Lagrangian and Hamiltonian Dynamics by Peter Mann (PDF)

Description

An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton’s classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed indifferential geometry and field theories and can be used to introduce these subject areas to newcomers.Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications.The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the ‘classical wavefunction’, Koopman-von Neumann theory, classical density functional theories, the ‘vakonomic’ variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I got this text on Lagrangian and Hamiltonian Dynamics to extend and complete my understanding of modern physics. This is a beautiful text, easy to read and understand. Quite a joy to have in my personal library.

⭐The starting point is my starting point. To understand this review of a technical math text such as this, you should know that the math presented is at the very envelope of what I can grasp. I bought the book hoping to gain an intuitive understanding of these issues, not to become an expert. In some respects, for my purposes the text was excellent. The author tries hard to present images and analogies that bring the concepts and equations to life. The weakness in the text is the author presents important terms without defining them, introduces variables into equations without defining them, and similar slips. Finding a mu in the middle of an equation suddenly without explanation is very frustrating. All in all, a useful text for my purpose.

⭐Cannot speak of the content of the book, but if you’re like me and you love putting sticky notes in the book then be careful because the notes will tear layers of the pages off! The paper itself feels like really high quality paper so it’s odd that this is happening.

⭐As a retired aerospace engineer, this is like a security blanket as my mind wanders back to the exciting glory days of 10 new discoveries/hr. It’s almost like a trophy on the shelf, but I delight in reviewing half-forgotten intellectual playgrounds of the past.I have nothing profound or of value to state.

⭐wonderful

⭐I got this book in paperback from a friend as a present. The only thing that I have been doing with this book is reading it alongside working through Taylor’s Classical Mechanics. This book was incredible in the sense that it explains graduate level L&H mechanics in a very friendly way, also the problems are interesting and very unique to say the least, this book would be really good to go through as a preliminary for something like Analytical Mechanics by Lemos (I consider Lemos better than Goldstein) or Goldstein (he never gets to the bloody point, it’s like walking through 5 feet thick snow) or alongside either. The mathematics is concrete with their being plenty of vector calculus and partial derivatives (I think I noticed one typo on equation 1.3.5 where there is supposed to be a closed paranthesis before the dt’) so one doesn’t have to worry about that, diagrams are beautiful, the section on preliminary mathematics is actually very good, one shouldn’t be surprised that at this point so many authors botch the appendix section, this guy doesn’t, he actually dedicates a lot to the appendix and ironically enough, considering that the author in question isn’t even a university professor, he makes a really good detailed appendix.It actually helped me a lot when it came to the conceptual questions portion on my physics exams (the chapter summaries at the end of each chapter helped out with this) for analytically mechanics, i got them all completely correct, full points and everything, others couldn’t even explain the stuff but they knew how to calculate for these things.This book is pretty good if you want a nice comprehensional and conceptual introduction to langrangian and hamiltonians as long as you know your vector calculus, but primarily know your partial derivatives.

⭐I have read several mechanics books throughout my life, from very basic to advanced (i.e. Marden’s books). I can say this is a very original and very complete book, with several interesting applications, some unusual topics for basic mechanics texts such as Dirac brackets, the interface with statistical mechanics, path integrals, and an introduction of the modern geometric formulation of mechanics. For this reason I highly recommend this book for anyone who has a genuine interest and wants to learn the subject beyond what is required in exams. It can also serve as an introduction advanced topics such as geometric mechanics and classical field theory that can be a helpful before embarking on more advanced texts.

⭐There is definitely a need for a book like this. Most undergraduate physics courses start with Newtons laws, cover the Lagrangian formulation in great detail, give a thumbnail sketch of classical Hamiltonian dynamics and then it is straight into quantum mechanics. Hamilton-Jacobi theory, canonical transformations and the like are skipped over meaning that the classical inspiration for many developments in the quantum realm are not clear.Unfortunately, this book is a lot harder to read than it needs to be. The author has a fairly circuitous way of introducing topics that probably only makes full sense if you know the theory anyway and many of his explanations are opaque to say the least. Even relatively straightforward derivations are laboured and unintuitive. Quite often, you end up eventually deriving the same result yourself from scratch because the text makes little sense.If this was not bad enough, the equations are littered with errors. Subscripts are transposed, summation conventions are used in some places but not others, symbols are mis-typed or omitted. Relatively straightforward algebraic manipulation is needlessly performed in great detail, whereas simplifying assumptions are rarely spelled out.The subject matter is great and the author includes many worked examples which is a big plus. If a good editor knocked the text into shape and tidied up the equations, this could well be a classic. Right now it is not.

⭐Es un excelente libro para llevar como libro de texto de un curso formal de nivel licenciatura en ciencias. El libro inicia con un repaso de conceptos de mecánica de Newton y luego entra al tratamiento de la mecánica desde el enfoque de Lagrange y termina con el enfoque de Hammilton para sistemas no solo mecánicos si no híbridos.El libro esta perfectamente para que un estudiante de ciencias de nivel intermedio lo pueda seguir y entender, trae varios problemas propuestos de excelente nivel. También es un buen libro para estudiantes de nivel posgrado.El libro tiene una excelente calidad de hojas, las cuales vienen impresas con figuras a color, lo que permite una mejor comprensión de las figuras para así poderentender conceptos.

⭐

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