3DOF (Body Axes)
Implement three-degrees-of-freedom equations of motion with respect to body axes
Libraries:
Aerospace Blockset /
Equations of Motion /
3DOF
Description
The 3DOF (Body Axes) block implements three-degrees-of-freedom equations of motion with respect to body axes. It considers the rotation in the vertical plane of a body-fixed coordinate frame about a flat Earth reference frame. For more information about the rotation and equations of motion, see Algorithms.
Ports
Input
Fx — Applied force along x-axis
scalar
Applied force along the body x-axis, specified as a scalar, in the units selected in Units.
Data Types: double
Fz — Applied force along z-axis
scalar
Applied force along the body z-axis, specified as a scalar.
Data Types: double
M — Applied pitching moment
scalar
Applied pitching moment, specified as a scalar.
Data Types: double
g — Gravity
scalar
Gravity, specified as a scalar.
Dependencies
To enable this port, set Gravity source to
External
.
Data Types: double
Output
θ — Pitch altitude
scalar
Pitch attitude, within ±pi, returned as a scalar, in radians.
Data Types: double
q — Pitch angular rate
scalar
Pitch angular rate, returned as a scalar, in radians per second.
Data Types: double
dq/dt — Pitch angular acceleration
scalar
Pitch angular acceleration, returned as a scalar, in radians per second squared.
Data Types: double
XeZe — Location of body
two-element vector
Location of the body in the flat Earth reference frame, (Xe, Ze), returned as a two-element vector.
Data Types: double
U w — Velocity of body
two-element vector
Velocity of the body resolved into the body-fixed coordinate frame, (u, w), returned as a two-element vector.
Data Types: double
AxbAzb — Acceleration of body
two-element vector
Acceleration of the body with respect to the body-fixed coordinate frame, (Ax, Az), returned as a two-element vector.
Data Types: double
AxeAze — Acceleration of body
two-element vector
Accelerations of the body with respect to the inertial (flat Earth) coordinate frame, returned as a two-element vector. You typically connect this signal to the accelerometer.
Dependencies
To enable this port, select the Include inertial acceleration check box.
Data Types: double
Parameters
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) |
Axes — Body or wind axes
Body
(default) | Wind
Body or wind axes, specified as Wind
or
Body
.
Programmatic Use
Block Parameter:
axes |
Type: character vector |
Values:
Wind | Body |
Default:
Body |
Mass Type — Mass type
Fixed
(default) | Simple Variable
| Custom Variable
Mass type, specified according to the following table.
Mass Type | Description | Default for |
---|---|---|
Fixed | Mass is constant throughout the simulation. | |
Simple Variable | Mass and inertia vary linearly as a function of mass rate. | |
Custom Variable | Mass and inertia variations are customizable. |
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:
'Fixed' |
Initial velocity — Initial velocity of body
100
(default) | scalar
Initial velocity of the body, (V0), specified as a scalar.
Programmatic Use
Block
Parameter:
v_ini |
Type: character vector |
Values:
'100' | scalar |
Default:
'100' |
Initial body attitude — Initial pitch altitude
0
(default) | scalar
Initial pitch attitude of the body, (θ0), specified as a scalar.
Programmatic Use
Block Parameter: theta_ini |
Type: character vector |
Values:
'0' | scalar |
Default: '0' |
Initial body rotation rate — Initial pitch rotation rate
0
(default) | scalar
Initial pitch rotation rate, (q0), specified as a scalar.
Programmatic Use
Block
Parameter:
q_ini |
Type: character vector |
Values:
'0' | scalar |
Default:
'0' |
Initial incidence — Initial angle
0
(default) | scalar
Initial angle between the velocity vector and the body, (α0), specified as a scalar.
Programmatic Use
Block Parameter: alpha_ini |
Type: character vector |
Values:
'0' | scalar |
Default: '0' |
Initial position (x,z) — Initial location
[0 0]
(default) | two-element vector
Initial location of the body in the flat Earth reference frame, specified as a two-element vector.
Programmatic Use
Block Parameter:
pos_ini |
Type: character vector |
Values:
'[0 0]' | two-element vector |
Default:
'[0 0]' |
Initial mass — Initial mass
1.0
(default) | scalar
Initial mass of the rigid body, specified as a scalar.
Programmatic Use
Block Parameter: mass |
Type: character vector |
Values:
'1.0' | scalar |
Default:
'1.0' |
Inertia — Inertia
1.0
(default) | scalar
Inertia of the body, specified as a scalar.
Dependencies
To enable this parameter, set Mass type to Fixed
.
Programmatic Use
Block Parameter: Iyy |
Type: character vector |
Values:
'1.0' | scalar |
Default: '1.0' |
Gravity Source — Gravity source
Internal
(default) | External
Gravity source, specified as:
External | Variable gravity input to block |
Internal | Constant gravity specified in mask |
Programmatic Use
Block Parameter: g_in |
Type: character vector |
Values: 'Internal' | 'External' |
Default: 'Internal' |
Acceleration due to gravity — Gravity source
9.81
(default) | scalar
Acceleration due to gravity, specified as a double scalar and used if internal gravity source
is selected. If gravity is to be neglected in the simulation, this value can be set to
0
.
Dependencies
To enable this parameter, set Gravity Source to
Internal
.
Programmatic Use
Block Parameter: g |
Type: character vector |
Values:
'9.81' | scalar |
Default: '9.81' |
Include inertial acceleration — Include inertial acceleration port
off
(default) | on
Select this check box to add an inertial acceleration in flat Earth frame output port. You typically connect this signal to the accelerometer.
Dependencies
To enable the AxeAze port, select this parameter.
Programmatic Use
Block Parameter: abi_flag |
Type: character vector |
Values:
'off' |
'on' |
Default:
'off' |
State Attributes
Assign a unique name to each state. You can use state names instead of block paths during linearization.
The number of names must match the number of states, as shown for each item, or be empty. Set all or none of the block states.
To assign names to single-variable states, enter unique names between quotes, for example,
'q'
or"q"
.To assign names to two-variable states, enter a comma-separated list surrounded by braces, for example,
{'Xe','Ze'}
.If a state parameter is empty (
' '
), no name is assigned.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 of character vectors, or string.
Velocity: e.g., {'u, 'w'} — Velocity state name
''
(default) | comma-separated list surrounded by braces
Velocity state names, specified as a comma-separated list surrounded by braces.
Programmatic Use
Block Parameter: vel_statename |
Type: character vector |
Values:
'' | comma-separated list surrounded by braces |
Default: '' |
Position: e.g., {'Xe', 'Ze'} — Position state name
''
(default) | comma-separated list surrounded by braces
Position state names, specified as a comma-separated list surrounded by braces.
Programmatic Use
Block Parameter: pos_statename |
Type: character vector |
Values:
'' | comma-separated list surrounded by braces |
Default: '' |
Pitch angular rate e.g., 'q' — Pitch angular rate state name
''
(default)
Pitch angular rate state name, specified as a character vector or string.
Programmatic Use
Block Parameter:
q_statename |
Type: character vector | string |
Values:
'' | scalar |
Default:
'' |
Pitch attitude: e.g., 'theta' — Pitch attitude state name
''
(default)
Pitch attitude state name, specified as a character vector or string.
Programmatic Use
Block Parameter:
theta_statename |
Type: character vector | string |
Values:
'' |
Default:
'' |
Algorithms
The block considers the rotation in the vertical plane of a body-fixed coordinate frame about a flat Earth reference frame.
The equations of motion are
where the applied forces are assumed to act at the center of gravity of the body. Input variables are Fx, Fz, My. g is an optional input variable.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2006aR2021b: 3DOF (Body Axes) Block Changes
The 3DOF equations of motion have been updated. Existing models created prior to R2021b that contain 3DOF equations of motion blocks continue to run. If you replace a pre-R2021b version of a 3DOF equation of motion block with an R2021b or later version, your updated model might have a higher tendency for algebraic loops. For an example of how to remove algebraic loops using unit delays, see Remove Algebraic Loops. For further information about algebraic loops, see Identify Algebraic Loops in Your Model.
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