Apply transport theorem to differentiate vectors, derive frame dependent velocity and acceleration vectors, and solve kinematic particle problems,
Translate between sets of attitude descriptions; add and subtract relative attitude descriptions for the movement of rigid bodies
Apply the static stability conditions of a dual-spinner configuration to derive equations of motion for rigid bodies with momentum exchange devices
Apply Lyapunov method to argue stability and convergence on a range of systems, analyze rigid body control convergence with unmodeled torque
Spacecraft Dynamics and Control covers three core topic areas: the description of the motion and rates of motion of rigid bodies (Kinematics), developing the equations of motion that prediction the movement of rigid bodies taking into account mass, torque, and inertia (Kinetics), and finally non-linear controls to program specific orientations and achieve precise aiming goals in three-dimensional space (Control). The specialization invites learners to develop competency in these three areas through targeted content delivery, continuous concept reinforcement, and project applications.
The goal of the specialization is to introduce the theories related to spacecraft dynamics and control. This includes the three-dimensional description of orientation, creating the dynamical rotation models, as well as the feedback control development to achieve desired attitude trajectories.
Kinematics: Describing the Motions of Spacecraft
The movement of bodies in space (like spacecraft, satellites, and space stations) must be predicted and controlled with precision in order to ensure safety and efficacy. Kinematics is a field that develops descriptions and predictions of the motion of these bodies in 3D space. This course in Kinematics covers four major topic areas: an introduction to particle kinematics, a deep dive into rigid body kinematics in two parts (starting with classic descriptions of motion using the directional cosine matrix and Euler angles, and concluding with a review of modern descriptors like quaternions and Classical and Modified Rodrigues parameters). The course ends with a look at static attitude determination, using modern algorithms to predict and execute relative orientations of bodies in space. After this course, you will be able to... * Differentiate a vector as seen by another rotating frame and derive frame dependent velocity and acceleration vectors * Apply the Transport Theorem to solve kinematic particle problems and translate between various sets of attitude descriptions * Add and subtract relative attitude descriptions and integrate those descriptions numerically to predict orientations over time * Derive the fundamental attitude coordinate properties of rigid bodies and determine attitude from a series of heading measurements
Kinetics: Studying Spacecraft Motion
As they tumble through space, objects like spacecraft move in dynamical ways. Understanding and predicting the equations that represent that motion is critical to the safety and efficacy of spacecraft mission development. Kinetics: Modeling the Motions of Spacecraft trains your skills in topics like rigid body angular momentum and kinetic energy expression shown in a coordinate frame agnostic manner, single and dual rigid body systems tumbling without the forces of external torque, how differential gravity across a rigid body is approximated to the first order to study disturbances in both the attitude and orbital motion, and how these systems change when general momentum exchange devices are introduced. After this course, you will be able to... *Derive from basic angular momentum formulation the rotational equations of motion and predict and determine torque-free motion equilibria and associated stabilities * Develop equations of motion for a rigid body with multiple spinning components and derive and apply the gravity gradient torque * Apply the static stability conditions of a dual-spinner configuration and predict changes as momentum exchange devices are introduced * Derive equations of motion for systems in which various momentum exchange devices are present Please note: this is an advanced course, best suited for working engineers or students with college-level knowledge in mathematics and physics.
Control of Nonlinear Spacecraft Attitude Motion
This course trains you in the skills needed to program specific orientation and achieve precise aiming goals for spacecraft moving through three dimensional space. First, we cover stability definitions of nonlinear dynamical systems, covering the difference between local and global stability. We then analyze and apply Lyapunov's Direct Method to prove these stability properties, and develop a nonlinear 3-axis attitude pointing control law using Lyapunov theory. Finally, we look at alternate feedback control laws and closed loop dynamics. After this course, you will be able to... * Differentiate between a range of nonlinear stability concepts * Apply Lyapunov’s direct method to argue stability and convergence on a range of dynamical systems * Develop rate and attitude error measures for a 3-axis attitude control using Lyapunov theory * Analyze rigid body control convergence with unmodeled torque
Spacecraft Dynamics Capstone: Mars Mission
The goal of this capstone spacecraft dynamics project is to employ the skills developed in the rigid body Kinematics, Kinetics and Control courses. An exciting two-spacecraft mission to Mars is considered where a primary mother craft is in communication with a daughter vehicle in another orbit. The challenges include determining the kinematics of the orbit frame and several desired reference frames, numerically simulating the attitude dynamics of the spacecraft in orbit, and implementing a feedback control that then drives different spacecraft body frames to a range of mission modes including sun pointing for power generation, nadir pointing for science gathering, mother spacecraft pointing for communication and data transfer. Finally, an integrated mission simulation is developed that implements these attitude modes and explores the resulting autonomous closed-loop performance. Tasks 1 and 2 use three-dimensional kinematics to create the mission related orbit simulation and the associated orbit frames. The introductory step ensures the satellite is undergoing the correct motion, and that the orbit frame orientation relative to the planet is being properly evaluated. Tasks 3 through 5 create the required attitude reference frame for the three attitude pointing modes called sun-pointing, nadir-pointing and GMO-pointing. The reference attitude frame is a critical component to ensure the feedback control drives the satellite to the desired orientation. The control employed remains the same for all three pointing modes, but the performance is different because different attitude reference frames are employed. Tasks 6 through 7 create simulation routines to first evaluate the attitude tracking error between a body-fixed frame and a particular reference frame of the current attitude mode. Next the inertial attitude dynamics is evaluated through a numerical simulation to be able to numerically analyze the control performance. Tasks 8-11 simulate the closed-loop attitude performance for the three attitude modes. Tasks 8 through 10 first simulate a single attitude at a time, while tasks 11 develops a comprehensive attitude mission simulation which considers the attitude modes switching autonomously as a function of the spacecraft location relative to the planet.