Implement three-degrees-of-freedom equations of motion of simple variable mass with respect to body axes
Equations of Motion/3DOF
The Simple 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.
The equations of motion are
where the applied forces are assumed to act at the center of gravity of the body. Ureb and Wreb are the relative velocities of the mass flow () being added to or ejected from the body in body-fixed axes.
Specifies the input and output units:
Units | Forces | Moment | Acceleration | Velocity | Position | Mass | Inertia |
---|---|---|---|---|---|---|---|
| Newton | Newton meter | Meters per second squared | Meters per second | Meters | Kilogram | Kilogram meter squared |
| Pound | Foot pound | Feet per second squared | Feet per second | Feet | Slug | Slug foot squared |
| Pound | Foot pound | Feet per second squared | Knots | Feet | Slug | Slug foot squared |
Select the type of mass to use:
| Mass is constant throughout the simulation. |
| Mass and inertia vary linearly as a function of mass rate. |
| Mass and inertia variations are customizable. |
The Simple Variable
selection conforms to the
previously described equations of motion.
A scalar value for the initial velocity of the body, (V0).
A scalar value for the initial pitch attitude of the body, (θ0).
A scalar value for the initial angle between the velocity vector and the body, .
A scalar value for the initial body rotation rate, (q0).
A two-element vector containing the initial location of the body in the flat Earth reference frame.
A scalar value for the initial mass of the body.
A scalar value for the inertia of the body.
A scalar value for the empty mass of the body.
A scalar value for the full mass of the body.
A scalar value for the empty inertia of the body.
A scalar value for the full inertia of the body.
Specify source of gravity:
| Variable gravity input to block |
| Constant gravity specified in Acceleration due to gravity |
A scalar value for the acceleration due to gravity used if internal
gravity source is selected. If gravity is to be neglected in the
simulation, this value can be set to 0. This parameter appears if you
set Gravity source to
Internal
.
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.
Select this check box to enable an additional output port for the accelerations in body-fixed axes with respect to the inertial frame. You typically connect this signal to the accelerometer.
Assign 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-delimited list
surrounded by braces, for example, {'a', 'b', 'c'}
. Each
name must be unique.
If a parameter is empty (' '
), no name assignment
occurs.
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.
Specify velocity state names.
Default value is ''
.
Specify pitch attitude state name.
Default value is ''
.
Specify position state names.
Default value is ''
.
Specify pitch angular rate state name.
Default value is ''
.
Specify mass state name.
Default value is ''
.
Input | Dimension Type | Description |
---|---|---|
First | Contains the force acting along the body x-axis, (Fx). | |
Second | Contains the force acting along the body z-axis, (Fz). | |
Third | Contains the applied pitch moment, (M). | |
Fourth | Contains one or more rates of change of mass, (positive if accreted, negative if ablated). | |
Fifth (Optional) | Contains the gravity in the selected units. | |
Sixth (Optional) | Two-element vector | Contains one or more relative velocities at which the mass is accreted to or ablated from the body in body-fixed axes. |
Output | Dimension Type | Description |
---|---|---|
First | Contains the pitch attitude, within ±pi, in radians (θ). | |
Second | Contains the pitch angular rate, in radians per second (q). | |
Third | Contains the pitch angular acceleration, in radians per second squared . | |
Fourth | Two-element vector | Contains the location of the body, in the flat Earth reference frame, (Xe, Ze). |
Fifth | Two-element vector | Contains the velocity of the body resolved into the body-fixed coordinate frame, (u, w). |
Sixth | Two-element vector | Contains the acceleration of the body resolved into the body-fixed coordinate frame, (Ax,Az). |
Seventh | Scalar element | Contains a flag for fuel tank status, (Fuel):
|
Eighth (Optional) | Two-element vector | Contains the accelerations in body-fixed axes with respect to inertial frame (flat Earth). You typically connect this signal to the accelerometer. |