Graph y = x
3/3 - x
2/2
Imagine a small circle sitting inside the local minimum. Gravity pulls in the negative y direction so it is quite stable there.
Now increase the size of the circle. At some point it will become too large to fit in this hollow and will be forced to roll away down into the third quadrant.
At what radius does this happen?
(In reply to
An approximate look by graphing by Charlie)
Using (in the final stage of refinement)
For r = 2.5281618 To 2.5281619 Step 0.0000000001
x = 2.3
diff = r - Sqr(r * r - x * x) - (x * x * x / 3 - x * x / 2)
For x = 2.429 To 2.44 Step 0.0000001
prev = diff
If r * r > x * x Then
diff = r - Sqr(r * r - x * x) - (x * x * x / 3 - x * x / 2)
If diff * prev <= 0 Then Text1.Text = Text1.Text & r & " " & Str(prev) & " " & Str(diff) & " " & Str(x) & crlf
End If
DoEvents
Next x
Next r
the radius is narrowed down to about
2.528161852
based on where the program starts finding intersections of the two curves.
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Posted by Charlie
on 2018-08-15 12:40:11 |
re: An approximate look by graphing
