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 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
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: Mechanisms, Gruebler’s equation, inversion of mechanism,
Kinematics analysis, Inertia force in reciprocating parts, Friction clutches,
Brakes and Dynamometers, Gear trains.
This note covers the
following topics: Kinematics of Particles, Rectilinear, Curvilinear x-y,
Normal-tangential n-t, Polar r-theta, Relative motion, Force Mass Acceleration,
Work Energy, Impulse Momentum, Kinematics of Rigid Bodies, Rotation, Absolute
Motion, Relative Velocity, Relative Acceleration, Motion Relative to Rotating
Axes, Force Mass Acceleration and Kinetics of 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 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 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