Calculate forces used by fourth-order point mass

Equations of Motion/Point Mass

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

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. They are functions of lift (*L*), drag (*D*),
thrust (*T*), weight (*W*), flight
path angle (*γ*), angle of attack (*α*),
and bank angle (*μ*).

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

Input | Dimension Type | Description |
---|---|---|

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. |

Output | Dimension Type | Description |
---|---|---|

First | Contains the force in x-axis in units
of force. | |

Second | Contains the force in z-axis in units
of force. |

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.

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