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T. Gladd", "Subtitle", CellChangeTimes->{{3.691434597547227*^9, 3.691434612619321*^9}}], Cell[TextData[{ StyleBox["Initialization: ", FontWeight->"Bold"], "Be sure the file ", StyleBox["NTGUtilityFunctions.m", FontSlant->"Italic"], " is in the same directory as that from which this notebook was loaded. Then \ execute the cell immediately below by mousing left on the cell bar to the \ right of that cell and then typing \[OpenCurlyDoubleQuote]shift\ \[CloseCurlyDoubleQuote] + \[OpenCurlyDoubleQuote]enter\ \[CloseCurlyDoubleQuote]. Respond \[OpenCurlyDoubleQuote]Yes\ \[CloseCurlyDoubleQuote] in response to the query to evaluate initialization \ cells." }], "Text", CellChangeTimes->{{3.69023148371922*^9, 3.6902314907825966`*^9}, { 3.690231568228395*^9, 3.690231573307065*^9}, {3.690231629378787*^9, 3.6902317034648433`*^9}, {3.6902318285880823`*^9, 3.6902318790622425`*^9}, {3.690561803160874*^9, 3.690561837304328*^9}, 3.6914346883149395`*^9, {3.691434721455573*^9, 3.691434844326234*^9}, { 3.6914349066404066`*^9, 3.6914349142663536`*^9}, {3.691434956254755*^9, 3.6914349884966564`*^9}, {3.7330653691000385`*^9, 3.733065381155084*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"SetDirectory", "[", RowBox[{"NotebookDirectory", "[", "]"}], "]"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{ "set", " ", "directory", " ", "where", " ", "source", " ", "files", " ", "are", " ", "located"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"Get", "[", "\"\\"", "]"}], ";"}], " ", RowBox[{"(*", " ", RowBox[{"Load", " ", "utilities", " ", "package"}], " ", "*)"}]}]}], "Input", InitializationCell->True, CellChangeTimes->{{3.690231304262511*^9, 3.6902313300154333`*^9}, { 3.6902313821303463`*^9, 3.6902313878808374`*^9}, {3.690231423337756*^9, 3.6902314287291145`*^9}, {3.6902315145507984`*^9, 3.6902315306304874`*^9}, {3.6905614204501295`*^9, 3.6905616087617702`*^9}, {3.690561669084352*^9, 3.6905616745378094`*^9}, { 3.690561776716816*^9, 3.6905617961927767`*^9}, 3.6911973050047274`*^9, { 3.733065402347458*^9, 3.733065404123144*^9}, {3.733066601122711*^9, 3.733066602035139*^9}}], Cell[CellGroupData[{ Cell["Background", "Section", CellChangeTimes->{{3.751721279324704*^9, 3.751721283875556*^9}}], Cell[TextData[{ "This is the fourth in a series of Mathematica notebooks on classical \ mechanics. This series was motivated by a close reading and problem solving \ project I undertook in 2014. The focus of my attention was the text ", StyleBox["Introduction to Classical Mechanics with Problems and Solutions", FontWeight->"Bold", FontSlant->"Italic"], ", by David Morin. This is a good book from which to learn and has a great \ collection of problems. I purchased it and recommend that those with \ interests in this topic acquire it for their library. I do note that an \ earlier version can be found on the web. This year, when I returned to this \ project, I decided to focus on generating Mathematica notebooks on material \ covered in ", StyleBox["Chapter 9 Angular Momentum, Part II (General ", FontSlant->"Italic"], Cell[BoxData[ FormBox[ OverscriptBox["L", "\[Rule]"], TraditionalForm]], FontSlant->"Italic"], StyleBox["), ", FontSlant->"Italic"], "which deals the 3-D rigid body dynamics. This topic is notorious \ difficult/confusing for students and I felt I just skimmed by as a graduate \ student. I return in retirement after all these years to pay my dues and \ really understand how to solve problems is this area.\n\nAlthough Morin\ \[CloseCurlyQuote]s Chapter 9 guides these notebooks, I made frequent use of \ other sources such as textbooks available in libraries or on the web. I also \ found lots of video lectures available on YouTube. Confused about some \ physics topics? Google it and you\[CloseCurlyQuote]ll be amazed what you \ find. Some relevant texts are\n\n", StyleBox["Classical Mechanics", FontSlant->"Italic"], ", Hebert Goldstein (my original text at University, late 60s). Newer \ versions exist.\n", StyleBox["Mechanics: Volume1 A Course in Theoretical Physics", FontSlant->"Italic"], ", L. D. Landau and E. M. Lifshitz. \n", StyleBox["Classical Mechanics", FontSlant->"Italic"], ", John. R. Taylor\n", StyleBox["Classical Mechanics of Particles and Systems", FontSlant->"Italic"], ", Stephen T. Thornton, Jerry B. Marion\n", StyleBox["Analytical Mechanics", FontSlant->"Italic"], ", G. R. Fowles, G. L. Cassiday \n", StyleBox["Analytical Mechanics", FontSlant->"Italic"], ", Louis N. Hand, Janet D. Finch\n\nI find Mathematica useful for this \ topic. It facilitates calculations, provides a vehicle for creating \ instructive visualizations and allows one to quickly generate numerical \ solutions. Mathematica is a favorite tool of mine but I think it is crucially \ important to also work with pen and paper. Our brains are closely linked to \ our hands and one thinks differently with a pen in hand than when sitting \ before a computer screen. For serious thoughts on this, read ", StyleBox["The Craftsman", FontSlant->"Italic"], ", by Richard Sennett." }], "Text", CellChangeTimes->{{3.7517212869713*^9, 3.751721405924246*^9}, { 3.7517214427856855`*^9, 3.7517219272682652`*^9}, {3.7517219649225845`*^9, 3.751722083622211*^9}, {3.751722126316057*^9, 3.7517223827474065`*^9}, { 3.751722526024325*^9, 3.751722595896468*^9}, {3.7517226837091446`*^9, 3.751722725475541*^9}, {3.751722829740032*^9, 3.7517228326293473`*^9}, { 3.751722895999816*^9, 3.7517229758483105`*^9}, {3.75172302861619*^9, 3.751723038944604*^9}, {3.7517231106189227`*^9, 3.7517231445811167`*^9}, { 3.751723190547211*^9, 3.7517232594450283`*^9}, {3.7517232899564576`*^9, 3.7517234370102606`*^9}, {3.751723528564426*^9, 3.751723613146309*^9}, { 3.751723674889554*^9, 3.751723695104499*^9}, {3.751723823407473*^9, 3.7517238267505035`*^9}, {3.751723905179801*^9, 3.751723947609353*^9}, { 3.7517239800396757`*^9, 3.7517240207388544`*^9}, {3.7517330770582013`*^9, 3.7517330801897945`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Purpose", "Section", CellChangeTimes->{{3.7452346943250303`*^9, 3.7452346957309575`*^9}}], Cell["\<\ I solve several of Morin\[CloseCurlyQuote]s \[OpenCurlyDoubleQuote]type 2\ \[CloseCurlyDoubleQuote] problems - What is the frequency of rotation of a \ rigid body to which a torque is applied? The specific problems are 1 Morin 9.10 Rotating stick constrained by strings 2 Morin 9.11 Constrained stick driven by rotating ring 3 Morin 9.12 Three approaches to a spherical pendulum 4 Morin 9.13 Ring rolling in a cone \ \>", "Text", CellChangeTimes->{{3.749937010998847*^9, 3.7499370509103785`*^9}, { 3.75173813543465*^9, 3.7517381982170687`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["1 Morin 9.10 Rotating stick constrained by strings", "Section", CellChangeTimes->{{3.7452346943250303`*^9, 3.7452346957309575`*^9}, { 3.749937151926268*^9, 3.749937166591716*^9}, {3.749992867728024*^9, 3.7499928702891326`*^9}, 3.749994493574477*^9, {3.749997108071842*^9, 3.7499971219926195`*^9}, {3.750109343998489*^9, 3.7501093446728315`*^9}}], Cell["\<\ Morin 9.10 is a Type 2 problem as described in Section 9.4.2. 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These quantities do not have an explicit dependence on the angle around the \ ring, so\ \>", "Text", CellChangeTimes->{{3.746711999368437*^9, 3.7467120388501396`*^9}, { 3.7500749280955153`*^9, 3.750074968640107*^9}, {3.75007517229757*^9, 3.750075175385315*^9}}], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[Integral]", "dm"}], " ", "=", " ", RowBox[{ RowBox[{ SubsuperscriptBox["\[Integral]", "0", RowBox[{"2", " ", "\[Pi]"}]], RowBox[{ RowBox[{"(", FractionBox["M", RowBox[{"2", " ", "\[Pi]", " ", "a"}]], ")"}], " ", "a", " ", "d\[Beta]"}]}], " ", "=", " ", "M"}]}], TraditionalForm]], "Input", CellChangeTimes->{{3.7467120458629827`*^9, 3.7467121103236065`*^9}}], Cell["Thus", "Text", CellChangeTimes->{{3.7467121156575108`*^9, 3.746712116247919*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"w4", "[", "2", "]"}], " ", "=", " ", RowBox[{ RowBox[{"\[DoubleStruckCapitalL]", " ", "\[Equal]", " ", RowBox[{ RowBox[{"w4", "[", "1", "]"}], "\[LeftDoubleBracket]", "2", 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