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

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.

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