A Primer of Analytical Mechanics

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.