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A Primer of Analytical Mechanics (Hardcover, 1st ed. 2018)
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A Primer of Analytical Mechanics (Hardcover, 1st ed. 2018)
Series: UNITEXT for Physics
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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.
General
Imprint: |
Springer International Publishing AG
|
Country of origin: |
Switzerland |
Series: |
UNITEXT for Physics |
Release date: |
March 2018 |
First published: |
2018 |
Authors: |
Franco Strocchi
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Dimensions: |
235 x 155 x 18mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
114 |
Edition: |
1st ed. 2018 |
ISBN-13: |
978-3-319-73760-7 |
Categories: |
Books >
Science & Mathematics >
Physics >
Classical mechanics >
General
|
LSN: |
3-319-73760-0 |
Barcode: |
9783319737607 |
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