Astro, Dynamics and Control Courses

The purpose of this web page is to provide my graduate students with a list of potential courses that they could take while studying at the University of Colorado. There is a large breath of courses available in astrodynamics, nonlinear dynamics, control, and spacecraft design. There is also a CU course listing web site that shows all regular courses.

Aerospace Engineering Sciences Department

ASEN 5010	Spacecraft Dynamics and Control Studies the rotational motion of spacecrafts, including attitude parameters and spacecraft torques. Applies Euler equations to the attitude motions of simple spacecrafts and their stability. Pre: ASEN 3200 or equivalent, or permission of instructor. (3H, 3C)
ASEN 5014	Linear Control Systems Introduces the theory of linear systems, including vector spaces, linear equations, structure of linear operators, state space descriptions of dynamic systems, and state feedback control methods. Prereq., ASEN 3200.
ASEN 5022	Dynamics of Aerospace Structures Applies concepts covered in undergraduate dynamics, structures, and mathematics to the dynamics of aerospace structural components, including methods of dynamic analysis, vibrational characteristics, vibration measurements, and dynamic stability. Prereqs., ASEN 5012, 5227, or equivalent. Recommended prereq., MATH 3130.
ASEN 5024	Nonlinear Control Systems Introduces the analysis and control design methods for nonlinear systems, including Lyapunov and Describing Function methods. Prereq., ASEN 5014.
ASEN 5044	Statistical Estimation for Dynamical Systems Develops the theory of batch and sequential (Kalman) filtering, including a review of necessary concepts of probability and statistics.
ASEN 5050	Space Flight Dynamics Includes celestial mechanics, space navigation, and orbit determination; trajectory design and mission analysis trajectory requirements; and orbital transfer and rendezvous. Prereq., ASEN 3200 or instructor consent.
ASEN 6080	Introduction to Statistical Orbit Determination 2 Continuation of ASEN 5070. Emphasizes orthogonal transformation techniques such as Givens and Householder, square root filtering and smoothing, and considers covariance analysis. Also includes coordinate systems, force models, and time and polar motion. Requires term project that involves the application of many of the techniques required for precise orbit determination. Prereq., ASEN 5070.
ASEN 5090	Introduction to Global Navigation Satellite Systems Global Navigation Satellite Systems (GNSS) are important tools for navigation, science, and engineering. Introduces GNSS hardware, signal structure, algorithms, error sources, and modeling techniques. Programming experience is required. Restricted to graduate students.
ASEN 5114	Automatic Control Systems Methods of analysis and design of feedback control for dynamic systems. Covers nyquist, bode, and linear quadratic methods based on frequency domain and state space models. Laboratory experiments provide exposure to computation for simulation and real time control, and typical control system sensors and actuators. Prereqs., ASEN 3128 and 3200.
ASEN 5122	Control of Aerospace Structures 1 Introduces the basic problems in dynamic modeling and active control of large spacecraft and satellites. Includes system descriptions, model reduction, controller design, and closed-loop stability analysis. Prereq., ASEN 3200, graduate standing, or instructor consent.
ASEN 5347	Math Methods in Dynamics Two-part graduate-level course on dynamics. Covers both flexible and rigid multibody analytical dynamics and finite element method for dynamics. Emphasizes formulations that naturally lead to easy computer implementation and stability, linearization, and modern rotational kinematics. Prereqs., graduate standing and instructor consent.
ASEN 5517	Computational Methods In Dynamics Continuation of mathematical methods in dynamics. Covers numerical algorithms, computer implementation aspects, and treatment of constraints and nonlinear rotational computational techniques. Emphasizes the combined numerical and physics characterization for the solution of dynamical systems. Prereq., ASEN 5347.
ASEN 6010	Advanced Spacecraft Dynamics and Control Studies the dynamic modeling and control of spacecraft containing multiple momentum exchange devices, and/or flexible spacecraft components. Will develop feedback control algorithms, explore singularity avoidance strategies, and explore using analytical methods (Lagrange's equations, Boltzman Hamel equations) to model a hybrid rigid/flexible spacecraft system. Input shaped open-loop maneuvers are investigated to avoid large structural flexing. Pre: ASEN 5010 or equivalent, or permission of instructor (3H, 3C)
ASEN 6014	Spacecraft Formation Flying Studies the dynamic modeling and control of spacecraft formations orbiting about a planet. Investigate linear and nonlinear relative motion descriptions, rectilinear and curvilinear coordinates, orbit element difference based descriptions, J₂-invariant relative orbits, as well as Lyapunov-based relative motion control strategies. Pre: ASEN 5050 or equivalent, or permission of instructor (3H, 3C)
ASEN 6020	Optimal Trajectories An introduction to the theory and practice of trajectory optimization. The general theory behind optimization and optimal control will be introduced with an emphasis on the properties of optimal trajectories and their computation. The main application will be to space trajectory design, but re-entry and atmospheric trajectories will also be considered. Pre-requisites are familiarity with basic orbit mechanics and linear systems theory.
ASEN 6060	Advanced Space Flight Dynamics Topics include perturbations of orbital motion; classical orbit determination from angles-only observation; modern orbit determination using range and range-rate data; orbit transfer using impulses or continuous thrust; and others. Prereq., ASEN 5050 or instructor consent.
ASEN 6070	Satellite Geodesy Focuses on the measurement of the Earth's gravitational field, rotational characteristics, and shape using Earth and space-based tracking of artificial satellites. Particular emphasis on satellite altimetry and satellite gravity measurements. Prereq., ASEN 3200 or instructor consent. Credit not granted for this course and ASEN 5060.
ASEN 6519	Celestial Mechanics and Advanced Astrodynamics - Special Topics Course Introduction to the N-body problem and the modeling of naturally gravitating dynamical systems. Dynamical coupling between translational and rotational motion. The computation and characterization of space trajectories in highly dynamic environments. Topics will include computation of periodic orbits, stability analysis of orbital motion, and development of analytical theories for dynamics. Pre: ASEN 5050 or equivalent, or permission of instructor (3H, 3C)
ASEN 6519	Uncertainty Quantification - Special Topics Course This course will provide an introduction to recent techniques for representation and propagation of uncer- tainty in PDE-based systems. Students will be exposed to the state-of-the-art techniques for simulation of random processes as well as numerical solution of stochastic PDEs. A number of case studies from computational solid and fluid mechanics will be discussed.

Applied Mathematics Department

MATH 5030	Intermediate Mathematical Physics I (cross-listed as Physics 5030) Complex Variables, ODE's PDE's, Legendre/Associated Legendre equation and functions, spherical harmonics, Hypergeometric and confluent hypergeometric equations and functions.
APPM 5460	Methods in Applied Mathematics: Dynamical Systems and Differential Equations and Chaos Introduces the theory and applications of dynamical systems through solutions to differential equations. Covers existence and uniqueness theory, local stability properties, qualitative analysis, global phase portraits, perturbation theory, and bifurcation theory. Special topics may include Melnikov methods, averaging methods, bifurcations to chaos, and Hamiltonian systems. Prereqs., undergraduate courses equivalent to APPM 2360, 3310, and MATH 4310.
APPM 7100	Mathematical Methods in Dynamical Systems Covers dynamical systems defined by mappings and differential equations. Hamiltonian mechanics, action-angle variables, results from KAM and bifurcation theory, phase plane analysis, Melnikov theory, strange attractors, chaos, etc. Prereq., APPM 5460.

Electrical Engineering Department

ECEN 5418	Automatic Control Systems 1 Coverage of principles of control systems with Multiple Inputs and Multiple Outputs (MIMO). Topics include MIMO state-space theory, applications of the singular value decomposition (SVD), coprime factorization methods, frequency domain topics, and an introduction to H-infinity design. Prereqs., ECEN 3300, 4138, and 5448, or equivalents.
ECEN 5448	Advanced Linear Systems Offers a state space approach to analysis and synthesis of linear systems, state transition matrix, controllability and observability, system transformation, minimal realization, and analysis and synthesis of multi-input and multi-output systems. Prereq., ECEN 3300 and 4138.
ECEN 5458	Sampled Data and Digital Control Systems Provides an analysis and synthesis of discrete-time systems. Studies sampling theorem and sampling process characterization, z-transform theory and z-transfer function, and stability theory. Involves data converters (A/D and D/A), dead-beat design, and digital controller design. Prereqs., ECEN 3300 and 4138.
ECEN 7438	Theory of Nonlinear Systems Similar to ECEN 5438 except at a more advanced level and with more topics covered: limit cycles, functional analysis approach to input-output stability, analysis and synthesis of time-varying systems, feedback linearization and its applications, and bang-bang control. Prereqs., ECEN 5418 and 5448.

Department of Computer Science

CSCI 5446

Chaotic Dynamics

Physics Department

PHYS 5030	Intermediate Mathematical Physics I Complex Variables, ODE's PDE's, Legendre/Associated Legendre equation and functions, spherical harmonics, Hypergeometric and confluent hypergeometric equations and functions.
PHYS 5210	Theoretical Mechanics Variational principles, Lagrange's equations, Hamilton's equations, motion of rigid body, relativistic mechanics, transformation theory, continuum mechanics, small oscillations, Hamilton-Jacobi theory. Coreq., PHYS 5250.
PHYS 5220	Nonlinear Dynamics Conservative systems: canonical perturbation theory, adiabatic invariants, surface of section, overlap criterion, orbit stability, quasilinear diffusion, renormalization analysis of transition to chaos. Bifurcation theory: center manifolds, normal forms, singularity theory. Dissipative systems: strange attractors, renormalization analysis of period doubling, intermittency. Prereq., PHYS 5210. Same as ATOC 5220.

Engineering Management Programm

EMEN 5005

Introduction to Applied Statistical Methods

EMEN 5900

Research Methods (Stat II)