# 4th Order Point Mass (Longitudinal)

Calculate fourth-order point mass

**Libraries:**

Aerospace Blockset /
Equations of Motion /
Point Mass

## Description

The 4th Order Point Mass (Longitudinal) 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 4th Order Point Mass (Longitudinal) block port labels change based
on the input and output units selected from the **Units** list.

## Limitations

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

## Ports

### Input

### Output

## Parameters

## Algorithms

The translational motions of the point mass [*X*_{East}*X*_{Up}]^{T }are functions of airspeed
(*V*) and flight path angle (*γ*),

$$\begin{array}{c}{F}_{x}=m\dot{V}\\ {F}_{z}=mV\dot{\gamma}\\ {\dot{X}}_{East}=V\mathrm{cos}\gamma \\ {\dot{X}}_{Up}=V\mathrm{sin}\gamma \end{array}$$

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

*F*]

_{z}^{T }are in a system defined as follows:

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

*z*-axis is upward, and

*y*-axis completes the right-handed frame. The mass of the body

*m*is assumed constant.

## Extended Capabilities

## Version History

**Introduced before R2006a**

## See Also

Simple Variable Mass 3DOF (Body Axes) | Custom Variable Mass 3DOF (Wind Axes) | 4th Order Point Mass Forces (Longitudinal) | 3DOF (Body Axes) | 3DOF (Wind Axes) | 6th Order Point Mass (Coordinated Flight) | Custom Variable Mass 3DOF (Body Axes) | 6th Order Point Mass Forces (Coordinated Flight) | Simple Variable Mass 3DOF (Wind Axes)