Lectures on analytical mechanics /

Bibliographic Details
Main Authors:	Kotkin, G. L. (Gleb Leonidovich) (Author), Serbo, V. G. (Valeriĭ Georgievich) (Author, Translator), Chernykh, A. I. (Author)
Other Authors:	Karpushina, O. V. (Translator)
Format:	eBook
Language:	English
Published:	Oxford, United Kingdom ; New York, NY : Oxford University Press, [2024]
Subjects:	Mechanics, Analytic. Mechanics. Mécanique analytique. Mécanique. mechanics (physics) Mathematical & Computational. Physics. SCIENCE. Quantum Theory. Science. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

6 Isotropic oscillator
7 The two-body problem
8 Scattering cross section. Rutherford's formula
8.1 Setup of the scattering problem
8.2 Small angle scattering
8.3 Rutherford's formula
Problems
9 Virial theorem
Problem
II Lagrangian mechanics
10 Lagrangian equations
10.1 Lagrangian equations for the non-relativistic particles in a potential field as a covariant notation of Newton's equations
10.2 Generalized coordinates and momenta
Problem
11 Principle of a least action
11.1 Hamiltonian principle. Covariance of the Lagrangian equations with respect to replacement of coordinates
11.2 Transformation of the Lagrangian function under transformation of coordinates and time
12 Lagrangian function for a particle in an electromagnetic field. Ambiguity in the choice of the Lagrangian function
13 Classic Zeeman effect
13.1 Charged particle in the Coulomb and magnetic fields
13.2 Strong magnetic field. Drift
14 Lagrangian function in the relativistic case
15 The Lagrangian function for systems with ideal holonomic constraints
Problems
16 Cyclic coordinates. Energy in the Lagrangian approach
16.1 Cyclic coordinates
16.2 Energy in the Lagrangian approach
16.3 Is the energy in the Lagrangian approach equal to the sum of kinetic and potential energies?
16.4 Ambiguity in the definition of energy
17 Symmetry and integrals of motion. Noether's theorem
17.1 Examples
17.2 Generalization
17.3 Noether's theorem
Problems
18 Fundamental conservation laws for a closed system of particles
19 Galilean transforms
20 Non-inertial frames of reference
20.1 Translational reference frame
20.2 Rotating reference frame
20.3 Larmor's theorem
21 Deviation of a freely falling body from the vertical
22 Effective Lagrangian function for electromechanical systems
III Oscillations
23 Linear oscillations
23.1 One degree of freedom
23.2 Oscillations of systems with many degrees of freedom
23.3 Flat double pendulum
24 Orthogonality of normal oscillations. The case of frequency degeneracy
24.1 Orthogonality of normal oscillations
24.2 The case of frequency degeneracy. Normal coordinates
24.3 Oscillations of weakly coupled systems. Beats
Problems