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Custom Variable Mass 3DOF (Body Axes)

Implement three-degrees-of-freedom equations of motion of custom variable mass with respect to body axes

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  • Custom Variable Mass 3DOF (Body Axes) block

Libraries:
Aerospace Blockset / Equations of Motion / 3DOF

Description

The Custom Variable Mass 3DOF (Body Axes) block implements three-degrees-of-freedom equations of motion of custom 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

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Applied force along the body x-axis, specified as a scalar, in the units selected in Units.

Data Types: double

Applied force along the body z-axis, specified as a scalar.

Data Types: double

Applied pitching moment, specified as a scalar.

Data Types: double

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

Mass, specified as a scalar.

Data Types: double

Rate of change of inertia tensor, Iyy, specified as scalar.

Dependencies

To enable this port, set Mass type to Custom Variable.

Data Types: double

Inertia tensor, specified as a scalar.

Dependencies

To enable this port, set Mass type to Custom Variable.

Data Types: double

Gravity, specified as a scalar.

Dependencies

To enable this port, set Gravity source to External.

Data Types: double

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

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Pitch attitude, within ±pi, returned as a scalar, in radians (θ).

Data Types: double

Pitch angular rate, returned as a scalar, in radians per second.

Data Types: double

Pitch angular acceleration, returned as a scalar, in radians per second squared.

Data Types: double

Location of the body in the flat Earth reference frame, (Xe, Ze), returned as a two-element vector.

Data Types: double

Velocity of the body resolved into the body-fixed coordinate frame, (u, w), returned as a two-element vector.

Data Types: double

Acceleration of the body with respect to the body-fixed coordinate frame, (Ax, Az), returned as a two-element vector.

Data Types: double

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

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Main

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

UnitsForcesMomentAccelerationVelocityPositionMassInertia
Metric (MKS) NewtonNewton-meterMeters per second squaredMeters per secondMetersKilogramKilogram meter squared
English (Velocity in ft/s) PoundFoot-poundFeet per second squaredFeet per secondFeetSlugSlug foot squared
English (Velocity in kts) PoundFoot-poundFeet per second squaredKnotsFeetSlugSlug 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)

Body or wind axes, specified as Wind or Body.

Programmatic Use

Block Parameter: axes
Type: character vector
Values: Wind | Body
Default: Body

Mass type, specified according to the following table.

Mass TypeDescriptionDefault 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 Custom Variable selection conforms to the previously described equations of motion.

Programmatic Use

Block Parameter: mtype
Type: character vector
Values: Fixed | Simple Variable | Custom Variable
Default: 'Custom Variable'

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 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 pitch rotation rate, (q0), specified as a scalar.

Programmatic Use

Block Parameter: q_ini
Type: character vector
Values: '0' | scalar
Default: '0'

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 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]'

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, 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'

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'

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 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 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 state name, specified as a character vector or string.

Programmatic Use

Block Parameter: q_statename
Type: character vector | string
Values: '' | scalar
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 Custom Variable Mass 3DOF (Body Axes) block considers the rotation in the vertical plane of a body-fixed coordinate frame about a flat Earth reference frame.

Graphical view of rotation in the vertical plane of a body-fixed coordinate frame about a flat Earth reference frame.

The equations of motion are

Axb=u˙=Axe−qwAzb=w˙=Aze+quAxe=(Fx−m˙ure)m−gsinθAze=(Fz−m˙wre)m+gcosθX˙e=ucosθ+wsinθZ˙e=−usinθ+wcosθq˙=My−I˙yyqIyyθ˙=q

where the applied forces are assumed to act at the center of gravity of the body. Input variables are Fx, Fz, My, m˙ (dm/dt), m, I˙ (dIyy/dt), and Iyy. ure, wre, and g are optional input variables.

Extended Capabilities

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

Version History

Introduced in R2006a

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See Also

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