Content:
Front Matter....Pages i-xxv
General Principles....Pages 1-18
Mass Density....Pages 19-38
Analytical Mechanics....Pages 39-60
Ideal Fluids....Pages 61-94
Potential Flow....Pages 95-126
Viscous Fluids....Pages 127-156
Free Convection....Pages 157-184
Magnetohydrodynamics....Pages 185-206
Potential Flow in a Magnetic Field....Pages 207-222
Magnetohydrodynamic Waves....Pages 223-238
The Sunspots....Pages 239-266
The Hamilton Equations of Motion....Pages 267-292
Thermodynamics....Pages 293-332
The Magnetic Field in the Stability of the Stars....Pages 333-402
Back Matter....Pages 403-404
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