عنوان

A primer of analytical mechanics /

شابک

3030088537

شابک

3319737619

شابک

3319737627

شابک

9783030088538

شابک

9783319737614

شابک

9783319737621

شابک اشتباه

3319737600

شابک اشتباه

9783319737607

عنوان اصلي

A primer of analytical mechanics /

نام عام مواد

[Book]

نام نخستين پديدآور

Franco Strocchi.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2018.

نام خاص و کميت اثر

1 online resource (xi, 114 pages)

عنوان فروست

UNITEXT for physics,

شاپا ي ISSN فروست

2198-7882

متن يادداشت

Includes index.

متن يادداشت

Preface -- 1 Difficulties of Cartesian Newtonian Mechanics -- 1.1 Constraint forces -- 1.2 Non-inertial frames and fictitious forces -- 2 Lagrange equations -- 2.1 Degrees of freedom and Lagrangian coordinates -- 2.2 Lagrangian form of Newton's equations -- 2.3 Lagrange equations -- 2.4 Lagrange equations at work. Examples -- 2.5 Generalized potential -- 2.6 Larmor theorem -- 2.7 Physical meaning of Lagrange equations; conjugate momenta -- 2.8 Cyclic variables, symmetries and conserved conjugate momenta -- 2.9 Non-uniqueness of the Lagrangian -- 3 Hamilton equations -- 3.1 Energy conservation -- 3.2 Hamilton equations -- 3.3 Coordinate transformations and Hamilton equations -- 3.4 Canonical transformations -- 4 Poisson brackets and canonical structure -- 4.1 Constants of motion identified by -- Poisson brackets -- 4.2 General properties of Poisson brackets -- 4.3 Canonical structure -- 4.4 Invariance of Poisson brackets under canonical transformations -- 5 Generation of canonical transformations -- 5.1 Alternative characterization of canonical transformations -- 5.2 Extended canonical transformations -- 5.3 Generators of continuous groups of canonical transformations -- 5.4 Symmetries and conservation laws. Noether theorem -- 6 Small oscillations -- 6.1 Equilibrium configurations. Stability -- 6.2 Small oscillations -- 7 The common Poisson algebra of classical and quantum mechanics -- 7.1 Dirac Poisson algebra -- 7.2 A common Poisson algebra of classical and quantum mechanics -- Index.

بدون عنوان

0

متن يادداشت

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.

عنوان

Primer of analytical mechanics.

شماره استاندارد بين المللي کتاب و موسيقي

9783319737607

موضوع مستند نشده

Mechanics, Analytic.

موضوع مستند نشده

Mechanics, Analytic.

موضوع مستند نشده

PHD

موضوع مستند نشده

PHD

موضوع مستند نشده

SCI041000

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Strocchi, F.

تاريخ عمليات

20200823104427.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y