Simple Variable Mass 3DOF (Body Axes)
Implement three-degrees-of-freedom equations of motion of simple variable mass with respect to body axes
Libraries:
Aerospace Blockset /
Equations of Motion /
3DOF
Description
The Simple Variable Mass 3DOF (Body Axes) block implements three-degrees-of-freedom equations of motion of simple variable mass 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
dm/dt — Rate of change of mass
scalar
Rate of change of mass (positive if accreted, negative if ablated), specified as a scalar.
Dependencies
To enable this port, select Include mass flow relative velocity.
Data Types: double
g — Gravity
scalar
Gravity, specified as a scalar.
Dependencies
To enable this port, set Gravity source to
External
.
Data Types: double
Vre — Relative velocity
two-element vector
Relative velocity at which mass is accreted to or ablated from the body in body-fixed axes, specified as a two-element vector.
Dependencies
To enable this port, select Include mass flow relative velocity.
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
Fuel — Fuel tank status
scalar
Fuel tank status, returned as:
1
— Tank is full.0
— Tank is neither full nor empty.-1
— Tank is empty.
Dependencies
To enable this port, set Mass type to Simple Variable
.
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
Simple Variable
(default) | Fixed
| 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 Simple Variable
selection conforms to the
equations of motion described in Algorithms.
Programmatic Use
Block Parameter:
mtype |
Type: character vector |
Values:
Fixed | Simple Variable |
Custom Variable |
Default:
'Simple Variable' |
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' |
Empty mass — Mass of body when fuel tank is empty
0.5
(default) | scalar
Mass of body when fuel tank is empty, specified as a scalar.
Programmatic Use
Block Parameter:
mass_e |
Type: character vector |
Values:
'0.5' | scalar |
Default:
'0.5' |
Full mass — Mass of body when fuel tank is full
3.0
(default) | scalar
Mass of body when fuel tank is full, specified as a scalar.
Programmatic Use
Block Parameter:
mass_f |
Type: character vector |
Values:
'3.0' | scalar |
Default:
'3.0' |
Empty inertia — Body inertia when fuel tank is full
0.5
(default) | scalar
Body inertia when the fuel tank is full, specified as a double scalar.
Programmatic Use
Block Parameter:
Iyy_e |
Type: character vector |
Values:
'0.5' | scalar |
Default:
'0.5' |
Full inertia — Full inertia
3.0
(default) | scalar
Full inertia of the body, specified as a scalar.
Programmatic Use
Block Parameter: Iyy_f |
Type: character vector |
Values:
'3.0' | scalar |
Default: '3.0' |
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 mass flow relative velocity — Mass flow relative velocity port
off
(default) | on
Select this check box to add a mass flow relative velocity port. This is the relative velocity at which the mass is accreted or ablated.
Programmatic Use
Block Parameter: vre_flag |
Type: character vector |
Values: off | on |
Default:
'off' |
Limit mass flow when mass is empty or full — Limit mass flow
on
(default) | off
Select this check box to limit the input mass flow rate when one of these is true:
Fuel tank is full and input mass flow rate is positive.
Fuel tank is empty and input mass flow rate is negative.
When the input mass flow rate might cause the mass to exceed its limits, the block uses a zero mass flow rate value in the equations of motion. For more information, see Algorithms.
If you do not want to limit the input mass flow rate, clear this check box.
Dependencies
To enable this parameter, set Mass type to
Simple Variable
.
Programmatic Use
Block Parameter:
mdot_flag |
Type: character vector |
Values:
'off' | 'on' |
Default:
'on' |
Data Types: double
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: '' |
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:
'' |
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:
'' |
Mass: e.g., 'mass' — Mass state name
''
(default) | scalar
Mass state name, specified as a character vector or string.
Programmatic Use
Block Parameter: mass_statename |
Type: character vector | string |
Values: '' | scalar |
Default: '' |
Algorithms
It 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, . ure, wre, and g are optional input variables. Mass m is limited to between mempty and mfull. Whenever mass is saturated at empty or full, for consistency, limit within the equations of motion.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2006aSimple Variable Mass 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.
MATLAB 명령
다음 MATLAB 명령에 해당하는 링크를 클릭했습니다.
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