Lagrangian and Hamiltonian dynamics 1st Edition by Peter Mann 0192555410 9780192555410

Lagrangian & Hamiltonian dynamics 1st Edition by Peter Mann – Ebook PDF Instant Download/DeliveryISBN:  0192555410, 9780192555410 

Full download Lagrangian & Hamiltonian dynamics 1st Edition after payment.

Product details:

ISBN-10 :  0192555410 

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.

Lagrangian & Hamiltonian dynamics 1st table of contents:

Part I: Newtonian Mechanics
1: Newton’s Three Laws
1.1 Phase Space
1.2 Systems of Particles
1.3 The N-body Problem
Chapter summary
2: Energy and Work
Chapter summary
3: Introductory Rotational Dynamics
Chapter summary
4: The Harmonic Oscillator
Chapter summary
5: Wave Mechanics & Elements ofMathematical Physics
Part II: Lagrangian Mechanics
6: Coordinates & Constraints
Chapter summary
7: The Stationary Action Principle
7.1 The Inverse Problem
7.2 Higher-Order Theories & the Ostrogradsky Equation
7.3 The Second Variation
7.4 Functions & Functionals
7.5 Boundary Conditions
7.6 Variations
7.7 Weierstrass-Erdmann Conditions for Broken Extremals
7.8 Hamilton-Suslov Principle
Chapter summary
8: Constrained Lagrangian Mechanics
8.1 Holonomic Constraints
8.2 Non-Holonomic Constraints
Chapter summary
9: Point Transformations in Lagrangian Mechanics
Chapter summary
10: The Jacobi Energy Function
Chapter summary
11: Symmetries & Lagrangian-Hamilton-Jacobi Theory
11.1 Noether’s Theorem
11.2 Gauge Theory
11.3 Isotropic Symmetries
11.4 Caratheodory-Hamilton-Jacobi theory
Chapter summary
12: Near-Equilibrium Oscillations
12.1 Normal Modes
Chapter summary
13: Virtual Work & d’Alembert’s Principle
13.1 Gauss’s Least Constraint & Jourdain’s Principle
13.2 The Gibbs-Appell Equations
Chapter summary
Part III: Canonical Mechanics
14: The Hamiltonian & Phase Space
Chapter summary
15: Hamilton’s Principle in Phase Space
Chapter summary
16: Hamilton’s Equations & RouthianReduction
16.1 Phase Space Conservation Laws
16.2 Routhian Mechanics
17: Poisson Brackets & AngularMomentum
17.1 Poisson Brackets & Angular Momenta
17.2 Poisson Brackets & Symmetries
Chapter summary
18: Canonical & Gauge Transformations
18.1 Canonical Transformations I
18.2 Canonical Transformations II
18.3 In�nitesimal Canonical Transformations
Chapter summary
19: Hamilton-Jacobi Theory
19.1 Hamilton-Jacobi Theory I
19.2 Hamilton-Jacobi Theory II
Chapter summary
20: Liouville’s Theorem & ClassicalStatistical Mechanics
20.1 Liouville’s Theorem & the Classical Propagator
20.2 Koopman-von Neumann Theory
20.3 Classical Statistical Mechanics
20.4 Symplectic Integrators
Chapter summary
21: Constrained Hamiltonian Dynamics
Chapter summary
22: Autonomous Geometrical Mechanics
22.1 A Coordinate-Free Picture
22.2 Poisson Manifolds & Symplectic Reduction
22.3 Geometrical Lagrangian Mechanics
22.4 Elements of Constrained Geometry
Chapter summary
23: The Structure of Phase Space
23.1 Time-Dependent Geometrical Mechanics
23.2 Picturing Phase Space
Chapter summary
24: Near-Integrable Systems
24.1 Canonical Perturbation Theory
24.2 KAM Theory & Elements of Chaos
Part IV: Classical Field Theory
25: Lagrangian Field Theory
Chapter summary
26: Hamiltonian Field Theory
27: Classical Electromagnetism
Chapter summary
28: Noether’s Theorem for Fields
Chapter summary
29: Classical Path-Integrals
29.1 Con�guration Space Integrals
29.2 Phase Space Integrals
Part V: Preliminary Mathematics
30: The (Not So?) Basics
31: Matrices
32 :Partial Differentiation
33: Legendre Transforms
34:Vector Calculus
35:Differential Equations
36: Calculus of Variations
Part VI: Advanced Mathematics
37:Linear Algebra
38: Differential Geometry
Part VII: Exam-Style Questions

People also search for Lagrangian & Hamiltonian dynamics 1st:

lagrangian and hamiltonian dynamics pdf
    
lagrangian and hamiltonian dynamics usyd
    
global formulations of lagrangian and hamiltonian dynamics on manifolds
    
peter mann lagrangian and hamiltonian dynamics
    
lagrangian dynamics and hamiltonian formulation

Tags: Lagrangian, Hamiltonian, dynamics, Peter Mann