Calculate sixth-order point mass in coordinated flight

Equations of Motion/Point Mass

The 6th Order Point Mass (Coordinated Flight) block performs the calculations for the translational motion of a single point mass or multiple point masses.

The translational motion
of the point mass [*X _{East}*

$$\begin{array}{l}{F}_{x}=mV\\ {F}_{y}=(mV\mathrm{cos}\gamma )\dot{\chi}\\ {F}_{z}=mV\dot{\gamma}\\ {\dot{X}}_{East}=V\mathrm{cos}\chi \mathrm{cos}\gamma \\ {\dot{X}}_{North}=V\mathrm{sin}\chi \mathrm{cos}\gamma \\ {\dot{X}}_{Up}=V\mathrm{sin}\gamma \end{array}$$

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 initial flight path angle of the point mass(es).

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

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

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

**Initial crossrange [North]**The scalar or vector containing initial crossrange of the point mass(es).

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

**Initial mass**The scalar or vector containing 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 y-axis in selected
units. | |

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

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

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

Second | Contains the heading angle in radians. | |

Third | Contains the airspeed in selected units. | |

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

Fifth | Contains the crossrange or amount traveled North in selected units. | |

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

The block assumes that there is fully coordinated flight, i.e., there is no side force (wind axes) and sideslip is always zero.

The flat 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 (Longitudinal)

4th Order Point Mass Forces (Longitudinal)

6th Order Point Mass Forces (Coordinated Flight)

Custom Variable Mass 6DOF (Euler Angles)

Custom Variable Mass 6DOF (Quaternion)

Custom Variable Mass 6DOF ECEF (Quaternion)

Custom Variable Mass 6DOF Wind (Quaternion)

Custom Variable Mass 6DOF Wind (Wind Angles)

Simple Variable Mass 6DOF (Euler Angles)

Simple Variable Mass 6DOF (Quaternion)

Simple Variable Mass 6DOF ECEF (Quaternion)

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