# 4th Order Point Mass Forces (Longitudinal)

Calculate forces used by fourth-order point mass

## Library

Equations of Motion/Point Mass

## Description

The 4th Order Point Mass Forces (Longitudinal) block calculates the applied forces for a single point mass or multiple point masses.

The applied forces [Fx Fz]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. They are functions of lift (L), drag (D), thrust (T), weight (W), flight path angle (γ), angle of attack (α), and bank angle (μ).

`$\begin{array}{l}{F}_{z}=\left(L+T\mathrm{sin}\alpha \right)\mathrm{cos}\mu -W\mathrm{cos}\gamma \\ {F}_{x}=T\mathrm{cos}\alpha -D-W\mathrm{sin}\gamma \end{array}$`

## Inputs and Outputs

InputDimension TypeDescription
First Contains the lift in units of force.
Second Contains the drag in units of force.
Third Contains the weight in units of force.
Fourth Contains the thrust in units of force.
Fifth Contains the flight path angle in radians.
Sixth Contains the bank angle in radians.
Seventh Contains the angle of attack in radians.
OutputDimension TypeDescription
First Contains the force in x-axis in units of force.
Second Contains the force in z-axis in units of force.

## Assumptions and Limitations

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