Title
Description

A basic bang-bang control about single axis was implemented in this scenario.
The model of a linearized spacecraft dynamics with a proportional and derivative
control was considered, which is shown in the illustration below.

Block Diagram

Inputs

J                             Spacecraft Moment of inertia
wn                           Desired natural frequency
damping                   Desired damping coefficient
Torque                    Torque level of the bang-bang actuator
Dead Zone               Range in which no torque should be applied
theta_com                Commanded angular position

Initial Condition

theta                     Spacecraft angular position for an actuator with no constraint
thetaDot                Spacecraft angular velocity for an actuator with no constraint
thetaBang              Spacecraft angular position for the bang-bang actuator
thetaDotBang         Spacecraft angular velocity for the bang-bang actuator






CMG Control
Title
Description

In this project, to simulate a reorientation maneuver of a rigid spacecraft
using CMGs, a configuration of 3 single-gimbal control moment gyros (CMGs)
aligned with the principal axis was used. The illustration shows the CMG
configuration used.

CMG Assembly
Inputs

Ixx, Iyy, Izz                    Principal moments of inertia
J                                  CMG inertia
A                                  CMG ginbal rate
psi                                Commanded Euler angle
phi                          Commanded Euler angle
theta                             Commanded Euler angle

Initial Condition

w1, w2, w3:                 Spacecraft angular velocities
q1, q2, q3, q4:             Quaternions
Omega 1                     Gimbal rate of CMG 1
Omega 2                     Gimbal rate of CMG 2
Omega 3                     Gimbal rate of CMG 3






Constant Torque
Title
Description

This scenario uses Eulerfs rotational equations of motion to simulate the
attitude dynamics of a rigid spacecraft with optional body-fixed, constant
torques. Eulerfs rotational equations of motion is found in most of the
textbooks on spacecraft dynamics

Inputs

Ixx, Iyy, Izz Principal moments of inertia
M1,M2,M3 External torque acting in the b1 direction

Initial Condition

w1, w2, w3: Spacecraft angular velocities
q1, q2, q3, q4: Quaternions




Four Reaction Wheels
RW Control
Description

An attitude maneuver via momentum transfer based on the conservation of
angular momentum was simulated. In this project, 4 reaction wheels in
a pyramid configuration was used; this configuration provides redundancy
such that if one wheels become unable to operate for some reason,
the other three reaction wheels can provide control torque in all three direction.

Four Reaction wheels in a pyramid configuration

Inputs

Ixx, Iyy, Izz             Moments of inertia
J                             Reaction wheel inertia
RW angle             Tilt angle of reaction wheel axis
psi                         Commanded Euler angle
phi                          Commanded Euler angle
theta                     Commanded Euler angle

Initial Condition
w1, w2, w3:                 Spacecraft angular velocities
q1, q2, q3, q4:             Quaternions
Omega1                      Angular velocity of RW 1
Omega2                     Angular velocity of RW 2
Omega3                      Angular velocity of RW 3
Omega4                     Angular velocity of RW 4



GG Circular
Title
A rigid spacecraft is subjected to a gravity gradient torque in a circular
orbit.

Inputs

Ixx, Iyy, Izz              Principal moments of inertia

Initial Condition

w1, w2, w3:             Spacecraft angular velocities
q1, q2, q3, q4:         Quaternions






GG Eccentric
Title
Description

A rigid spacecraft is subjected to gravity gradient torque while it revolves
around an eccentric orbit.

Inputs

Ixx, Iyy, Izz Principal moments of inertia (kg m2)
e Eccentricity


Initial Condition

w1, w2, w3: Spacecraft angular velocities
q1, q2, q3, q4: Quaternions







Simple 2D Flexible Spacecraft
Title
Simulation Control

time step: Time step for the numerical integration routine
time: Duration of the simulation periond in seconds

Description

A flexible spacecraft is modeled as a central rigid body with two massless beams
attachd symmetrically to the side of the central body. Each beam has a
concentrated mass at the tip. The flexibility comes from the flexural rigidity EI of
the beams.
2D Flexible Spacecraft Illustration
Inputs

J:                     Moment of inertia
m:                     Tip mass
a:                     Distance as indicated in the illustration above (m)
L:                     Length of the beam (m)
EI:                     Flexural rigidity of the beam (N m2)

Initial Condition

Alpha:             Spacecraft angular position
u1:                 Position of the first mass
u2:                 Position of the second mass
AlphaDot:        Spacecraft angular velocity
u1Dot:             Velocity of the first mass
u2Dot:             Velocity of the second mass

Input and Output







Simple 3D Flexible Spacecraft
Title
Simulation Control
time step: Time step for the numerical integration routine
time: Duration of the simulation periond in seconds

Description
A flexible spacecraft is modeled as a central rigid body with two massless beams
attachd symmetrically to the side of the central body. Each beam has a
concentrated mass at the tip. The flexibility comes from the flexural rigidity EI of
the beams. Although the flexible elements are constrained to move in 1-2 plane
only, the applet is able to simulate the effect of flexibility on the spacecraft
attitude in three dimensional space.
2D Flexible Spacecraft Illustration
Inputs
Ixx, Iyy, Izz:             Principal moments if inertia
m:                            Tip mass (kg)
a:                             Distance as indicated in the illustration (m)
L:                             Length of the beam as illustrated (m)
EI:                             Flexural rigidity (N m2)

Initial Condition
u1:                         Position of the first mass
u2:                         Position of the second mass
psi, theta, phi:         Euler angles in a sequence of 3-2-1
u1Dot:                     Velocity of the first mass
u2Dot:                     Velocity of the second mass
psiDot:                     Time rate of psi angle
thetaDot :                 Time rate of theta angle
phiDot:                     Time rate of phi angle









Spherical Damper
Title
Simulation Control
time step: Time step for the numerical integration routine
time: Duration of the simulation periond in seconds

Description
A damper in a rigid spacecraft in a circular orbit may be able to stabilize the spacecraft
that otherwise goes unstable without it. To simulate such a behavior, a rigid spacecraft
with a damper of spherical shape was modeled as illustrated.

Illustration of a damper and spacecraft

Inputs
Ixx, Iyy, Izz                 Principal moments of inertia
c                            Damping Coefficient
j                                 Spherical damper inertia

Initial Condition
w1, w2, w3:                   Spacecraft angular velocities
q1, q2, q3, q4:              Quaternions
alpha, beta, gamma:     Damper angular velocities