Hiroshi Takano
Publications:
Takano H.
Analyzing the Motion of a Washer on a Rod
2023, vol. 28, no. 2, pp. 227250
Abstract
This paper investigates the dynamics of a toy known as the chatter ring. Specifically,
it examines the mechanism by which the small ring rotates around the large ring, the mechanism
by which the force from the large ring provides torque to the small ring, and whether the motion
of the small ring is the same as that of a hula hoop. The dynamics of a chatter ring has been
investigated in previous work [13–15]; however, a detailed analysis has not yet been performed.
Thus, to understand the mechanisms described above, the equations of motion and constraint
conditions are obtained, and an analysis of the motion is performed. To simplify the problem,
a model consisting of a straight rod and a washer ring is analyzed under the noslip condition.
The motion of a washer has two modes: the one point of contact (1PC) mode and two points
of contact (2PC) mode. The motion of the small ring of the chatter ring is similar to that of a
washer in the 2PC mode, whereas the motion of a hula hoop is similar to that of a washer in
the 1PC mode. The analysis indicates that the motion of a washer with two points of contact
is equivalent to free fall motion. However, in practice, the velocity reaches a constant value
through energy dissipation. The washer rotates around an axis that passes through the two
points of contact. The components of the forces exerted by the rod at the points of contact
that are normal to the plane of the washer provide rotational torque acting at the center of
mass. The components of the forces parallel to the horizontal plane are centripetal forces, which
induce the circular motion of the center of mass.

Takano H.
Spin Reversal of a Rattleback with Viscous Friction
2014, vol. 19, no. 1, pp. 8199
Abstract
An effective equation of motion of a rattleback is obtained from the basic equation of motion with viscous friction depending on slip velocity. This effective equation of motion is used to estimate the number of spin reversals and the rattleback’s shape that causes the maximum number of spin reversals. These estimates are compared with numerical simulations based on the basic equation of motion.
