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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Analyzing the Motion of a Washer on a Rod
Hiroshi Takano Educational Studies on Global-ICT-Teaching and Learning,
Joetsu University of Education,
Yamayashiki, Joetsu, 943-8512 Niigata, Japan
Аннотация:
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 no-slip 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.
Ключевые слова:
rigid body, chatterring, jitter ring, hula hoop, washer, rod, numerical simulation.
Поступила в редакцию: 03.08.2022 Принята в печать: 11.03.2023
Образец цитирования:
Hiroshi Takano, “Analyzing the Motion of a Washer on a Rod”, Regul. Chaotic Dyn., 28:2 (2023), 227–250
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1203 https://www.mathnet.ru/rus/rcd/v28/i2/p227
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