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
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.
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
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
This note explains the following topics: Introduction to the
dynamics and vibrations of lumped-parameter models of mechanical systems,
Work-energy concepts, Kinematics, Force-momentum formulation for systems of
particles and rigid bodies in planar motion, Lagrange's
equations for systems of particles and rigid bodies in planar motion,
Virtual displacements and virtual work, Linearization of equations of
motion, Linear stability analysis of mechanical systems.
Author(s): Prof. Nicholas Hadjiconstantinou, Prof. Peter So, Prof. Sanjay Sarma and Prof.
Thomas Peacock
This note explains the
following topics: Mechanisms, Gruebler’s equation, inversion of mechanism,
Kinematics analysis, Inertia force in reciprocating parts, Friction clutches,
Brakes and Dynamometers, Gear trains.
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 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 covers
the following topics: Circle Diffeomorphisms, The Combinatorics of Endomorphisms,
Structural Stability and Hyperbolicity, Structure of Smooth Maps, Ergodic
Properties and Invariant Measures, Renormalization.
Author(s): Welington de Melo and Sebastian van Strien
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
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 book covers the following topics:
What Is Geometry, The Fitzgerald Contraction, Relativity, The World Of Four
Dimensions, Fields Of Force, Kinds Of Space, The New Law Of Gravitation And The
Old Law, Momentum And Energy, Electricity And Gravitation.