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.

4th Order Point Mass Forces (Longitudinal)

6th Order Point Mass (Coordinated Flight)

6th Order Point Mass Forces (Coordinated Flight)

Custom Variable Mass 3DOF (Body Axes)

Custom Variable Mass 3DOF (Wind Axes)

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