Courses

Spaceflight Mechanics

LM-20 MSAR - Master Degree in Space and Astronautical Engineering (2016 - ongoing)

1. Math fundamentals. Spherical trigonometry, vectors, matrices, transport theorem, rotations

2. Keplerian trajectories. Fundamental principles, two-body problem, gravitational potential, first integrals, position and velocity, energy, position in time, special Keplerian trajectories, general classification, orbit elements, three-dimensional representations of elliptic orbits, ground track, exercises

3. Impulsive orbit transfers. Impulsive thrust approximation, effect of velocity impulses, globally optimal transfers between coplanar circular orbits, globally optimal transfers from elliptic orbit to hyperbolic path, three-dimensional orbit transfers, exercises

4. Interplanetary mission analysis. Planetary spheres of influence, patched conics, gravity assist technique and related applications, exercises

5. Orbital motion in multibody environments. Problem of N bodies and integrals of motion. Problem of 2 bodies. Circular restricted three-body problem: synodic frame, equations of motion, Jacobi integral, libration points, zero velocity curves and surfaces, stability of libration equilibrium conditions.

6. Fundamentals of rocket dynamics. Newton law with propulsion, Tsiolkovsky's law, loss equation, staging, optimal staging. Ascent trajectory of a multistage launch vehicle. Three-dimensional equations of powered spaceflight, exercises

7. Relative orbit motion. Hill-Clohessy-Wiltshire equations, general solution, special solutions, impulsive rendezvous, exercises

8. Orbital perturbations. Lagrange planetary equations, Earth gravitational harmonics, effect of a third body gravitational attraction, effect of aerodynamic drag, effect of solar radiation pressure, exercises

9. Rigid body kinematics. Euler theorem, different representations of orientation (direction cosines, sequences of angles, Euler parameters, Euler principal axis and angle), kinematics equations, exercises

10. Complements of Newton mechanics. Dynamics of systems of particles and continuous bodies (mass center, linear momentum, kinetic energy, mechanical energy, and angular momentum)

11. Fundamentals of rigid body dynamics. Angular momentum, inertia matrix, principal axes of inertia, Euler equations, torque-free rigid body dynamics of axisymmetric spacecraft, energy and momentum integrals, equilibrium and stability of pure spin, nutation of axisymmetric bodies with energy dissipation, attitude maneuvers of spinning spacecraft, exercises

More detailed info on course and final exam https://corsidilaurea.uniroma1.it/it/users/mauropontaniuniroma1it

Advanced Spacecraft Dynamics

LM-20 MSAR - Master Degree in Space and Astronautical Engineering (2019 - ongoing)

1. Eulerian attitude dynamics. Vectors and dyadics. Reference frames. Relations for angular velocities. Single rigid body. Spacecraft with a single wheel. Dual-spin spacecraft. Axisymmetric dual-spin spacecraft. Viscous ring for nutation damping. Spacecraft with damper. Spacecraft with wheel and damper. Spacecraft with multiple wheels. Alternate forms of the dynamics equations. Spacecraft with single-gimbal gyroscope.

2. Attitude dynamics of multibody spacecraft (Kane's method). Constraints. Multibody tree structures. Two bodies and a joint: velocities and partial velocities. Generalized forces. Kane's dynamical equations. Two bodies and a joint: accelerations and dynamics equations. Kane's equations for multibody spacecraft with tree structure. Methodology for simulations. Application: dynamics of a spacecraft with two appendages.

3. Nonlinear attitude control using momentum exchange devices. Introduction. An overview on momentum exchange devices. Common architectures for momentum devices arrays. Steering laws for spacecraft equipped with single-gimbal control momentum gyros (SG-CMGs). Steering law for spacecraft equipped with reaction wheels (RWs). Attitude maneuvering via nonlinear quaternion and angular rate feedback. Application: pointing maneuver via nonlinear control and array of SG-CMGs. Attitude tracking via nonlinear quaternion and angular rate feedback. Application: attitude tracking for a geostationary satellite.

4. Nonlinear orbit control using continuous thrust. Introduction. Orbit dynamics. Variable-thrust nonlinear orbit control. Near-Lyapunov-optimal orbit control. Nonlinear control for spacecraft in circular orbit. Application 1: nonlinear control on medium Earth orbit. Application 2: nonlinear control on low Earth orbit.

5. Finite-thrust orbit transfers. Types of finite-thrust engines. Equations of motion. Minimum-time orbit transfers using constant-specific-impulse low-thrust. Minimum-fuel orbit transfers using constant-specific-impulse finite-thrust. Minimum-fuel orbit transfers using variable-specific-impulse low-thrust. Spacecraft attitude along orbit transfers. Concluding remarks.

6. Planetary entry. Introduction. Reference frames for trajectory and attitude. General flight equations. Entry heating. Ballistic entry. Gliding entry. Overview of the Shuttle reentry trajectory. Terminal descent and landing of a lifting reentry vehicle: an example. Concluding remarks.

7. An introduction to satellite constellations. Introducti. Flower constellations: an introduction.

More detailed info on course and final exam http://www.ingaero.uniroma1.it/index.php?option=com_course&view=course&id=245&Itemid=2783&lang=it

Flight Mechanics - mod. II (spaceflight)

L-9 BAER - Bachelor Degree in Aerospace Engineering (2017 - 2019)

1. Math fundamentals. Vectors, transport theorem, rotations

3. Representations of Keplerian elliptic orbits. Representations in two dimensions, representation in three dimensions, orbit elements, exercises

4. Impulsive orbit transfers. Impulsive thrust approximation, effect of velocity impulses, globally optimal transfers between coplanar circular orbits, globally optimal transfers from elliptic orbit to hyperbolic path, three-dimensional orbit transfers, exercises

5. Ground segment. Ground track, motion relative to a ground station, exercises

6. Fundamentals of rocket dynamics. Newton law with propulsion, rocket staging, optimal rocket staging, exercises

Aerospace Trajectories - mod. II (dynamic game theory in flight mechanics)

LSS-SIA - Special Master Degree in Aerospace Engineering (2016 - 2017)

1. Orbital motion in multibody environments. Problem of N bodies and integrals of motion. Problem of 2 bodies. Circular restricted three-body problem: synodic frame, equations of motion, Jacobi integral, libration points, zero velocity curves and surfaces, low-energy Earth-Moon mission (numerical example), theorem on optimal location and magnitude of velocity changes, stability of libration equilibrium conditions.

2. General flight equations. Reference frames. Three-dimensional kinematics and dynamics equations, equations of atmospheric flight, inertial and relative state components, spaceflight equations (in two forms). Equations of relative orbit motion: general solution, special solutions.

3. Optimal control theory and aerospace applications. Necessary conditions for optimality. Minimum-time orbit transfer problem: formulation, necessary conditions, numerical solution, low-thrust vs. high-thrust propulsion.

4. Dynamic game theory and aerospace applications. Zero-sum games: saddle-point equilibrium and related necessary conditions, open loop strategies, example of elementary zero-sum game. Pursuit-evasion game between two spacecraft in close proximity: remarkable analytical properties, numerical solution. Cooperative and competitive interception.

5. Ballistic entry. Assumptions, acceleration and heat-flux constraints and extremals, entry corridor.