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Satellite Halo Model

Source Notebook

Model of a satellite's motion in a halo orbit

Examples

Basic Examples (3) 

Retrieve the model:

In[1]:=
ResourceData[\!\(\* TagBox["\"\<Satellite Halo Model\>\"", #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\)]
Out[1]=

The icon:

In[2]:=
ResourceData[\!\(\* TagBox["\"\<Satellite Halo Model\>\"", #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\), "Icon"]
Out[2]=

The annotation:

In[3]:=
ResourceData[\!\(\* TagBox["\"\<Satellite Halo Model\>\"", #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\), "Annotation"]
Out[3]=

Scope & Additional Elements (4) 

Available content elements:

In[4]:=
\!\(\* TagBox[ RowBox[{"ResourceObject", "[", "\"\<Satellite Halo Model\>\"", "]"}], #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\)["ContentElements"]
Out[4]=

The available model types:

In[5]:=
ResourceData[\!\(\* TagBox["\"\<Satellite Halo Model\>\"", #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\), "AvailableModelTypes"]
Out[5]=

The operating point:

In[6]:=
ResourceData[\!\(\* TagBox["\"\<Satellite Halo Model\>\"", #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\), "OperatingPoint"]
Out[6]=

The parameters:

In[7]:=
ResourceData[\!\(\* TagBox["\"\<Satellite Halo Model\>\"", #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\), "Parameters"]
Out[7]=

Analysis (3) 

The numerical model:

In[8]:=
sat = ResourceData[\!\(\* TagBox["\"\<Satellite Halo Model\>\"", #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\)] /. ResourceData[\!\(\* TagBox["\"\<Satellite Halo Model\>\"", #& , BoxID -> "ResourceTag-Satellite Halo Model-Input", AutoDelete->True]\), "Parameters"]
Out[8]=

The satellite's orbit is unstable to an initial disturbance in the η state:

In[9]:=
OutputResponse[{sat, {0, 10^-2}}, {0, 0, 0, 0}, {t, 0, 10}]; Plot[%, {t, 0, 5}, PlotRange -> All, PlotLegends -> {\[Zeta], \[Eta], \[Xi]}]
Out[10]=

At least thruster 𝓊ξ and another thruster are necessary to control the satellite:

In[11]:=
Grid[{#, ControllableModelQ[SystemsModelExtract[sat, #, All]]} & /@ Subsets[{1, 2, 3}, {1, 3}], Sequence[ Frame -> True, Background -> {None, {{ RGBColor[0.87, 0.94, 1], GrayLevel[1]}}}]]
Out[11]=
In[12]:=
Subsets[{1, 2, 3}, {1, 3}]
Out[12]=

Suba Thomas, "Satellite Halo Model" from the Wolfram Data Repository (2025)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation:
    • B. L. Jones and R. H. Bishop, "H₂ optimal halo orbit guidance", Journal of Guidance, Control, and Dynamics, vol. 16, no. 6, pp. 1118–1124, Nov.–Dec. 1993.

Publisher Information

  • Prepared for the Wolfram Data Repository By: Maher Kuzbari, Suba Thomas
  • Publisher of Record: Suba Thomas