Lecture Notes on Dynamical Systems, Chaos And Fractal Geometry
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Lecture Notes on Dynamical Systems, Chaos And Fractal Geometry
Lecture Notes on Dynamical Systems, Chaos And Fractal Geometry
Topics covered in
this notes include: The Orbits of One-Dimensional Maps, Bifurcation and the
Logistic Family, Sharkovsky’s Theorem, Metric Spaces, Devaney’s Definition
of Chaos, Conjugacy of Dynamical Systems, Singer’s Theorem, Fractals,
Newton’s Method, Iteration of Continuous Functions, Linear Transformation
and Transformations Induced by Linear Transformations, Some Elementary
Complex Dynamics, Examples of Substitutions, Compactness in Metric Spaces
and the Metric Properties of Substitutions, Substitution Dynamical Systems,
Sturmian Sequences and Irrational Rotations.
Author(s): Geoffrey
R. Goodson, Towson University, Mathematics Department
This note describes the following topics: Equation of motion, Equations of motion for an inviscid fluid,
Bernoulli equation, The vorticity field, Two dimensional flow of a homogeneous,
incompressible, inviscid fluid and boundary layers in nonrotating fluids.
Topics covered in the
notes include : Introduction and Newton’s Laws , Kinematics, Forces, Energy,
Motion near equilibrium, Damped vibrations, Conservation of momentum,
Angular momentum and central forces, Waves on a string.
The contents of this pdf include : Introduction
to Mechanical Vibrations, Vibration Under Harmonic Forcing Conditions,
Vibration Under General Forcing Conditions, Two and Multi - Dof System,
Continuous Systems.
Author(s): G S D Madhav,
Assistant Professor, Y Shwetha, Assistant Professor, G Ram Vishal,
Assistant Professor, Department of Aeronautical Engineering, Institute
of Aeronautical Engineering
Dynamics
is the study of motion through phase space. The phase space of a given
dynamical system is described as an N-dimensional manifold, M. The topics
covered in this pdf are: Reference Materials, Dynamical Systems,
Bifurcations, Two-Dimensional Phase Flows, Nonlinear Oscillators,
Hamiltonian Mechanics, Maps, Strange Attractors, and Chaos, Ergodicity and
the Approach to Equilibrium, Front Propagation, Pattern Formation, Solitons,
Shock Waves.
Author(s): Daniel
Arovas, Department of Physics, University of California, San Diego
Molecular dynamics is a
computer simulation technique where the time evolution of a set of interacting
particles is followed by integrating their equation of motion. Topics covered
includes: Classical mechanics, Statistical averaging, Physical models of the
system, The time integration algorithm, Average properties, Static properties,
Dynamic properties.
This note describes the following topics: Newtonian
mechanics, Forces and dynamics, Motion in one dimension, Motion in higher
dimensions, Constrained systems, The Kepler problem, Systems of particles,
Rotating frames and rigid bodies.
This set of
lecture notes is an attempt to convey the excitement of classical dynamics from
a contemporary point of view. Topics covered includes: Dynamical Systems,
Newtonian System, Variational Principle and Lagrange equations, The Hamiltonian
Formulation, Hamilton-Jacobi Theory, Non-linear Maps and Chaos.
This note
provides a broad introduction to Newtonian dynamics of particles and rigid
bodies with applications to engineering design. Topics covered includes:
kinematics and dynamics of particles and rigid bodies, conservation laws,
vibrations of single degree of freedom systems, and use of MATLAB to solve
equations of motion and optimize engineering designs.
This note the explains the following
topics: Newton’s Laws of Motion, One-Dimensional Motion, Multi-Dimensional
Motion, Planetary Motion, Two-Body Dynamics, Rotating Reference Frames, Rigid
Body Rotation, Lagrangian Dynamics, Hamiltonian Dynamics, Coupled
Oscillations, Gravitational Potential Theory, Lunar Motion and The
Chaotic Pendulum.
This is an introductory course on Newtonian mechanics and special
relativity given to first year undergraduates. The notes were last updated
in April 2012. Individual chapters and problem sheets are available on the
link below. The full set of lecture notes come in around 145 pages and can
be downloaded here. This covers the following topics: Newtonian Mechanics,
Forces, Interlude, Dimensional Analysis, Systems of Particles, Central
Forces, Rigid Bodies, Non-Inertial Frames and Special Relativity.The lecture
notes can be downloaded in both PDF and PS formats
This is
a second course in classical mechanics, given to final year undergraduates.
They were last updated in July 2012. Individual chapters and problem sheets
are available below. The full set of lecture notes, weighing in at around
130 pages, can be downloaded here. This contains the following categories:
Newtonian Mechanics, The Lagrangian Formulation, The Motion of Rigid Bodies,
The Hamiltonian Formulation. The lecture notes can be downloaded in both PDF
and PS formats