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 note
exlains Newtonian remarks, Oscillations, Gravitation, Variational calculus, Lagrangian and hamiltonian mechanics, Central force
motion, Systems of particles, Motion in a noninertial reference frame,
Dynamics of rigid bodies and small oscillations.
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
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 is about the Lagrangian and Hamiltonian
formulations of classical mechanics. Topics covered includes: Newtonian
mechanics, Lagrangian mechanics, Small oscillations, Rigid body dynamics,
Hamiltonian mechanics and Levi-Civita alternating symbol.
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 note explains the following topics: Newtonian and
Lagrangian mechanics of point particles, Hamiltonian formalism of mechanics,
Canonical transformations, Rigid body mechanics, Dynamics of continuous
media/deformable bodies: Lagrangian and Eulerian descriptions, Vibrations of
a stretched string.