Ebook: Mathematical Methods of Classical Mechanics

In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.

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In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.

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In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Content:
Front Matter....Pages N3-xvi
Front Matter....Pages 1-1
Experimental facts....Pages 3-14
Investigation of the equations of motion....Pages 15-52
Front Matter....Pages 53-53
Variational principles....Pages 55-74
Lagrangian mechanics on manifolds....Pages 75-97
Oscillations....Pages 98-122
Rigid bodies....Pages 123-159
Front Matter....Pages 161-161
Differential forms....Pages 163-200
Symplectic manifolds....Pages 201-232
Canonical formalism....Pages 233-270
Introduction to perturbation theory....Pages 271-300
Back Matter....Pages 301-519

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In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
Content:
Front Matter....Pages N3-xvi
Front Matter....Pages 1-1
Experimental facts....Pages 3-14
Investigation of the equations of motion....Pages 15-52
Front Matter....Pages 53-53
Variational principles....Pages 55-74
Lagrangian mechanics on manifolds....Pages 75-97
Oscillations....Pages 98-122
Rigid bodies....Pages 123-159
Front Matter....Pages 161-161
Differential forms....Pages 163-200
Symplectic manifolds....Pages 201-232
Canonical formalism....Pages 233-270
Introduction to perturbation theory....Pages 271-300
Back Matter....Pages 301-519
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