New Mexico State University
Department of Astronomy
PO Box 30001, MSC 4500 Las Cruces, NM 88003
wlyra - nospam - nmsu.edu
+1 575-646-1400
Lectures for the course Dynamics and Hydrodynamics PhD course at NMSU.
Orbital elements, angular momentum, energy, semimajor axis, barycentric orbits.
Notes on 2-body problem.
Notes on barycentric orbits.
Tisserand Parameter, Triangular Lagrangian Points
Notes.
Lagrangian Points and the Jacobi Constant, Colinear Lagrangian Points
Notes.
Stability Of Lagrangian Points - Linear analysis, Instability of collinear points and stability of triangular points, Tadpole and Horseshoe Orbits
Notes.
Hamiltonian Formulation, Angle-Action Variables: Intro, Angle-Action variables as Polar Coordinates
Notes.
Poincare Invariant Theorem, Green's Theorem, Hamilton-Jacobi Equation and the Generating Function, Harmonic Oscillator via Angle-Action variables
Delaunay variables: Intro, Kepler problem in angle-action variables. I. Actions, Kepler problem in angle-action variables. II. Change of actions, Kepler problem in angle-action variables. III. Angles: Longitude of Ascending Node, Kepler problem in angle-action variables. IV. Angles: Argument of Pericenter, Kepler problem in Angle-Action variables. V. Angles: Mean Anomaly.
Notes.
Splitting the Hamiltonian, Force splitting, The Disturbing Function.
Hierarchical Triples: The Hamiltonian in orbital elements.
Notes.
Averaging over the outer binary: conservation of vertical angular momentum; Averaging the Hamiltonian over the inner binary: conservation of energy
Kozai-Lidov resonance: Oscillations in eccentricity and inclination, Critical Inclination for KL cycles and libration of argument of pericenter, Critical Angle and Examples of Kozai-Lidov oscillations.
Notes.
Gravitational Potential, Poisson Equation, Newton First Theorem, Newton's Second Theorem
Gravitational Potential Energy, NFW Dark Matter Halo, Non-Spherical Potentials - Thin Disk, Thick Disk Potential
Homoeoid, Elliptic Coordinates, Potential of Homoeoids, Potential of Homogeneous Ellipsoid, Hernquist potential and Exponential Disk
Orbits in a dark halo potential; epicyclic approximation.
Two-Body Scattering, Relaxation Time, Dynamical Friction.
Boltzmann equation, conservation theorem, continuity equation.
Discretization, stencil diagrams, von Neumann stability analysis, donor cell, second order schemes, slope limiters.
Notes on GitHub (python notebook).
Notes on GitHub (python notebook).
Linearization, wave solution, dispersion relation.