John,

Thanks for the nice explanation and drawing.  You are correct about the =
lengthening effect.
http://jjlahr.com/science/psn/pivots

To further the discussion, would not the center of rotation move from =
the contact point at no displacement to a point behind the plane and in =
the direction of travel as the boom is displaced rather than be =
considered a lengthening of the boom on the boom side?  The radius to =
any point from the center of rotation must be perpendicular to the =
velocity of the point.  Thus the center of the pivot ball to the contact =
point will define one line and a line perpendicular to the now flatter =
motion of the mass on the end define a second line.  When the system is =
rotated to the horizontal, the movement of the center away from the mass =
to a point behind the support will also tilt the axis of rotation =
between the pivots to a more stable direction. =20

As you say, the upper pivot would best be designed to accomodate axis =
change.  In the arrangements I have seen in PSN, the upper ball is on =
the opposite side of a support so as to be in compression.  Therefore =
the rolling would now move the center of rotation in the upper pivot =
toward the mass with an end result of the new axis tilting the boom down =
to a shorter period.  A ball style support will require a good bit more =
engineering than just using a conveniently sized ball.  Do the =
proponents have anything to offer regarding design?

Randy








John,
 
Thanks for the nice explanation and =
drawing. =20
You are correct about the lengthening effect.

http://jjlahr.com/science/p=
sn/pivots
 
To further the discussion, would not the center of rotation move =
from the=20
contact point at no displacement to a point behind the plane and in the=20
direction of travel as the boom is displaced rather than be considered a =

lengthening of the boom on the boom side?  The radius to any point =
from the=20
center of rotation must be perpendicular to the velocity of the=20
point.  Thus the center of the pivot ball to the contact point will =
define=20
one line and a line perpendicular to the now flatter motion of the mass =
on the=20
end define a second line.  When the system is rotated to the =
horizontal,=20
the movement of the center away from the mass to a point behind the =
support will=20
also tilt the axis of rotation between the pivots to a more stable=20
direction.  
 
As you say, the upper pivot would best be designed =
to=20
accomodate axis change.  In the arrangements I have seen in =
PSN, the=20
upper ball is on the opposite side of a support so as to be in=20
compression.  Therefore the rolling would now move the center of=20
rotation in the upper pivot toward the mass with an end result of =
the new=20
axis tilting the boom down to a shorter period.  A ball style =
support will=20
require a good bit more engineering than just using a conveniently sized =

ball.  Do the proponents have anything to offer regarding =
design?
 
Randy