Documentation

# 4th Order Point Mass (Longitudinal)

Calculate fourth-order point mass

• Library:
• 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.

## 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

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Force in x-axis, specified as a scalar or array, in selected units.

Data Types: double

Force in z-axis, specified as a scalar or array, in selected units.

Data Types: double

### Output

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Flight path angle, returned as a scalar or array, in radians.

Data Types: double

Airspeed, returned as a scalar or array, in selected units.

Data Types: double

Downrange or amount traveled east, returned as a scalar or array, in selected units.

Data Types: double

Altitude or amount traveled up, returned as a scalar or array, in selected units.

Data Types: double

## Parameters

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Input and output units, specified as:

Units

Forces

Velocity

Position

Metric (MKS)

Newton

Meters per second

Meters

English (Velocity in ft/s)

Pound

Feet per second

Feet

English (Velocity in kts)

Pound

Knots

Feet

#### Programmatic Use

 Block Parameter: units Type: character vector Values: 'Metric (MKS)' | 'English (Velocity in ft/s)' | 'English (Velocity in kts)' Default: 'Metric (MKS)'

Initial flight path angle of the point mass(es), specified as a scalar or vector.

#### Programmatic Use

 Block Parameter: gamma0 Type: character vector Values: scalar | vector Default: '0'

Initial airspeed of the point mass(es), specified as a scalar or vector.

#### Programmatic Use

 Block Parameter: V0 Type: character vector Values: scalar | vector Default: '100'

Initial downrange of the point mass(es), specified as a scalar or vector.

#### Programmatic Use

 Block Parameter: x0 Type: character vector Values: scalar | vector Default: '0'

Initial altitude of the point mass(es), specified as a scalar or vector.

#### Programmatic Use

 Block Parameter: h0 Type: character vector Values: scalar | vector Default: '0'

Mass of the point mass(es), specified as a scalar or vector.

#### Programmatic Use

 Block Parameter: mass0 Type: character vector Values: scalar | vector Default: '1.0'

## Algorithms

The translational motions of the point mass [XEastXUp]T are functions of airspeed (V) and flight path angle (γ),

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

where the applied forces [FxFz]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.

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