This note describes the
following topics: The Calculus of Variations, Fermat's Principle of Least
Time, Hamilton's Principle and Noether's Theorem, Mechanical Similarity,
Hamilton's Equations, Poisson Brackets, A New Expression for the Action,
Maupertuis' Principle, Canonical Transformations, Liouville's Theorem, The
Hamilton-Jacobi Equation, Adiabatic Invariants and Action-Angle Variables,
Mathematics for Orbits, Keplerian Orbits, Elastic Scattering, Small
Oscillations, Driven Oscillator, One-Dimensional Crystal Dynamics,
Parametric Resonance, The Ponderomotive Force, Resonant Nonlinear
Oscillations, Rigid Body Motion, Moments of Inertia, Rigid Body Moving
Freely, Euler Angles, Eulers Equations, Non Inertial Frame, Coriolis effect,
A Rolling Sphere on a Rotating Plane.
The topics in this lecture
notes are : Linear and Nonlinear Oscillators, Lagrangian and Hamiltonian
equations of motion, Canonical transformations, Liouville’s theorem,
Action-angle variables, Coordinate system and Hamiltonian in an accelerator,
Equations of motion in accelerator, Action-angle variables for circular
machines, Field errors and nonlinear resonances, Resonance overlapping and
dynamic aperture, The kinetic equation, Radiation damping effects, Primer in
Special Relativity, Selected electrostatic and magnetostatic problems, Self
field of a relativistic beam, Effect of environment on electromagnetic field
of a beam, Plane electromagnetic waves and Gaussian beams, Radiation and
retarded potentials, Scattering of electromagnetic waves, Synchrotron
radiation, Undulator radiation, Transition and diffraction radiation,
Formation length of radiation and coherent effects, Synchrotron radiation
reaction force, Waveguides and RF cavities, Laser acceleration in vacuum.
Inverse FEL acceleration.
Author(s): G.
Stupakov, The US Particle Accelerator School
Classical mechanics is the branch of physics that deals
with the study of the motion of anything larger than an atom or a molecule. This
book explains the following topics: Reference frames, displacement, and
velocity, Acceleration, Momentum and Inertia, Kinetic Energy, Interactions and
energy, Interactions, Forces, Impulse, Work and Power, Motion in two
dimensions, Rotational dynamics, Gravity, Simple harmonic motion, Waves in one
dimension, Thermodynamics.
Author(s): Julio Gea-Banacloche University of
Arkansas, Fayetteville
This is a “minimalist” textbook for a first semester of
university, calculus-based physics, covering classical mechanics, plus a
brief introduction to thermodynamics. Topics covered includes: Acceleration,
Momentum and Inertia, Kinetic Energy, Interactions and energy, Interactions,
Forces, Impulse, Work and Power, Motion in two dimensions, Rotational
dynamics, Gravity, Simple harmonic motion, Waves in one dimension,
Thermodynamics.
This note describes the
following topics: The Calculus of Variations, Fermat's Principle of Least
Time, Hamilton's Principle and Noether's Theorem, Mechanical Similarity,
Hamilton's Equations, Poisson Brackets, A New Expression for the Action,
Maupertuis' Principle, Canonical Transformations, Liouville's Theorem, The
Hamilton-Jacobi Equation, Adiabatic Invariants and Action-Angle Variables,
Mathematics for Orbits, Keplerian Orbits, Elastic Scattering, Small
Oscillations, Driven Oscillator, One-Dimensional Crystal Dynamics,
Parametric Resonance, The Ponderomotive Force, Resonant Nonlinear
Oscillations, Rigid Body Motion, Moments of Inertia, Rigid Body Moving
Freely, Euler Angles, Eulers Equations, Non Inertial Frame, Coriolis effect,
A Rolling Sphere on a Rotating Plane.
This
lecture note covers Lagrangian and Hamiltonian mechanics, systems with
constraints, rigid body dynamics, vibrations, central forces, Hamilton-Jacobi
theory, action-angle variables, perturbation theory, and continuous systems.
It provides an introduction to ideal and viscous fluid mechanics, including
turbulence, as well as an introduction to nonlinear dynamics, including
chaos.
This note covers
the following topics: Lagrangian, metric and coordinates, Legendre transform
and the Hamiltonian, Canonical transformations, Tensor transformation and
the derivative, Parallel transport on a sphere, Infinitesimal
transformations, Newtonian gravity, The Riemann tensor and curvature, Matter
coupling and variation, Linearized gravity and metric interpretation,
Schwarzschild geodesics.
This lecture note explains the
following topics: History and Limitations of Classical Mechanics, Units,
Dimensional Analysis, Problem Solving, and Estimation, Vectors, Dimensional
Kinematics, Newton’s Laws of Motion, Circular Motion, Momentum, System of
Particles, and Conservation of Momentum, Potential Energy and Conservation
of Energy, Angular Momentum, Simple Harmonic Motion, Celestial Mechanics,
Kinetic Theory.
This book is designed for students with
some previous acquaintance with the elementary concepts of mechanics, but
the book starts from first principles, and little detailed knowledge is
assumed. An essential prerequisite is a reasonable familiarity with
differential and integral calculus, including partial differentiation.
This book explains
the following topics: Hamilton’s Principle of Least Action, Conservation
Laws and Symmetries of the Lagrangian, Solving the Equations of Motion,
Scattering Processes, Small Oscillations, Rigid body motion and Hamiltonian
Formulation of Mechanics.
The level of this note
is appropriate for an advanced under graduate or a first year graduate course in
classical mechanics. This note covers the following topics: introduction to
Dynamics, Systems of Particles, one-Dimensional Conservative Systems, linear
Oscillations, Calculus of Variations, Lagrangian Mechanics, Noether’s Theorem,
Central Forces and Orbital Mechanics, Small Oscillations, Elastic Collisions,
Noninertial Reference Frames, Rigid Body Motion and Rotational Dynamics,
Continuum Mechanics, Special Relativity and Hamiltonian Mechanics.
This note covers
the following topics: introduction , force as a vector, static equilibrium,
addition and subtraction of vectors ,kinematics: describing 1D motion and
relative velocity , kinematics and velocity , kinematics: 2D motion and
circular motion , Newton's three laws , friction , springs , circular
motion with gravity , potential energy diagrams, potential energy of
springs , conservation of momentum , momentum, combining momentum and energy ,
2D collisions , power, impulse, center of mass , simple harmonic motion ,
gravity, properties of fluids , introduction to angular motion , statics and
dynamics of angular motion , pendulums and kinetic energy of rotation , energy
and momentum of rotation.
This note covers the following topics: Motion in 1 dimension,
Motion in 3 dimension, Newton's laws of motion, Conservation of energy, Circular
motion, Rotational motion, Angular momentum, Statics, Oscillatory motion and
Orbital motion.
Author(s): Richard Fitzpatrick, University
of Texas at Austin
This note covers the following topics: Centres of Mass, Moment of
Inertia, Systems of Particles, Rigid Body Rotation, Collisions, Motion in a
Resisting Medium, Projectiles, Conservative Forces, Rocket Motion, Simple and
Damped Oscillatory Motion, Forced Oscillations, Lagrangian Mechanics,
Hydrostatics, The Cycloid, Central Forces and Equivalent Potential, Vibrating Systems and Dimensions.