Lagrangian and Hamiltonian Dynamics First Edition Mann – Ebook Instant Download/Delivery ISBN(s): 9780198822370,9780198822387,0198822375,0198822383,9780192555410, 0192555413
Product details:
- ISBN 10: 0192555413
- ISBN 13: 9780192555410
- Author: Peter Mann
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton’s classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Most notable examples include the ‘classical wavefunction’, Koopman-von Neumann theory, classical density functional theories, the ‘vakonomic’ variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals, Nambu brackets and the full framing of mechanics in the language of differential geometry.
Table contents:
1: Newton’s Three Laws
3: Introductory Rotational Dynamics
4: The Harmonic Oscillator
5: Wave Mechanics & Elements ofMathematical Physics
6: Coordinates & Constraints
7: The Stationary Action Principle
8: Constrained Lagrangian Mechanics
9: Point Transformations in Lagrangian Mechanics
10: The Jacobi Energy Function
11: Symmetries & Lagrangian-Hamilton-Jacobi Theory
12: Near-Equilibrium Oscillations
13: Virtual Work & d’Alembert’s Principle
14: The Hamiltonian & Phase Space
15: Hamilton’s Principle in Phase Space
16: Hamilton’s Equations & RouthianReduction
17: Poisson Brackets & AngularMomentum
18: Canonical & Gauge Transformations
19: Hamilton-Jacobi Theory
20: Liouville’s Theorem & ClassicalStatistical Mechanics
21: Constrained Hamiltonian Dynamics
22: Autonomous Geometrical Mechanics
23: The Structure of Phase Space
24: Near-Integrable Systems
25: Lagrangian Field Theory
26: Hamiltonian Field Theory
27: Classical Electromagnetism
28: Noether’s Theorem for Fields
29: Classical Path-Integrals
30: The (Not So?) Basics
31: Matrices
32 :Partial Differentiation
33: Legendre Transforms
34:Vector Calculus
35:Differential Equations
36: Calculus of Variations
37:Linear Algebra
38: Differential Geometry
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