6DOF ECEF (Quaternion)

Implement quaternion representation of six-degrees-of-freedom equations of motion in Earth-centered Earth-fixed (ECEF) coordinates

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Libraries:
Aerospace Blockset / Equations of Motion / 6DOF

Description

The 6DOF ECEF (Quaternion) block Implement quaternion representation of six-degrees-of-freedom equations of motion in Earth-centered Earth-fixed (ECEF) coordinates. It considers the rotation of a Earth-centered Earth-fixed (ECEF) coordinate frame (X_ECEF, Y_ECEF, Z_ECEF) about an Earth-centered inertial (ECI) reference frame (X_ECI, Y_ECI, Z_ECI). The origin of the ECEF coordinate frame is the center of the Earth. For more information on the ECEF coordinate frame, see Algorithms.

Examples

Developing the Apollo Lunar Module Digital Autopilot

Develop Apollo Lunar Module digital autopilot using Simulink^® and Aerospace Blockset™.

Open Live Script

Limitations

This implementation assumes that the applied forces act at the center of gravity of the body, and that the mass and inertia are constant.
This implementation generates a geodetic latitude that lies between ±90 degrees, and longitude that lies between ±180 degrees. Additionally, the MSL altitude is approximate.
The Earth is assumed to be ellipsoidal. By setting flattening to 0.0, a spherical planet can be achieved. The Earth's precession, nutation, and polar motion are neglected. The celestial longitude of Greenwich is Greenwich Mean Sidereal Time (GMST) and provides a rough approximation to the sidereal time.
The implementation of the ECEF coordinate system assumes that the origin is at the center of the planet, the x-axis intersects the Greenwich meridian and the equator, the z-axis is the mean spin axis of the planet, positive to the north, and the y-axis completes the right-handed system.
The implementation of the ECI coordinate system assumes that the origin is at the center of the planet, the x-axis is the continuation of the line from the center of the Earth toward the vernal equinox, the z-axis points in the direction of the mean equatorial plane's north pole, positive to the north, and the y-axis completes the right-handed system.

Ports

Input

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F_xyz — Applied forces
three-element vector

Applied forces, specified as a three-element vector.

Data Types: double

M_xyz — Applied moments
three-element vector

Applied moments, specified as a three-element vector.

Data Types: double

L_G(0) — Initial celestial longitude of Greenwich
scalar

Greenwich meridian initial celestial longitude angle, specified as a scalar.

Dependencies

To enable this port

Set Celestial longitude of Greenwich to External.
set Planet model to Earth.

Data Types: double

L_PM(0) — Prime meridian initial celestial longitude angle
scalar

Prime meridian initial celestial longitude angle, specified as a scalar.

Dependencies

To enable this port

Set Celestial longitude of prime meridian to External.
Set Planet model to Custom.

Data Types: double

Output

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V_ff — Velocity of body with respect to ECEF frame,
three-element vector

Velocity of body with respect to ECEF frame, expressed in ECEF frame, returned as a three-element vector.

Data Types: double

X_ff — Position in ECEF reference frame
three-element vector

Position in ECEF reference frame, returned as a three-element vector.

Data Types: double

μ l h — Position in geodetic latitude, longitude, and altitude
three-element vector | M-by-3 array

Position in geodetic latitude, longitude, and altitude, in degrees, returned as a three-element vector or M-by-3 array, in selected units of length, respectively.

Data Types: double

φ θ Ψ (rad) — Body rotation angles
three-element vector

Body rotation angles [roll, pitch, yaw], returned as a three-element vector, in radians. Euler rotation angles are those between body and NED coordinate systems.

Data Types: double

DCM_bi — Coordinate transformation from ECI axes
3-by-3 matrix

Coordinate transformation from ECI axes to body-fixed axes, returned as a 3-by-3 matrix.

Data Types: double

DCM_be — Coordinate transformation from NED axes to body-fixed axes
3-by-3 matrix

Coordinate transformation from NED axes to body-fixed axes, returned as a 3-by-3 matrix.

Data Types: double

DCM_ef — Coordinate transformation from fixed-frame axes
3-by-3 matrix

Coordinate transformation from fixed-frame axes to NED axes, returned as a 3-by-3 matrix.

Data Types: double

V_b — Velocity of body with respect to fixed-frame
three-element vector

Velocity of body with respect to fixed-frame, returned as a three-element vector.

Data Types: double

ω_rel — Relative angular rates of body with respect to NED frame
three-element vector

Relative angular rates of body with respect to NED frame, expressed in body frame and returned as a three-element vector, in radians per second.

Data Types: double

ω_b — Angular rates of body with respect to inertial frame
three-element vector

Angular rates of the body with respect to inertial frame, expressed in body frame and returned as a three-element vector, in radians per second.

Data Types: double

dω_b/dt — Angular accelerations of the body with respect to inertial frame
three-element vector

Angular accelerations of the body with respect to inertial frame, expressed in body frame and returned as a three-element vector, in radians per second squared.

Data Types: double

A_bb — Accelerations in body-fixed axes
three-element vector

Accelerations of the body with respect to the fixed-frame, returned as a three-element vector.

Data Types: double

A_{b ff} — Accelerations in body-fixed axes
three-element vector

Accelerations in body-fixed axes with respect to fixed-frame, returned as a three-element vector.

Dependencies

To enable this point, Include inertial acceleration.

Data Types: double

Parameters

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Main

Units — Input and output units
`Metric (MKS)` (default) | `English (Velocity in ft/s)` | `English (Velocity in kts)`

Input and output units, specified as Metric (MKS), English (Velocity in ft/s), or English (Velocity in kts).

Units	Forces	Moment	Acceleration	Velocity	Position	Mass	Inertia
`Metric (MKS)`	Newton	Newton-meter	Meters per second squared	Meters per second	Meters	Kilogram	Kilogram meter squared
`English (Velocity in ft/s)`	Pound	Foot-pound	Feet per second squared	Feet per second	Feet	Slug	Slug foot squared
`English (Velocity in kts)`	Pound	Foot-pound	Feet per second squared	Knots	Feet	Slug	Slug foot squared

Programmatic Use

Block Parameter: units

Type: character vector

Values: Metric (MKS) | English (Velocity in ft/s) | English (Velocity in kts)

Default: Metric (MKS)

Mass type — Mass type
`Fixed` (default) | `Simple Variable` | `Custom Variable`

Select the type of mass to use:

Mass Type	Description	Default for
`Fixed`	Mass is constant throughout the simulation.	6DOF (Euler Angles) 6DOF (Quaternion) 6DOF Wind (Wind Angles) 6DOF Wind (Quaternion) 6DOF ECEF (Quaternion)
`Simple Variable`	Mass and inertia vary linearly as a function of mass rate.	Simple Variable Mass 6DOF (Euler Angles) Simple Variable Mass 6DOF (Quaternion) Simple Variable Mass 6DOF Wind (Wind Angles) Simple Variable Mass 6DOF Wind (Quaternion) Simple Variable Mass 6DOF ECEF (Quaternion)
`Custom Variable`	Mass and inertia variations are customizable.	Custom Variable Mass 6DOF (Euler Angles) Custom Variable Mass 6DOF (Quaternion) Custom Variable Mass 6DOF Wind (Wind Angles) Custom Variable Mass 6DOF Wind (Quaternion) Custom Variable Mass 6DOF ECEF (Quaternion)

The Fixed selection conforms to the previously described equations of motion.

Programmatic Use

Block Parameter: mtype

Type: character vector

Values: Fixed | Simple Variable | Custom Variable

Default: 'Simple Variable'

Initial position in geodetic latitude, longitude and altitude [mu,l,h] — Initial location of rigid body
`[0 0 0]` (default) | three-element vector

Initial location of the rigid body in the geodetic reference frame, specified as a three-element vector. Latitude and longitude values can be any value. However, latitude values of +90 and -90 may return unexpected values because of singularity at the poles.

Programmatic Use

Block Parameter: xg_0

Type: character vector

Values: '[0 0 0]' | three-element vector

Default: '[0 0 0]'

Initial velocity in body axes [U,v,w] — Velocity in body axes
`[0 0 0]` (default) | three-element vector

Initial velocity in body axes, specified as a three-element vector, in the body-fixed coordinate frame.

Programmatic Use

Block Parameter: Vm_0

Type: character vector

Values: '[0 0 0]' | three-element vector

Default: '[0 0 0]'

Initial Euler orientation [roll, pitch, yaw] — Initial Euler orientation
`[0 0 0]` (default) | three-element vector

Initial Euler orientation angles [roll, pitch, yaw], specified as a three-element vector, in radians. Euler rotation angles are those between the body and north-east-down (NED) coordinate systems.

Programmatic Use

Block Parameter: eul_0

Type: character vector

Values: '[0 0 0]' | three-element vector

Default: '[0 0 0]'

Initial body rotation rates [p,q,r] — Initial body rotation
`[0 0 0]` (default) | three-element vector

Initial body-fixed angular rates with respect to the NED frame, specified as a three-element vector, in radians per second.

Programmatic Use

Block Parameter: pm_0

Type: character vector

Values: '[0 0 0]' | three-element vector

Default: '[0 0 0]'

Initial mass — Initial mass
`1.0` (default) | scalar

Initial mass of the rigid body, specified as a double scalar.

Programmatic Use

Block Parameter: mass_0

Type: character vector

Values: '1.0' | double scalar

Default: '1.0'

Inertia — Inertia
`eye(3)` (default) | scalar

Inertia of the body, specified as a double scalar.

Dependencies

To enable this parameter, set Mass type to Fixed.

Programmatic Use

Block Parameter: inertia

Type: character vector

Values: eye(3) | double scalar

Default: eye(3)

Include inertial acceleration — Include inertial acceleration port
`off` (default) | `on`

Select this check box to add an inertial acceleration port.

Dependencies

To enable the A_{b ff} port, select this parameter.

Programmatic Use

Block Parameter: abi_flag

Type: character vector

Values: 'off' | 'on'

Default: off

Planet

Planet model — Planet model
`Earth (WGS84)` (default) | `Custom`

Planet model to use, Custom or Earth (WGS84).

Programmatic Use

Block Parameter: ptype

Type: character vector

Values: 'Earth (WGS84)' | 'Custom'

Default: 'Earth (WGS84)'

Equatorial radius of planet — Radius of planet at equator
`6378137` (default) | scalar

Radius of the planet at its equator, specified as a double scalar, in the same units as the desired units for the ECEF position.

Dependencies

To enable this parameter, set Planet model to Custom.

Programmatic Use

Block Parameter: R

Type: character vector

Values: double scalar

Default: '6378137'

Flattening — Flattening of planet
`1/298.257223563` (default) | scalar

Flattening of the planet, specified as a double scalar.

Dependencies

To enable this parameter, set Planet model to Custom.

Programmatic Use

Block Parameter: F

Type: character vector

Values: double scalar

Default: '1/298.257223563'

Rotational rate — Rotational rate
`7292115e-11` (default) | scalar

Rotational rate of the planet, specified as a scalar, in rad/s.

Dependencies

To enable this parameter, set Planet model to Custom.

Programmatic Use

Block Parameter: w_E

Type: character vector

Values: double scalar

Default: '7292115e-11'

Celestial longitude of Greenwich source — Source of Greenwich meridian initial celestial longitude
`Internal` (default) | `External`

Source of Greenwich meridian initial celestial longitude, specified as:

`Internal`	Use celestial longitude value from Celestial longitude of Greenwich.
`External`	Use external input for celestial longitude value.

Dependencies

To enable this parameter, set Planet model to Earth.
Setting this parameter to External enables the L_G(0) port.
If Planet model is set to Custom, the parameter name changes to Celestial longitude of prime meridian source.

Programmatic Use

Block Parameter: angle_in

Type: character vector

Values: 'Internal' | 'External'

Default: 'Internal'

Celestial longitude of Greenwich [deg] — Initial angle
`0` (default) | scalar

Initial angle between Greenwich meridian and the x-axis of the inertial frame, specified as a double scalar.

Dependencies

To enable this parameter, set:
- Celestial longitude of Greenwich source to Internal.
- Planet model to Earth (WGS84).
If Planet model is set to Custom, the parameter name changes to Celestial longitude of prime meridian [deg].

Programmatic Use

Block Parameter: LPM0

Type: character vector

Values: double scalar

Default: '0'

Celestial longitude of prime meridian source — Source of prime meridian initial celestial longitude
`Internal` (default) | `External`

Source of prime meridian initial celestial longitude, specified as:

`Internal`	Use celestial longitude value from Celestial longitude of prime meridian.
`External`	Use external input for celestial longitude value.

Dependencies

To enable this parameter, set Planet model to Custom.
Setting this parameter to External enables the L_PM(0) port.
If Planet model is set to Earth (WGS84), the parameter name changes to Celestial longitude of Greenwich source.

Programmatic Use

Block Parameter: angle_in

Type: character vector

Values: 'Internal' | 'External'

Default: 'Internal'

Celestial longitude of prime meridian [deg] — Initial angle
`0` (default) | scalar

Initial angle between prime meridian and the x-axis of the ECI frame, specified as a double scalar.

Dependencies

To enable this parameter, set:
- Celestial longitude of prime meridian source to Internal.
- Planet model to Custom.
If Planet model is set to Earth (WGS84), the parameter name changes to Celestial longitude of Greenwich [deg].

Programmatic Use

Block Parameter: LPM0

Type: character vector

Values: double scalar

Default: '0'

State Attributes

Assign a unique name to each state. You can use state names instead of block paths during linearization.

To assign a name to a single state, enter a unique name between quotes, for example, 'velocity'.
To assign names to multiple states, enter a comma-separated list surrounded by braces, for example, {'a', 'b', 'c'}. Each name must be unique.
If a parameter is empty (' '), no name is assigned.
The state names apply only to the selected block with the name parameter.
The number of states must divide evenly among the number of state names.
You can specify fewer names than states, but you cannot specify more names than states.
For example, you can specify two names in a system with four states. The first name applies to the first two states and the second name to the last two states.
To assign state names with a variable in the MATLAB^® workspace, enter the variable without quotes. A variable can be a character vector, cell array, or structure.

Quaternion vector: e.g., {'qr', 'qi', 'qj', 'qk'} — Quaternion vector state name
`''` (default) | comma-separated list surrounded by braces

Quaternion vector state names, specified as a comma-separated list surrounded by braces.

Programmatic Use

Block Parameter: quat_statename

Type: character vector

Values: '' | comma-separated list surrounded by braces

Default: ''

Body rotation rates: e.g., {'p', 'q', 'r'} — Body rotation state names
`''` (default) | comma-separated list surrounded by braces

Body rotation rate state names, specified comma-separated list surrounded by braces.

Programmatic Use

Block Parameter: pm_statename

Type: character vector

Values: '' | comma-separated list surrounded by braces

Default: ''

Velocity: e.g., {'U', 'v', 'w'} — Velocity state name
`''` (default) | comma-separated list surrounded by braces

Velocity state names, specified as comma-separated list surrounded by braces.

Programmatic Use

Block Parameter: Vm_statename

Type: character vector

Values: '' | comma-separated list surrounded by braces

Default: ''

Fixed frame position: e.g., {'Xff', 'Yff', 'Zff'} — ECEF position state name
`''` (default) | comma-separated list surrounded by braces

ECEF position state names, specified as a comma-separated list surrounded by braces.

Programmatic Use

Block Parameter: posfixedframe_statename

Type: character vector

Values: '' | comma-separated list surrounded by braces

Default: ''

Inertial position: e.g., {'Xinertial', 'Yinertial', 'Zinertial'} — Inertial position state names
`''` (default) | comma-separated list surrounded by braces

Inertial position state names, specified as a comma-separated list surrounded by braces.

Default value is ''.

Programmatic Use

Block Parameter: posinertial_statename

Type: character vector

Values: '' | comma-separated list surrounded by braces

Default: ''

Celestial longitude of Greenwich: e.g., 'LG' — Celestial longitude state name
`''` (default) | character vector

Celestial longitude of Greenwich state name, specified as a character vector.

Dependencies

To enable this parameter, set:Planet model to Earth (WGS84).
If Planet model is set to Custom, the parameter name changes to Celestial longitude of prime meridian: e.g., 'LPM'.

Programmatic Use

Block Parameter: LPM_statename

Type: character vector

Values: '' | scalar

Default: ''

Celestial longitude of prime meridian: e.g., 'LPM' — Celestial longitude prime meridian
`''` (default) | character vector

Celestial longitude of prime meridian state name, specified as a character vector.

Dependencies

To enable this parameter, set:Planet model to Custom.
If Planet model is set to Earth (WGS84), the parameter name changes to Celestial longitude of Greenwich: e.g., 'LG'.

Programmatic Use

Block Parameter: LPM_statename

Type: character vector

Values: '' | scalar

Default: ''

Algorithms

The origin of the ECEF coordinate frame is the center of the Earth. In addition, the body of interest is assumed to be rigid, an assumption that eliminates the need to consider the forces acting between individual elements of mass. The representation of the rotation of ECEF frame from ECI frame is simplified to consider only the constant rotation of the ellipsoid Earth (ω_e) including an initial celestial longitude (L_G(0)). This excellent approximation allows the forces due to the Earth's complex motion relative to the “fixed stars” to be neglected.

The translational motion of the ECEF coordinate frame is given below, where the applied forces [F_x F_y F_z]^T are in the body frame and the mass of the body m is assumed constant.

${\bar{F}}_{b} = [\begin{matrix} F_{x} \\ F_{y} \\ F_{z} \end{matrix}] = m ({\dot{\bar{V}}}_{b} + {\bar{ω}}_{b} \times {\bar{V}}_{b} + D C M_{b f} {\bar{ω}}_{e} \times {\bar{V}}_{b} + D C M_{b f} ({\bar{ω}}_{e} \times ({\bar{ω}}_{e} \times {\bar{X}}_{f})))$

where the change of position in ECEF ${\dot{\bar{x}}}_{f}$ is calculated by

${\dot{\bar{x}}}_{f} = D C M_{f b} {\bar{V}}_{b}$

and the velocity of the body with respect to ECEF frame, expressed in body frame $({\bar{V}}_{b})$ , angular rates of the body with respect to ECI frame, expressed in body frame $({\bar{ω}}_{b})$ . Earth rotation rate $({\bar{ω}}_{e})$ , and relative angular rates of the body with respect to north-east-down (NED) frame, expressed in body frame $({\bar{ω}}_{r e l})$ , are defined as

$\begin{array}{l} {\bar{V}}_{b} = [\begin{matrix} u \\ v \\ w \end{matrix}], {\bar{ω}}_{r e l} = [\begin{matrix} p \\ q \\ r \end{matrix}], {\bar{ω}}_{e} = [\begin{matrix} 0 \\ 0 \\ ω_{e} \end{matrix}], {\bar{ω}}_{b} = {\bar{ω}}_{r e l} + D C M_{b f} {\bar{ω}}_{e} + D C M_{b e} {\bar{ω}}_{n e d} \\ {\bar{ω}}_{n e d} = [\begin{matrix} \dot{l} \cos μ \\ - \dot{μ} \\ - \dot{l} \sin μ \end{matrix}] = [\begin{matrix} V_{E} / (N + h) \\ - V_{N} / (M + h) \\ - V_{E} • \tan μ / (N + h) \end{matrix}] \end{array}$

The rotational dynamics of the body defined in body-fixed frame are given below, where the applied moments are [L M N]^T, and the inertia tensor I is with respect to the origin O.

$\begin{array}{l} A_{b b} = [\begin{matrix} {\dot{u}}_{b} \\ {\dot{v}}_{b} \\ {\dot{ω}}_{b} \end{matrix}] = \frac{1}{m} {\bar{F}}_{b} - [{\bar{ω}}_{b} \times {\bar{V}}_{b} + D C M_{b f} {\bar{ω}}_{e} \times {\bar{V}}_{b} + D C M_{b f} ({\bar{ω}}_{e} \times ({\bar{ω}}_{e} \times {\bar{X}}_{f}))] \\ A_{b} _{e c e f} = \frac{F_{b}}{m} \\ {\bar{M}}_{b} = [\begin{matrix} L \\ M \\ N \end{matrix}] = I {\dot{\bar{ω}}}_{b} + {\bar{ω}}_{b} \times (I {\bar{ω}}_{b}) \\ I = [\begin{matrix} I_{x x} & - I_{x y} & - I_{x z} \\ - I_{y x} & I_{y y} & - I_{y z} \\ - I_{z x} & - I_{z y} & I_{z z} \end{matrix}] \end{array}$

The integration of the rate of change of the quaternion vector is given below.

$[\begin{matrix} {\dot{q}}_{0} \\ {\dot{q}}_{1} \\ {\dot{q}}_{2} \\ {\dot{q}}_{3} \end{matrix}] = - \frac{1}{2} [\begin{matrix} 0 & ω_{b} (1) & ω_{b} (2) & ω_{b} (3) \\ - ω_{b} (1) & 0 & - ω_{b} (3) & ω_{b} (2) \\ - ω_{b} (2) & ω_{b} (3) & 0 & - ω_{b} (1) \\ - ω_{b} (3) & - ω_{b} (2) & ω_{b} (1) & 0 \end{matrix}] [\begin{matrix} q_{0} \\ q_{1} \\ q_{2} \\ q_{3} \end{matrix}]$

Aerospace Blockset uses quaternions that are defined using the scalar-first convention.

References

[1] Stevens, Brian, and Frank Lewis. Aircraft Control and Simulation, 2nd ed. Hoboken, NJ: John Wiley & Sons, 2003.

[2] McFarland, Richard E. "A Standard Kinematic Model for Flight simulation at NASA-Ames." NASA CR-2497.

[3] "Supplement to Department of Defense World Geodetic System 1984 Technical Report: Part I - Methods, Techniques and Data Used in WGS84 Development." DMA TR8350.2-A.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2006a

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R2023b: 6DOF ECEF (Quaternion) Block Coordinate Frame Changes

These updates better clarify the coordinate frame of the 6DOF ECEF (Quaternion) block when Central body is Custom:

New block icon.
Port name subscripts of ecef have changed to ff.
The Celestial longitude of Greenwich source programmatic name has changed from LG0 to LPM. Existing scripts continue to work.

Updated block parameter names, but models from previous releases continue to work.

Old Parameter Name or Setting	New Parameter Name
ECEF position...	Fixed frame position...
When Planet model is `Earth`	Celestial longitude of Greenwich source and Celestial longitude of Greenwich [deg]
When Planet model is `Custom`	Celestial longitude of prime meridian source and Celestial longitude of prime meridian [deg]

6DOF ECEF (Quaternion)

Description

Examples

Developing the Apollo Lunar Module Digital Autopilot

Limitations

Ports

Input

Fxyz — Applied forces three-element vector

Mxyz — Applied moments three-element vector

LG(0) — Initial celestial longitude of Greenwich scalar

Dependencies

LPM(0) — Prime meridian initial celestial longitude angle scalar

Dependencies

Output

Vff — Velocity of body with respect to ECEF frame, three-element vector

Xff — Position in ECEF reference frame three-element vector

μ l h — Position in geodetic latitude, longitude, and altitude three-element vector | M-by-3 array

φ θ Ψ (rad) — Body rotation angles three-element vector

DCMbi — Coordinate transformation from ECI axes 3-by-3 matrix

DCMbe — Coordinate transformation from NED axes to body-fixed axes 3-by-3 matrix

DCMef — Coordinate transformation from fixed-frame axes 3-by-3 matrix

Vb — Velocity of body with respect to fixed-frame three-element vector

ωrel — Relative angular rates of body with respect to NED frame three-element vector

ωb — Angular rates of body with respect to inertial frame three-element vector

dωb/dt — Angular accelerations of the body with respect to inertial frame three-element vector

Abb — Accelerations in body-fixed axes three-element vector

Ab ff — Accelerations in body-fixed axes three-element vector

Dependencies

Parameters

Main

Units — Input and output units Metric (MKS) (default) | English (Velocity in ft/s) | English (Velocity in kts)

Programmatic Use

Mass type — Mass type Fixed (default) | Simple Variable | Custom Variable

Programmatic Use

Initial position in geodetic latitude, longitude and altitude [mu,l,h] — Initial location of rigid body [0 0 0] (default) | three-element vector

Programmatic Use

Initial velocity in body axes [U,v,w] — Velocity in body axes [0 0 0] (default) | three-element vector

Programmatic Use

Initial Euler orientation [roll, pitch, yaw] — Initial Euler orientation [0 0 0] (default) | three-element vector

Programmatic Use

Initial body rotation rates [p,q,r] — Initial body rotation [0 0 0] (default) | three-element vector

Programmatic Use

Initial mass — Initial mass 1.0 (default) | scalar

Programmatic Use

Inertia — Inertia eye(3) (default) | scalar

Dependencies

Programmatic Use

Include inertial acceleration — Include inertial acceleration port off (default) | on

Dependencies

Programmatic Use

Planet

Planet model — Planet model Earth (WGS84) (default) | Custom

Programmatic Use

Equatorial radius of planet — Radius of planet at equator 6378137 (default) | scalar

Dependencies

Programmatic Use

Flattening — Flattening of planet 1/298.257223563 (default) | scalar

Dependencies

Programmatic Use

Rotational rate — Rotational rate 7292115e-11 (default) | scalar

Dependencies

Programmatic Use

Celestial longitude of Greenwich source — Source of Greenwich meridian initial celestial longitude Internal (default) | External

Dependencies

Programmatic Use

Celestial longitude of Greenwich [deg] — Initial angle 0 (default) | scalar

Dependencies

Programmatic Use

Celestial longitude of prime meridian source — Source of prime meridian initial celestial longitude Internal (default) | External

Dependencies

Programmatic Use

Celestial longitude of prime meridian [deg] — Initial angle 0 (default) | scalar

Dependencies

Programmatic Use

State Attributes

Quaternion vector: e.g., {'qr', 'qi', 'qj', 'qk'} — Quaternion vector state name '' (default) | comma-separated list surrounded by braces

Programmatic Use

Body rotation rates: e.g., {'p', 'q', 'r'} — Body rotation state names '' (default) | comma-separated list surrounded by braces

Programmatic Use

Velocity: e.g., {'U', 'v', 'w'} — Velocity state name '' (default) | comma-separated list surrounded by braces

F_xyz — Applied forces
three-element vector

M_xyz — Applied moments
three-element vector

L_G(0) — Initial celestial longitude of Greenwich
scalar

L_PM(0) — Prime meridian initial celestial longitude angle
scalar

V_ff — Velocity of body with respect to ECEF frame,
three-element vector

X_ff — Position in ECEF reference frame
three-element vector

μ l h — Position in geodetic latitude, longitude, and altitude
three-element vector | M-by-3 array

φ θ Ψ (rad) — Body rotation angles
three-element vector

DCM_bi — Coordinate transformation from ECI axes
3-by-3 matrix

DCM_be — Coordinate transformation from NED axes to body-fixed axes
3-by-3 matrix

DCM_ef — Coordinate transformation from fixed-frame axes
3-by-3 matrix

V_b — Velocity of body with respect to fixed-frame
three-element vector

ω_rel — Relative angular rates of body with respect to NED frame
three-element vector

ω_b — Angular rates of body with respect to inertial frame
three-element vector

dω_b/dt — Angular accelerations of the body with respect to inertial frame
three-element vector

A_bb — Accelerations in body-fixed axes
three-element vector

A_{b ff} — Accelerations in body-fixed axes
three-element vector

Units — Input and output units
`Metric (MKS)` (default) | `English (Velocity in ft/s)` | `English (Velocity in kts)`

Mass type — Mass type
`Fixed` (default) | `Simple Variable` | `Custom Variable`

Initial position in geodetic latitude, longitude and altitude [mu,l,h] — Initial location of rigid body
`[0 0 0]` (default) | three-element vector

Initial velocity in body axes [U,v,w] — Velocity in body axes
`[0 0 0]` (default) | three-element vector

Initial Euler orientation [roll, pitch, yaw] — Initial Euler orientation
`[0 0 0]` (default) | three-element vector

Initial body rotation rates [p,q,r] — Initial body rotation
`[0 0 0]` (default) | three-element vector

Initial mass — Initial mass
`1.0` (default) | scalar

Inertia — Inertia
`eye(3)` (default) | scalar

Include inertial acceleration — Include inertial acceleration port
`off` (default) | `on`

Planet model — Planet model
`Earth (WGS84)` (default) | `Custom`

Equatorial radius of planet — Radius of planet at equator
`6378137` (default) | scalar

Flattening — Flattening of planet
`1/298.257223563` (default) | scalar

Rotational rate — Rotational rate
`7292115e-11` (default) | scalar

Celestial longitude of Greenwich source — Source of Greenwich meridian initial celestial longitude
`Internal` (default) | `External`

Celestial longitude of Greenwich [deg] — Initial angle
`0` (default) | scalar

Celestial longitude of prime meridian source — Source of prime meridian initial celestial longitude
`Internal` (default) | `External`

Celestial longitude of prime meridian [deg] — Initial angle
`0` (default) | scalar

Quaternion vector: e.g., {'qr', 'qi', 'qj', 'qk'} — Quaternion vector state name
`''` (default) | comma-separated list surrounded by braces

Body rotation rates: e.g., {'p', 'q', 'r'} — Body rotation state names
`''` (default) | comma-separated list surrounded by braces

Velocity: e.g., {'U', 'v', 'w'} — Velocity state name
`''` (default) | comma-separated list surrounded by braces

Fixed frame position: e.g., {'Xff', 'Yff', 'Zff'} — ECEF position state name
`''` (default) | comma-separated list surrounded by braces

Inertial position: e.g., {'Xinertial', 'Yinertial', 'Zinertial'} — Inertial position state names
`''` (default) | comma-separated list surrounded by braces

Celestial longitude of Greenwich: e.g., 'LG' — Celestial longitude state name
`''` (default) | character vector

Celestial longitude of prime meridian: e.g., 'LPM' — Celestial longitude prime meridian
`''` (default) | character vector

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