Spacecraft dynamics is the subfield of celestial mechanics which studies human-created objects’ movements through space. It encompasses calculations, refinement and planning for such bodies such as spacecraft or satellites.

Spacecraft Dynamics block computes position, velocity and attitude over time of six degree-of-freedom rigid-body systems with six degrees-of-freedom rigid bodies. Mass tab allows specifying an initial mass value m, mass flow rate dm/dt and inertia tensor imom.

## Attitude

Attitude refers to a spacecraft’s orientation, making its precise measurement critical in ensuring it does not end up millions of miles off course. Tiny thrusters used for controlling this aspect of space travel make small adjustments that keep its course on target.

As spacecraft attitude cannot be determined with one measurement alone, its estimates must be estimated from various sensors (often using a Kalman filter). Gyroscopes are most frequently used for attitude estimation while sun and moon position and horizon detectors and magnetometers may also provide valuable data for attitude estimation.

GMAT attitudes are typically represented using the Attitude Ephemeris Message (AEM) format outlined by CCSDS 504.0-B-1. An AEM file comprises of a header section containing high level information about its format as well as two blocks: Metadata and Data; in particular, Data contains initial attitude information in either quaternions, direction cosine matrices or Euler angles sequences depending on which representation method has been selected by GMAT.

## Orbit

An orbit of a spacecraft depends on two factors: velocity — which measures how fast the craft travels straight-line — and Earth’s gravity force. As satellites get closer, their velocity must increase in order to counter the intensified gravitational pull.

At lower altitudes, spacecraft may encounter trace amounts of Earth’s atmosphere which create drag that gradually decays their orbit until they return home. At higher altitudes this effect is greatly diminished.

Spacecraft designed to reach planets must enter an interplanetary trajectory at precisely the right moment; this can be accomplished using its engine to decelerate and achieve orbit insertion.

## Thrust

Spacecraft thrust is determined by two forces – gravity pulling it toward Earth and centripetal forces due to circular movement – balancing against propulsion forces provided by their engines.

This block can be configured to simulate a spacecraft constellation by providing multiple values in Mass, Orbit and Attitude tabs. As a result, each satellite will be represented as a constellation by row outputs corresponding to individual satellites while state outputs include current time tutc and transformations from inertial frame to fixed frame qicrf2ff outputs.

This capstone course builds upon the skills acquired in rigid body Kinematics, Kinetics and Control courses to explore vehicle dynamics of spacecraft in orbit – particularly its attitude. Students gain skills necessary for analyzing natural spacecraft orientation motion as well as stabilizing stability using feedback control.

## Entry/Descent

As part of its powered flight mission, spacecraft must enter and land on planets or small bodies to complete its mission. To achieve success during this entry-to-landing (EDL) phase requires high degrees of accuracy and fidelity for testing system performance in environments which are impossible to replicate before launch.

The Spacecraft Dynamics block can be configured to model either a single spacecraft or constellation of spacecrafts, with model parameters being defined on the Mass, Orbit, and Attitude tabs. Mass m, mass flow rate m/dt, and inertia tensor Imom serve as inputs into this block and integrated to form its dynamics system equations.

The system equations control a spacecraft’s velocity and acceleration, producing a trajectory which could take many forms depending on its starting point, gravitational forces acting on it and trajectory options available to it. These could include circles, ellipses, parabolic paths or hyperbolas depending on which may prevail at any one time.

Spacecraft dynamics refers to the study and control of space vehicles. Simulink offers spacecraft dynamics models which predict their motion from initial conditions.

Spacecraft trajectory typically follows a conic section (circle, ellipse, parabola or hyperbola) with gravity from its central body as the driving force and solar radiation pressure as secondary forces.

## Attitude

Spacecraft attitudes refer to the relative positions of three mutually perpendicular axes of rotation: roll, pitch, and yaw. Controlling spacecraft orientation requires sensors for tracking dynamics onboard the vehicle as well as actuators capable of applying torques necessary to orient it properly; algorithms then direct these actuators according to measured sensor data as well as desired attitude goals – this integrated field is called guidance navigation and control (GNC).

This book presents spacecraft rigid body equations of motion in terms of quaternions with external torques applied, to achieve rotational stability while investigating orbital dynamics for different scenarios through numerical simulations.

Embedded Model Control is an approach for attitude and orbit control design that integrates embedded model, uncertainty estimation feedback into a state predictor that feeds into a control law. Once implemented, reduced model controllers are implemented so as to predict their relative positions, velocitys and accelerations over time.

## Velocity

Spacecraft velocity can be defined as the vector sum of its speed and direction. Acceleration defines velocity; speed can be expressed as a simple number while its direction requires additional math calculations.

Spacecraft orbital velocity depends on its departure and destination planet’s gravitational fields, plus rocket thrust. This may result in circular, elliptical, parabolic or hyperbolic trajectories; for instance, in heliocentric transfer orbits, spacecraft will have their perihelion at their departure planet; therefore they require an excess velocity that allows it to leave their gravitational field.

The Spacecraft Dynamics block represents translational and rotational dynamics by numerical integration. It calculates position, velocity, attitude, angular velocity over time using ephemerides and gravity models selected on its Central Body tab; additionally it takes atmospheric drag into account in high precision orbit propagation models.

## Orbit

Orbits play an integral part in controlling the translational and rotational dynamics of spacecraft, as well as the location of their center of mass (CoM). Orbital mechanics is essential in understanding spacecraft movement because it defines forces and moments that must be overcome by spacecraft to maintain desired attitude control.

An eccentric orbit can result in spacecraft with an off-center Center of Mass (CoM), leading to nonlinear aerodynamic forces which result in perturbations to its flight path angle (ph).

Spacecraft Dynamics uses numerical integration to model nonlinear dynamical behavior. This block propagates initial spacecraft state values (Quaternions, Direction cosine matrices and Euler angles) as well as gravity model selected for central body into current position and momentum as well as angular velocity over time. Furthermore, expansion for all input ports except Moon libration angles at J2000 right ascension/declination for Custom central bodies is supported; such values can be expanded across all spacecraft in a model.

## Mass

Space does not have gravity; as a result, objects do not experience weight, but still possess mass. Larger objects tend to possess more inertia and therefore resist acceleration more effectively.

On Earth, weight can be calculated using the equation W = mg because objects resistant to gravity produce forces which can be measured using a balance scale.

Aerospace Blockset’s system dynamics blocks are used to implement the equations of motion for a central body assuming its gravity remains constant (which is generally true). User-defined acceleration and forces are provided via external acceleration input port while internal mass flow rate and inertia tensor calculations are derived by selecting parameter on Mass tab – this model assumes shifting masses are centered on CoM of host spacecraft.