# Spacecraft Dynamics

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.

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