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with Discontinuities", "Title", CellMargins->0, CellFrameMargins->{{60, 9}, {9, 12}}, CellChangeTimes->{{3.3992364245*^9, 3.3992364675625*^9}}, FontColor->GrayLevel[1], Background->GrayLevel[0]], Cell["Rob Knapp", "Author", CellChangeTimes->{{3.39923654371875*^9, 3.399236546078125*^9}}], Cell["Wolfram Research, Inc.", "Affiliation", CellChangeTimes->{{3.399236549515625*^9, 3.399236553203125*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Introduction", FontColor->RGBColor[0., 0.254032196536202, 0.7862973983367666]]], "Section", CellChangeTimes->{{3.400241122296875*^9, 3.400241124953125*^9}}], Cell["\<\ The methods for NDSolve typically assume some level of smoothness of the \ right hand side of the differential quations. When this assumption is \ violated, the methods can be inefficient, or even give very inaccurate \ results.\ \>", "Text", CellChangeTimes->{{3.40024114790625*^9, 3.400241198828125*^9}, { 3.400247008859375*^9, 3.400247073359375*^9}}], Cell["\<\ A method for handling discontinuities by treating them as events is currently \ under development. The method is designed to use symbolic analysis to \ automatically detect both impulse (DiracDelta) and jump discontinuities in \ the differential equation. In this presentation, I will show you several \ examples of the new method at work.\ \>", "Text", CellChangeTimes->{{3.40024114790625*^9, 3.400241198828125*^9}, { 3.400247008859375*^9, 3.400247073359375*^9}, {3.400247195203125*^9, 3.400247370359375*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[StyleBox["Stick-slip Example", FontColor->RGBColor[ 0.9584954604409858, 0.7702754253452354, 0.16601815823605706`]]], "Subsection", CellChangeTimes->{{3.399373747046875*^9, 3.399373749109375*^9}, { 3.400416136109375*^9, 3.40041613721875*^9}}], Cell[TextData[{ "Drag a block (position ", Cell[BoxData[ FormBox[ RowBox[{"x", "(", "t", ")"}], TraditionalForm]]], ") across a surface by moving the anchor point of a spring (position ", Cell[BoxData[ FormBox[ RowBox[{"a", "(", "t", ")"}], TraditionalForm]]], ").\nAssume that static friction is exceeds the sliding friction at low \ velocities." }], "Text", CellChangeTimes->{{3.400005741765625*^9, 3.400005917734375*^9}, { 3.400006190453125*^9, 3.40000619809375*^9}, 3.400247431328125*^9}], Cell["\<\ Starting from rest, initially the block will remain stuck until the force \ from the spring is sufficient to break the static friction, at which point it \ begins to slip.\ \>", "Text", CellChangeTimes->{{3.400005922421875*^9, 3.400006040265625*^9}, { 3.40000607259375*^9, 3.4000061448125*^9}, 3.40024746953125*^9}], Cell["\<\ If the movement of the spring anchor is slow enough, the action of the spring \ will be such that the velocity is zero again at some point. 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