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: 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 note explains the following topics:
Newtonian Mechanics, Newtonian Gravitation, Simple Dynamical Systems, Fixed
Points and Limit Cycles, Lagranian Mechanics, Central Force Motion, Scattering
from Central Force Potential, Dynamics in Rotating Frames of Reference, Rigid
Body Dynamics , Oscillations, Hamiltonian Mechanics, Canonical Transformations,
Action-Angle Coordinates, Hamilton-Jacobi Theory.
This note covers the following topics:Dynamics of a Single
Particle, Kinematics of a Single Particle, Kinetics of a Single Particle,
Lagrange’s Equations of Motion for a Single Particle, Dynamics of a System of
Particles, Dynamics of Systems of Particles, Kinematics and Dynamics of a Single
Rigid Body, Constraints on and Potentials for Rigid Bodies, Kinetics of a Rigid
Body, Lagrange’s Equations of Motion for a Single Rigid Body.
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 course reviews
momentum and energy principles, and then covers the following topics:
Hamilton's principle and Lagrange's equations; three-dimensional kinematics
and dynamics of rigid bodies, steady motions and small deviations therefrom,
gyroscopic effects, and causes of instability, free and forced vibrations of
lumped-parameter and continuous systems; nonlinear oscillations and the phase
plane, nonholonomic systems, and an introduction to wave propagation in
continuous systems.
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
This note covers the following topics: Projectile
Motion, scillations: Mass on a Spring, forced Oscillations, Polar co-ordinates,
Simple Pendulum, Motion Under a Central Force, Kepler’s Laws, Polar equations of
motion, Differential Equation for the Particle Path, Planetary motion, Momentum,
Angular Momentum and Energy, Particle Motion under Gravity on Surface of
Revolution with Vertical Axis of Symmetry, Stability and Instability, Rotating
Systems, Many particle systems, Rigid body motion, Axisymmetric top.
Author(s): Prof. Sheila Widnall, Prof. John Deyst and Prof. Edward
Greitzer