Re: About the error message Indeterminate

*To*: mathgroup at smc.vnet.net*Subject*: [mg91375] Re: About the error message Indeterminate*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Tue, 19 Aug 2008 07:14:06 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <g88v76$guj$1@smc.vnet.net>

MarvelousTau wrote: > I think you all might have been check the example the bouncer in the > entry Dynamic. But it is on a flat ground. So I want to make some > change to let it bounce on hills, which formed by Sine function. The > collisional consummation and reflection angle have been taken > considered, but when the point touches the ground, it doesn't move any > longer and the velocity shows indeterminate. I know indeterminate > means such an issue like 0/0, but I replace my reflecting function > with the colliding position and get a certain answer. I don't know if > is there any other issues will cause indeterminate. > > Anyway, check the code first. > > function[x_] := Sin[x] + 0.5 Sin[6 x]; > Reflection[{{x_, y_}, {vx_, vy_}}] := {{x, y}, > 0.8 Sqrt[vx^2 + vy^2] {Cos[2 ArcTan[function'[x]] - ArcTan[vy/vx]], > Sin[2 ArcTan[function'[x]] - ArcTan[vy/vx]]}} > > (* where function[] means the ground and Reflection[] shows how the > ball bounces up, where x, y means position and vx, vy means velocity. > 0.8 Is the consummation of collision, Sqrt is the norm of speed and > the latter stuff is the new velocity in x and y direction. *) > > PointSet = {{4, 6}, {0, -0.01}}; > Plot[function[x], {x, -5, 5}, Axes -> None, Filling -> Bottom, > PlotRange -> {{-5, 5}, {-2, 8}}, AspectRatio -> 1, > Epilog -> > Point[Dynamic[ > PointSet = > If[PointSet[[1, 2]] >= > function[PointSet[[1, 1]]], {PointSet[[1]] + PointSet[[2]], > PointSet[[2]] + {0, -0.001}}, Reflection[PointSet]]; > PointSet[[1]]]]] > Dynamic[PointSet] > > (*I used Epilog to draw the point. I didn't use Mouseclick because it > will cause a dump*) The function ArcTan[] has two forms: ArcTan[y/x], which does not trap division by zero or indeterminate forms, and ArcTan[x, y], which does handle such cases. Note that the second form may return an *Interval[]* object rather than a value. In[1]:= {ArcTan[y/x], ArcTan[x, y]} /. {x -> 0, y -> 0} During evaluation of In[1]:= Power::infy:Infinite expression 1/0 encountered. During evaluation of In[1]:= \[Infinity]::indet:Indeterminate expression 0 ComplexInfinity encountered. During evaluation of In[1]:= ArcTan::indet:Indeterminate expression ArcTan[0,0] encountered. Out[1]= {Indeterminate, Interval[{-Pi, Pi}]} In[2]:= {ArcTan[y/x], ArcTan[x, y]} /. {x -> 0, y -> 1} During evaluation of In[2]:= Power::infy:Infinite expression 1/0 encountered. Out[2]= {Indeterminate, Pi/2} So you could write your function as follows: In[1]:= function[x_] := Sin[x] + 0.5 Sin[6 x]; Reflection[{{x_, y_}, {vx_, vy_}}] := {{x, y}, 0.8 Sqrt[vx^2 + vy^2] {Cos[2 ArcTan[function'[x]] - ArcTan[vx, vy]], Sin[2 ArcTan[function'[x]] - ArcTan[vx, vy]]}} PointSet = {{4, 6}, {0, -0.01}}; Plot[function[x], {x, -5, 5}, Axes -> None, Filling -> Bottom, PlotRange -> {{-5, 5}, {-2, 8}}, AspectRatio -> 1, Epilog -> Point[Dynamic[ PointSet = If[PointSet[[1, 2]] >= function[PointSet[[1, 1]]], {PointSet[[1]] + PointSet[[2]], PointSet[[2]] + {0, -0.001}}, Reflection[PointSet]]; PointSet[[1]]]]] Dynamic[PointSet] Regards, -- Jean-Marc