## Teaching

#### Dynamics and Hydrodynamics - ASTR 506

Lectures for the course Dynamics and Hydrodynamics PhD course at NMSU.

• ### I: Solar System Dynamics

• Class 1: Two-body problem recap.

Orbital elements, angular momentum, energy, semimajor axis, barycentric orbits.
Notes on 2-body problem.
Notes on barycentric orbits.

• Class 2: Three-body problem.

Tisserand Parameter, Triangular Lagrangian Points
Notes.

• Class 3: Lagrange points, Jacobi constant.

Lagrangian Points and the Jacobi Constant, Colinear Lagrangian Points
Notes.

• Class 4: Stability/Instability of Lagrangian points.

Stability Of Lagrangian Points - Linear analysis, Instability of collinear points and stability of triangular points, Tadpole and Horseshoe Orbits
Notes.

• Class 5: Hamiltonian formulation.

Hamiltonian Formulation, Angle-Action Variables: Intro, Angle-Action variables as Polar Coordinates
Notes.

• Class 6: Hamiltonian formulation.

Poincare Invariant Theorem, Green's Theorem, Hamilton-Jacobi Equation and the Generating Function, Harmonic Oscillator via Angle-Action variables

• Class 7: Delaunay 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.

• Class 8: Perturbation Theory.

Splitting the Hamiltonian, Force splitting, The Disturbing Function. Hierarchical Triples: The Hamiltonian in orbital elements.
Notes.

• Class 9: Kozai-Lidov oscillations.

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.

• ### II: Galactic Dynamics

Notes on GitHub (python notebook).

• Class 10: Potential theory.

Gravitational Potential, Poisson Equation, Newton First Theorem, Newton's Second Theorem

• Class 11: Halo and disk potential.

Gravitational Potential Energy, NFW Dark Matter Halo, Non-Spherical Potentials - Thin Disk, Thick Disk Potential

• Class 12: Potential of ellipsoids.

Homoeoid, Elliptic Coordinates, Potential of Homoeoids, Potential of Homogeneous Ellipsoid, Hernquist potential and Exponential Disk

• Class 13: Orbits.

Orbits in a dark halo potential; epicyclic approximation.

• Class 14: Virial Theorem and Dynamical Friction.

• Class 15: Dynamical Friction.

Two-Body Scattering, Relaxation Time, Dynamical Friction.

• ### III: Hydrodynamics

Notes on GitHub (python notebook).

• Class 16: Boltzmann equation.

Boltzmann equation, conservation theorem, continuity equation.

• Class 17: The Navier-Stokes equation.

• Class 18: Numerical hydrodynamics.

Discretization, stencil diagrams, von Neumann stability analysis, donor cell, second order schemes, slope limiters.

Notes on GitHub (python notebook).

• Class 19: Primer on tensors.

Notes on GitHub (python notebook).

• Class 20: Acoustics.

Linearization, wave solution, dispersion relation.

• Example of Euler method in Fortran90 and in C++