Hi,

While going through the Wolfram Demonstration Project site, I came across an animation of a Trebuchet, http://demonstrations.wolfram.com/OptimizingTheCounterweightTrebuchet/.

I was wondering if it is possible to animate the Trebuchet in such a way that the projectile of the trebuchet actually leaves the sling and makes impact against a wall at a certain distance say x='some constant'.

Thanks

Hi David,

Is there any way to animate a 2-D body like a rectangle or a square that follows the same motion as the ball above for 5 bounces using elastic impacts so that the height of the bounce is equal everytime?

Thanks.

How do I do it similarly for a ball hitting the floor at y=0?

You just need kinematics for this. May be something like this? (this was for a HW assignment, so code is not very clean. Did it in about 3 hrs). Most of the code deal with handling the state of the running simulation (reset, stop, step, etc...) if you do not care about all of this, you can remove all that and the code will shrink to 10% of its current size.

Manipulate[
 tick;
 h = 1;
 g = 9.8;
 If[(statex == "RUN" || statex == "STEP") && statex2 == "",
  If[state == "down",
   delS = currentV*delT + 1/2 g delT^2;
   currentV += g *delT;
   currentH -= delS
   ,
   delS = currentV*delT - 1/2 g delT^2;
   currentV -= g *delT;
   currentH += delS
   ];
  distantTravelled += delS
  ];

 gr = Graphics[
   {
    Line[{{-.3, -r/2}, {.3, -r/2}}],
    (*{LightGray,Dashed,Line[{{0,0},{0,1}}]},*)
    {Red, Disk[{0, currentH}, r]}
    },
   PlotRange -> {{-.3, .3}, {-4 r, 1 + 4 r}}, Axes -> {False, True}, 
   ImageSize -> {300, 300}];
  gr = Grid[{
    {Grid[{
       {"height", "speed", "cycle #", "\[CapitalDelta]s", "direction"},
       {padIt2[currentH, {3, 2}], padIt2[currentV, {4, 3}], padIt2[n, {1}], 
        padIt2[delS, {4, 3}], state}
       }, Frame -> All]
     },
    {Grid[
      {
       {Column[{"Theoretical", "total time"}], Column[{"Current", "time"}], 
        Column[{"Theoretical", Column[{"total", "distant"}]}], 
        Column[{"current", "distance"}]},
       {padIt2[tTime, {6, 3}], padIt2[currentT, {6, 3}],
         padIt2[tDistance, {3, 2}], padIt2[totalDist, {6, 3}]
        }
       }, Frame -> All
      ]
     },

    {gr, SpanFromLeft}}];

 If[statex2 == "pass",
  statex2 = ""
  ,
  currentT += delT;
  totalDist += delS;
  If[Abs@distantTravelled >= maxH,
   distantTravelled = 0;

   If[state == "down",
    currentV = e*currentV;
    state = "up";
    n = n + 1;
    maxH = e^(2*n)*h;
    currentH = 0
    ,
    state = "down";
    currentV = 0;
    currentH = maxH
    ]
   ]
  ];

 If[statex == "RUN" && currentT < tTime,
  tick = Not[tick]
  ];
 gr,
 {{tick, False}, None},
 Text@Grid[{
    {Grid[{
       {Button[Text@Style["run", 12], {statex = "RUN"; tick = Not[tick]}, 
         ImageSize -> {50, 40}],
        Button[Text@Style["step", 12], {statex = "STEP"; tick = Not[tick]}, 
         ImageSize -> {50, 40}],
        Button[Text@Style["stop", 12], {statex = "STOP"; tick = Not[tick]}, 
         ImageSize -> {50, 40}],
        Button[
         Text@Style["reset", 12], {statex = "STEP"; currentH = 1; 
          currentT = 0; n = 0;
          distantTravelled = 0; currentV = 0; maxH = 1; state = "down"; 
          totalDist = 0; statex2 = "";
          tDistance = If[e == 1, Infinity, (1 + e^2)/(1 - e^2)];
          tTime = If[e == 1, Infinity, Sqrt[2/9.81]*((1 + e)/(1 - e))];
          tick = Not[tick]}, ImageSize -> {50, 40}]}
       }, Frame -> True, FrameStyle -> Gray
      ], SpanFromLeft},
    {Grid[{

       {"Coefficient of restitution",
        Manipulator[Dynamic[e, {e = #;
            statex = "STEP";
            currentH = 1;
            currentT = 0; n = 0;
            distantTravelled = 0;
            currentV = 0;
            maxH = 1;
            state = "down";
            totalDist = 0;
            tDistance = If[e == 1, Infinity, (1 + e^2)/(1 - e^2)];
            tTime = If[e == 1, Infinity, Sqrt[2/9.81]*((1 + e)/(1 - e))];
            tick = Not[tick];
            statex2 = "pass"} &], {0, 1, .01}, ImageSize -> Tiny], 
        Dynamic[padIt2[e, {2, 2}]],
        SpanFromLeft},

       {"Animation speed",
        Manipulator[Dynamic[delT, {delT = #} &], {0.001, 0.03, 0.001}, 
         ImageSize -> Tiny], Dynamic[padIt2[delT, {3, 3}]],
        SpanFromLeft},

       {"ball size",
        Manipulator[
         Dynamic[r, {r = #; tick = Not[tick], statex2 = "pass"} &], {0.01, 
          0.1, 0.001}, ImageSize -> Tiny], Dynamic[padIt2[r, {3, 3}]],
        SpanFromLeft}

       }, Alignment -> Left, Frame -> True, FrameStyle -> Gray]
     }}],
 {{n, 0}, None},
 {{currentH, 1}, None},
 {{currentT, 0}, None},
 {{state, "down"}, None},
 {{statex, "STEP"}, None},
 {{statex2, ""}, None},
 {{distantTravelled, 0}, None},
 {{currentV, 0}, None},
 {{maxH, 1}, None},
 {{gr, 0}, None},
 {{e, .9}, None},
 {{delT, 0.02}, None},
 {{r, 0.04}, None},
 {{totalDist, 0}, None},
 {{tDistance, (1 + (.9)^2)/(1 - (.9)^2)}, None},
 {{tTime, Sqrt[2/9.81]*((1 + .9)/(1 - .9))}, None},
 TrackedSymbols :> {tick},
 Alignment -> Center,
 SynchronousUpdating -> True,
 SynchronousInitialization -> True,
 FrameMargins -> 1,
 ImageMargins -> 1,
 ControlPlacement -> Left,
 Initialization :>
  {
   padIt1[v_, f_List] := 
    AccountingForm[Chop[v], f, NumberSigns -> {"-", "+"}, 
     NumberPadding -> {"0", "0"}, SignPadding -> True];
   padIt2[v_, f_List] := 
    AccountingForm[Chop[v], f, NumberSigns -> {"", ""}, 
     NumberPadding -> {"0", "0"}, SignPadding -> True]
   }
 ]