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A Primer of Analytical Mechanics

A Primer of Analytical Mechanics PDF Author: Franco Strocchi
Publisher: Springer
ISBN: 3319737619
Category : Science
Languages : en
Pages : 114
Book Description
This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a “gauge” transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book’s closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.

A Primer of Analytical Mechanics

A Primer of Analytical Mechanics PDF Author: Franco Strocchi
Publisher: Springer
ISBN: 3319737619
Category : Science
Languages : en
Pages : 114
Book Description
This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a “gauge” transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book’s closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.

A Primer of Analytical Mechanics

A Primer of Analytical Mechanics PDF Author: Franco Strocchi
Publisher: Springer
ISBN: 9783030088538
Category :
Languages : en
Pages : 114
Book Description


A Primer of Analytical Mechanics

A Primer of Analytical Mechanics PDF Author: F. Strocchi
Publisher:
ISBN: 9783319737621
Category : Mechanics, Analytic
Languages : en
Pages : 114
Book Description
This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a "gauge" transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book's closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.

A First Course in Analytical Mechanics

A First Course in Analytical Mechanics PDF Author: Klaus Rossberg
Publisher: John Wiley & Sons
ISBN:
Category : Mechanics, Analytic
Languages : en
Pages : 291
Book Description


Analytical Mechanics

Analytical Mechanics PDF Author: Nivaldo A. Lemos
Publisher: Cambridge University Press
ISBN: 1108416586
Category : Science
Languages : en
Pages : 470
Book Description
An introduction to the basic principles and methods of analytical mechanics, with selected examples of advanced topics and areas of ongoing research.

A Primer on Theoretical Soil Mechanics

A Primer on Theoretical Soil Mechanics PDF Author: Dimitrios Kolymbas
Publisher: Cambridge University Press
ISBN: 1009210327
Category : Technology & Engineering
Languages : en
Pages : 200
Book Description
A Primer to Theoretical Soil Mechanics is about adapting continuum mechanics to granular materials. The field of continuum mechanics offers many fruitful concepts and methods, however there is declining interest in the field due to its complex and fragmented nature. This book's purpose is therefore to facilitate the understanding of the theoretical principles of soil mechanics, as well as introducing the new theory of barodesy. This title argues for barodesy as a simple alternative to the plasticity theory used currently and provides a systematic insight into this new constitutive model for granular materials. This book therefore introduces a complex field from a fresh and innovative perspective using simple concepts, succinct equations and explanatory sketches. Intended for advanced undergraduates, graduates and PhD students, this title is also apt for researchers seeking advanced training on fundamental topics.

Analytical Mechanics for Relativity and Quantum Mechanics

Analytical Mechanics for Relativity and Quantum Mechanics PDF Author: Oliver Johns
Publisher: OUP Oxford
ISBN: 0191001627
Category : Science
Languages : en
Pages : 656
Book Description
An innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It presents classical mechanics in a way designed to assist the student's transition to quantum theory.

A Mathematical Primer on Quantum Mechanics

A Mathematical Primer on Quantum Mechanics PDF Author: Alessandro Teta
Publisher: Springer
ISBN: 3319778935
Category : Science
Languages : en
Pages : 259
Book Description
This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and spectral analysis of Schrödinger operators. The main content is complemented by numerous exercises that stimulate interactive learning and help readers check their progress.

Symmetry Breaking in the Standard Model

Symmetry Breaking in the Standard Model PDF Author: Franco Strocchi
Publisher: Springer
ISBN: 8876426604
Category : Science
Languages : en
Pages : 115
Book Description
The book provides a non-perturbative approach to the symmetry breaking in the standard model, in this way avoiding the critical issues which affect the standard presentations. The debated empirical meaning of global and local gauge symmetries is clarified. The absence of Goldstone bosons in the Higgs mechanism is non-perturbatively explained by the validity of Gauss laws obeyed by the currents which generate the relatedglobal gauge symmetry. The solution of the U(1) problem and the vacuum structure in quantum chromodynamics (QCD) are obtained without recourse to the problematic semiclassical instanton approximation, by rather exploiting the topology of the gauge group.

Complexity Management in Engineering Design – a Primer

Complexity Management in Engineering Design – a Primer PDF Author: Maik Maurer
Publisher: Springer
ISBN: 3662534487
Category : Technology & Engineering
Languages : en
Pages : 153
Book Description
The treatise supports understanding the phenomena of complexity in engineering, distinguishes complexity from other challenges and presents an overview of definitions and applied approaches.The historical background of complexity management is explained by highlighting the important epochs, their key actors and their discoveries, findings and developments. Knowing about the appearance of early system awareness in ancient Greece, the creation of mechanical philosophy in the 17th century and the discovery of classic physics enables the reader to better comprehend modern system sciences and management approaches.A classification of complexity management approaches by research fields indicates current focus areas and starting points for future discussions. In a comprehensive map, the classification points out mutual overlaps between engineering disciplines in terms of similar complexity management approaches.Finally, the treatise introduces a generic complexity management framework, which is based on structural management approaches.