A Primer of Analytical Mechanics

• Main Author: Strocchi, Franco (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: UNITEXT for Physics,
• Subjects: Mechanics.; Mathematical physics.; Classical Mechanics.; Mathematical Physics.; Theoretical, Mathematical and Computational Physics.

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 e...

Table of Contents:

• 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.