148 lines
		
	
	
		
			4.0 KiB
		
	
	
	
		
			Mathematica
		
	
	
			
		
		
	
	
			148 lines
		
	
	
		
			4.0 KiB
		
	
	
	
		
			Mathematica
		
	
	
| (* Content-type: application/vnd.wolfram.mathematica *)
 | |
| 
 | |
| (*** Wolfram Notebook File ***)
 | |
| (* http://www.wolfram.com/nb *)
 | |
| 
 | |
| (* CreatedBy='Mathematica 8.0' *)
 | |
| 
 | |
| (*CacheID: 234*)
 | |
| (* Internal cache information:
 | |
| NotebookFileLineBreakTest
 | |
| NotebookFileLineBreakTest
 | |
| NotebookDataPosition[       157,          7]
 | |
| NotebookDataLength[      3876,        137]
 | |
| NotebookOptionsPosition[      3514,        119]
 | |
| NotebookOutlinePosition[      3867,        135]
 | |
| CellTagsIndexPosition[      3824,        132]
 | |
| WindowFrame->Normal*)
 | |
| 
 | |
| (* Beginning of Notebook Content *)
 | |
| Notebook[{
 | |
| Cell[BoxData[{
 | |
|  RowBox[{
 | |
|   RowBox[{"roll", "=", 
 | |
|    RowBox[{"ArcTan", "[", 
 | |
|     RowBox[{"g3", ",", "g2"}], "]"}]}], ";"}], "\n", 
 | |
|  RowBox[{
 | |
|   RowBox[{"pitch", "=", 
 | |
|    RowBox[{"ArcTan", "[", 
 | |
|     RowBox[{
 | |
|      RowBox[{"-", "g1"}], ",", 
 | |
|      SqrtBox[
 | |
|       RowBox[{
 | |
|        SuperscriptBox["g2", "2"], "+", 
 | |
|        SuperscriptBox["g3", "2"]}]]}], "]"}]}], ";"}], "\n"}], "Input",
 | |
|  CellChangeTimes->{{3.535838264320565*^9, 3.535838380686434*^9}, {
 | |
|   3.53583852660116*^9, 3.5358385374458313`*^9}, {3.5358391717151127`*^9, 
 | |
|   3.535839173489215*^9}}],
 | |
| 
 | |
| Cell[CellGroupData[{
 | |
| 
 | |
| Cell[BoxData[
 | |
|  RowBox[{
 | |
|   RowBox[{"(", "\[NoBreak]", GridBox[{
 | |
|      {
 | |
|       RowBox[{"D", "[", 
 | |
|        RowBox[{"roll", ",", "g1"}], "]"}], 
 | |
|       RowBox[{"D", "[", 
 | |
|        RowBox[{"roll", ",", "g2"}], "]"}], 
 | |
|       RowBox[{"D", "[", 
 | |
|        RowBox[{"roll", ",", "g3"}], "]"}]},
 | |
|      {
 | |
|       RowBox[{"D", "[", 
 | |
|        RowBox[{"pitch", ",", "g1"}], "]"}], 
 | |
|       RowBox[{"D", "[", 
 | |
|        RowBox[{"pitch", ",", "g2"}], "]"}], 
 | |
|       RowBox[{"D", "[", 
 | |
|        RowBox[{"pitch", ",", "g3"}], "]"}]},
 | |
|      {"0", "0", "0"}
 | |
|     }], "\[NoBreak]", ")"}], "//", "FullSimplify"}]], "Input",
 | |
|  CellChangeTimes->{{3.535838384786139*^9, 3.535838492987266*^9}, {
 | |
|   3.535838580947555*^9, 3.535838595178028*^9}}],
 | |
| 
 | |
| Cell[BoxData[
 | |
|  RowBox[{"{", 
 | |
|   RowBox[{
 | |
|    RowBox[{"{", 
 | |
|     RowBox[{"0", ",", 
 | |
|      FractionBox["g3", 
 | |
|       RowBox[{
 | |
|        SuperscriptBox["g2", "2"], "+", 
 | |
|        SuperscriptBox["g3", "2"]}]], ",", 
 | |
|      RowBox[{"-", 
 | |
|       FractionBox["g2", 
 | |
|        RowBox[{
 | |
|         SuperscriptBox["g2", "2"], "+", 
 | |
|         SuperscriptBox["g3", "2"]}]]}]}], "}"}], ",", 
 | |
|    RowBox[{"{", 
 | |
|     RowBox[{
 | |
|      FractionBox[
 | |
|       SqrtBox[
 | |
|        RowBox[{
 | |
|         SuperscriptBox["g2", "2"], "+", 
 | |
|         SuperscriptBox["g3", "2"]}]], 
 | |
|       RowBox[{
 | |
|        SuperscriptBox["g1", "2"], "+", 
 | |
|        SuperscriptBox["g2", "2"], "+", 
 | |
|        SuperscriptBox["g3", "2"]}]], ",", 
 | |
|      RowBox[{"-", 
 | |
|       FractionBox[
 | |
|        RowBox[{"g1", " ", "g2"}], 
 | |
|        RowBox[{
 | |
|         SqrtBox[
 | |
|          RowBox[{
 | |
|           SuperscriptBox["g2", "2"], "+", 
 | |
|           SuperscriptBox["g3", "2"]}]], " ", 
 | |
|         RowBox[{"(", 
 | |
|          RowBox[{
 | |
|           SuperscriptBox["g1", "2"], "+", 
 | |
|           SuperscriptBox["g2", "2"], "+", 
 | |
|           SuperscriptBox["g3", "2"]}], ")"}]}]]}], ",", 
 | |
|      RowBox[{"-", 
 | |
|       FractionBox[
 | |
|        RowBox[{"g1", " ", "g3"}], 
 | |
|        RowBox[{
 | |
|         SqrtBox[
 | |
|          RowBox[{
 | |
|           SuperscriptBox["g2", "2"], "+", 
 | |
|           SuperscriptBox["g3", "2"]}]], " ", 
 | |
|         RowBox[{"(", 
 | |
|          RowBox[{
 | |
|           SuperscriptBox["g1", "2"], "+", 
 | |
|           SuperscriptBox["g2", "2"], "+", 
 | |
|           SuperscriptBox["g3", "2"]}], ")"}]}]]}]}], "}"}], ",", 
 | |
|    RowBox[{"{", 
 | |
|     RowBox[{"0", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output",
 | |
|  CellChangeTimes->{{3.5358383879873047`*^9, 3.535838493685678*^9}, 
 | |
|    3.53583853974876*^9, {3.535838581771779*^9, 3.535838595765464*^9}}]
 | |
| }, Open  ]]
 | |
| },
 | |
| WindowSize->{740, 752},
 | |
| WindowMargins->{{4, Automatic}, {Automatic, 4}},
 | |
| FrontEndVersion->"8.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (October 5, \
 | |
| 2011)",
 | |
| StyleDefinitions->"Default.nb"
 | |
| ]
 | |
| (* End of Notebook Content *)
 | |
| 
 | |
| (* Internal cache information *)
 | |
| (*CellTagsOutline
 | |
| CellTagsIndex->{}
 | |
| *)
 | |
| (*CellTagsIndex
 | |
| CellTagsIndex->{}
 | |
| *)
 | |
| (*NotebookFileOutline
 | |
| Notebook[{
 | |
| Cell[557, 20, 544, 16, 75, "Input"],
 | |
| Cell[CellGroupData[{
 | |
| Cell[1126, 40, 692, 20, 61, "Input"],
 | |
| Cell[1821, 62, 1677, 54, 109, "Output"]
 | |
| }, Open  ]]
 | |
| }
 | |
| ]
 | |
| *)
 | |
| 
 | |
| (* End of internal cache information *)
 | |
| 
 |