Lecture notes on Classical Mechanics and Electromagnetism in Accelerator Physics
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Lecture notes on Classical Mechanics and Electromagnetism in Accelerator Physics
Lecture notes on Classical Mechanics and Electromagnetism in Accelerator Physics
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 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.
This note
explains the following topics: Lagrange And Hamilton Equations , Newton’s
Laws Of Motion, Hamiltonian Methods, Hamilton’s Principle, Hamilton-jacobi
Theory, Canonical Transformations, Kinematics Of Rigid Body Motion And
Special Theory Of Reativity, : Small Oscillations And Normal Modes, Special
Theory Of Relativity, Lorentz Transformation, One Dimensional Oscillator.
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
The contents include: Newton’s Laws of Motion, The Lagrangian
Formalism, The Motion of Rigid Bodies , The Hamiltonian Formalism,
Introduction to Dynamics, Systems of Particles, Linear Oscillations,
Calculus of Variations, Lagrangian Mechanics, Constraints, Central Forces
and Orbital Mechanics, Small Oscillations, Elastic Collisions, Noninertial
Reference Frames, Rigid Body Motion and Rotational Dynamics, Continuum
Mechanics, Special Relativity, Hamiltonian Mechanics.
This lecture note explains the following topics:
Newtons laws of motion, Scalars and Vector, Units and Dimensions, Time rate
of change of vectors, Motion in one dimension, Motion under a constant
force, Force of friction, Kinematical relations, Simple Harmonic motion,
Motion in a plane, Central force, Rotating frame of reference.
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.
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 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 note covers the following topics: Particle Kinematics,
Lagrange’s and Hamilton’s Equations, Two Body Central Forces, Rigid Body
Motion, Small Oscillations, Hamilton’s Equations, Perturbation Theory and
Field Theory.
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.