Open AccessBook
Classical Dynamical Systems
TLDR
In this article, the Hamiltonian Formulation of the Electrodynamic Equation of Motion has been used to describe the structure of space and time in the universe and its properties.Abstract:
1 Introduction.- 1.1 Equations of Motion.- 1.2 The Mathematical Language.- 1.3 The Physical Interpretation.- 2 Analysis on Manifolds.- 2.1 Manifolds.- 2.2 Tangent Spaces.- 2.3 Flows.- 2.4 Tensors.- 2.5 Differentiation.- 2.6 Integration.- 3 Hamiltonian Systems.- 3.1 Canonical Transformations.- 3.2 Hamilton's Equations.- 3.3 Constants of Motion.- 3.4 The Limit t ? I +- ?.- 3.5 Perturbation Theory: Preliminaries.- 3.6 Perturbation Theory: The Iteration.- 4 Nonrelativistic Motion.- 4.1 Free Particles.- 4.2 The Two-Body Problem.- 4.3 The Problem of Two Centers of Force.- 4.4 The Restricted Three-Body Problems.- 4.5 The N-body Problem.- 5 Relativistic Motion.- 5.1 The Hamiltonian Formulation of the Electrodynamic Equation of Motion.- 5.2 The Constant Field.- 5.3 The Coulomb Field.- 5.4 The Betatron.- 5.5 The Traveling Plane Disturbance.- 5.6 Relativistic Motion in a Gravitational Field.- 5.7 Motion in the Schwarzschild Field.- 5.8 Motion in a Gravitational Plane Wave.- 6 The Structure of Space and Time.- 6.1 The Homogeneous Universe.- 6.2 The Isotropic Universe.- 6.3 Me according to Galileo.- 6.4 Me as Minkowski Space.- 6.5 Me as a Pseudo-Riemannian Space.read more
Citations
More filters
Journal ArticleDOI
The Magnus expansion and some of its applications
TL;DR: Magnusson expansion as discussed by the authors provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory (TEPT).
Journal ArticleDOI
Cortical connections and parallel processing: structure and function
TL;DR: In this article, the cerebral cortex is modeled as a connectionist computer that is especially suited for parallel problem solving, and a detailed consideration of this model has several implications for the underlying anatomy and physiology.
Journal ArticleDOI
The Fermi-Pasta-Ulam problem: Paradox turns discovery
TL;DR: The Fermi-Pasta-Ulam paradox is a cracker-jack mystery as mentioned in this paper, and it has been studied extensively in the field of nonlinear dynamics/chaos.
Journal ArticleDOI
Path integration in non-relativistic quantum mechanics
TL;DR: In this paper, path integrals for path on curved spaces and for paths on multiply-connected spaces are computed explicitly and applied to problems in nonrelativistic quantum mechanics, such as wave functions, propagators on configuration spaces and on phase space, caustic problems, bound states.
Journal ArticleDOI
Canonical theories of Lagrangian dynamical systems in physics
TL;DR: In this paper, the authors formulate the variational problem for a given classical Lagrangian field theory in the framework of differential forms, and show that for m⩾2 independent and for n ⩾ 2 dependent (field) variables z a = ƒ a (x) a much wider variety of Legendre transformations ν μ a = ∂ μ ǫ a (n) → p a μ, L → H, exists than has been employed in physics.