Calculate fourth-order point mass

Equations of Motion/Point Mass

The 4th Order Point Mass (Longitudinal) block performs the calculations for the translational motion of a single point mass or multiple point masses.

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}*

**Units**Specifies the input and output units:

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

**Initial flight path angle**The scalar or vector containing the initial flight path angle of the point mass(es).

**Initial airspeed**The scalar or vector containing the initial airspeed of the point mass(es).

**Initial downrange**The scalar or vector containing the initial downrange of the point mass(es).

**Initial altitude**The scalar or vector containing the initial altitude of the point mass(es).

**Initial mass**The scalar or vector containing the mass of the point mass(es).

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

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

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

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

First | Contains the flight path angle in radians. | |

Second | Contains the airspeed in selected units. | |

Third | Contains the downrange or amount traveled East in selected units. | |

Fourth | Contains the altitude or amount traveled Up in selected units. |

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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