# 6th Order Point Mass (Coordinated Flight)

Calculate sixth-order point mass in coordinated flight

**Libraries:**

Aerospace Blockset /
Equations of Motion /
Point Mass

## Description

The 6th Order Point Mass (Coordinated Flight) block performs the calculations for the translational motion of a single point mass or multiple point masses. For more information on the system for the translational motion of a single point mass or multiple mass, see Algorithms.

The 6th Order Point Mass (Coordinated Flight) block port labels change
based on the input and output units selected from the **Units**
list.

## Limitations

The block assumes that there is fully coordinated flight, i.e., there is no side force (wind axes) and sideslip is always zero.

The flat Earth reference frame is considered inertial, an approximation that allows the forces due to the Earth motion relative to the "fixed stars" to be neglected.

## Ports

### Input

### Output

## Parameters

## Algorithms

This figure shows the system for the translational motion of a single point mass or multiple point masses.

The translational motion of the point mass
[*X _{East}*

*X*

_{North}*X*]

_{Up}^{T }are functions of airspeed (

*V*), flight path angle (

*γ*), and heading angle (

*χ*),

$$\begin{array}{l}{F}_{x}=m\dot{V}\\ {F}_{y}=(mV\mathrm{cos}\gamma )\dot{\chi}\\ {F}_{z}=mV\dot{\gamma}\\ {\dot{X}}_{East}=V\mathrm{cos}\chi \mathrm{cos}\gamma \\ {\dot{X}}_{North}=V\mathrm{sin}\chi \mathrm{cos}\gamma \\ {\dot{X}}_{Up}=V\mathrm{sin}\gamma \end{array}$$

where the applied forces
[*F _{x}*

*F*

_{y}*F*]

_{h}^{T }are in a system is defined by

*x*-axis in the direction of vehicle velocity relative to air,

*z*-axis is upward, and

*y*-axis completes the right-handed frame, and the mass of the body

*m*is assumed constant.

## Extended Capabilities

## Version History

**Introduced before R2006a**

## See Also

4th Order Point Mass (Longitudinal) | 4th Order Point Mass Forces (Longitudinal) | 6th Order Point Mass Forces (Coordinated Flight) | 6DOF (Euler Angles) | 6DOF (Quaternion) | 6DOF ECEF (Quaternion) | 6DOF Wind (Wind Angles) | Custom Variable Mass 6DOF (Euler Angles) | Custom Variable Mass 6DOF (Quaternion) | Custom Variable Mass 6DOF ECEF (Quaternion) | Custom Variable Mass 6DOF Wind (Quaternion) | Custom Variable Mass 6DOF Wind (Wind Angles) | Simple Variable Mass 6DOF (Euler Angles) | Simple Variable Mass 6DOF (Quaternion) | Simple Variable Mass 6DOF ECEF (Quaternion) | Simple Variable Mass 6DOF Wind (Quaternion) | Simple Variable Mass 6DOF Wind (Wind Angles)