Aerospace Blockset    
Equations of Motion

Implement three-degrees-of-freedom equations of motion

Library

Equations of Motion/3DoF

Description

The 3DoF Equations of Motion block considers the rotation in the vertical plane of a body-fixed coordinate frame about an Earth-fixed reference frame.

The equations of motion are given below:

where the applied forces are assumed to act at the center of gravity of the body.

Dialog Box

Initial velocity [m/s]
A scalar value for the initial velocity of the body, (V0).
Initial body attitude [rad]
A scalar value for the initial pitch attitude of the body, .
Initial incidence [rad]
A scalar value for the initial angle between the velocity vector and the body, .
Initial body rotation rate [rad/sec]
A scalar value for the initial body rotation rate, (q0).
Initial position (x,z) [m]

A two-element vector containing the initial location of the body in the Earth-fixed reference frame.

Mass [kg]
A scalar value for the mass of the body.
Inertia [Kg.m2]
A scalar value for the inertia of the body.
Acceleration due to gravity [m/s2]
A scalar value for the acceleration due to gravity. If gravity is to be neglected in the simulation, this value can be set to 0.

Inputs and Outputs

The first input to the block is the force acting along the body x-axis, in Newtons .

The second input to the block is the force acting along the body z-axis, in Newtons .

The third input to the block is the applied pitch moment, in Newton.meters (M).

The first output from the block is the pitch attitude, in radians .

The second output is the pitch angular rate, in radians per second (q).

The third output is the pitch angular acceleration, in radians per second squared .

The fourth output is a two-element vector containing the location of the body, in the Earth-fixed reference frame, in meters (Xe,Ze).

The fifth output is a two-element vector containing the velocity of the body resolved into the body-fixed coordinate frame, in meters per second (u,w).

The sixth output is a two-element vector containing the acceleration of the body resolved into the body-fixed coordinate frame, in meters per second squared (Ax,Az).

Examples

See the Simulink model aeroblk_guidance.mdl for an example of the use of the 3DoF Equations of Motion block.

See Also

Incidence & Airspeed


  Euler Angles to Quaternions Force Conversion