## Classical Mechanics: Hamiltonian and Lagrangian FormalismFormalism of classical mechanics underlies a number of powerful mathematical methods that are widely used in theoretical and mathematical physics. This book considers the basics facts of Lagrangian and Hamiltonian mechanics, as well as related topics, such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. The mathematical constructions involved are explicitly described and explained, so the book can be a good starting point for the undergraduate student new to this field. At the same time and where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for the graduate students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included. |

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### Contents

1 | |

2 Hamiltonian Formalism | 91 |

3 Canonical Transformations of TwoDimensional Phase Space | 137 |

4 Properties of Canonical Transformations | 147 |

5 Integral Invariants | 175 |

6 Some Mechanical Problems in a Geometric Setting | 189 |

7 Transformations Symmetries and Noether Theorem | 235 |

8 Hamiltonian Formalism for Singular Theories | 271 |

9 Classical and Quantum Relativistic Mechanics of a Spinning Particle | 353 |

437 | |

441 | |

### Other editions - View all

Classical Mechanics: Hamiltonian and Lagrangian Formalism Alexei Deriglazov No preview available - 2016 |

Classical Mechanics: Hamiltonian and Lagrangian Formalism Alexei Deriglazov No preview available - 2014 |

Classical Mechanics: Hamiltonian and Lagrangian Formalism Alexei Deriglazov No preview available - 2010 |

### Common terms and phrases

ˇ ˇ ˇ According to Eq acquires the form algebraic canonical transformation classical mechanics compute configuration space conserved Consider const construct coordinate transformations corresponding covariant curve defined denote Dirac bracket Dirac equation Dirac procedure discuss dynamics electromagnetic field equations of motion equivalent evolution example expression first-class constraints geodesic line geometric given Hamiltonian action Hamiltonian equations Hamiltonian formulation Hence identity implies infinitesimal symmetry inverse inverse matrix Lagrangian action Lagrangian equations linear local symmetry Lorentz matrix metric momenta momentum Noether charge obeys obtain parallel transport parametrization phase space physical Poincaré Poisson bracket potential primary constraint properties PxgPx quantity relativistic reparametrization represents Riemann space rotation S D Z Schrödinger equation second-class constraints Sect singular theory solution spinning particle substitution symplectic matrix tensor trajectory vanishes variables variational problem vector field velocity