Odd sympathy
Encyclopedia
The phrase odd sympathy (the actual phrase was odd kind of sympathy) appears in the record of a letter by Dutch
mathematician
and physicist
Christiaan Huygens (1629–95) to Sir Robert Moray as presented to the Royal Society of London, relating to the tendency of two pendulum clocks to synchronize with opposite phases when suspended side by side. Huygens
, credited with being the inventor of the pendulum clock
, first noticed the effect while lying in bed. His two pendulum clocks, mounted together, would end up swinging in exactly opposite directions, regardless of their respective individual initial motions. This was one of the first observations of the phenomenon of mode locking in coupled driven oscillators, which has many applications in physics.
Huygens originally believed the synchronization was due to air currents shared between the two pendulums, but he dismissed the hypothesis himself after several tests. Huygens would later attribute sympathetic motion of pendulums to imperceptible movement in the beam from which both pendulums are suspended. This idea was later validated by researchers from the Georgia Institute of Technology
who tested Huygens' idea.
Using instruments capable of registering movement too small to have been measured in Huygens' time, the Georgia Tech researchers chronicled the nature of the forces at work on the supporting beam. They found that if the pendulums are moving in the same direction, together they tend to move the beam the opposite direction, giving rise to forces that resist motion in the same direction. If however, the pendulums are moving in opposite directions, these forces cancel each other out, causing the beam to remain nearly motionless. Thus, motion, in this example, tends to be perfectly asynchronous.
Huygens
only observed anti-phase synchronization of pendulum clocks. Bennett and co-workers reported both anti-phase and in-phase synchronization of their clocks as well as "death" states wherein one or both of the clocks stops. Synchronization of driven oscillators is also discussed in books written by I.I. Blekhman, and by Pikovsky and co-workers. A detailed analysis was provided by Fradkov and Andrievsky from Russia in 2007 regarding the conditions for in-phase or anti-phase synchronization of a 2-pendulum system.
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
Christiaan Huygens (1629–95) to Sir Robert Moray as presented to the Royal Society of London, relating to the tendency of two pendulum clocks to synchronize with opposite phases when suspended side by side. Huygens
Huygens
Huygens is a Dutch patronymic surname, meaning "son of Hugo". People with the name Huygens include:People* Constantijn Huygens , Dutch poet and composer...
, credited with being the inventor of the pendulum clock
Pendulum clock
A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is a resonant device; it swings back and forth in a precise time interval dependent on its length, and resists swinging at other rates...
, first noticed the effect while lying in bed. His two pendulum clocks, mounted together, would end up swinging in exactly opposite directions, regardless of their respective individual initial motions. This was one of the first observations of the phenomenon of mode locking in coupled driven oscillators, which has many applications in physics.
Huygens originally believed the synchronization was due to air currents shared between the two pendulums, but he dismissed the hypothesis himself after several tests. Huygens would later attribute sympathetic motion of pendulums to imperceptible movement in the beam from which both pendulums are suspended. This idea was later validated by researchers from the Georgia Institute of Technology
Georgia Institute of Technology
The Georgia Institute of Technology is a public research university in Atlanta, Georgia, in the United States...
who tested Huygens' idea.
Using instruments capable of registering movement too small to have been measured in Huygens' time, the Georgia Tech researchers chronicled the nature of the forces at work on the supporting beam. They found that if the pendulums are moving in the same direction, together they tend to move the beam the opposite direction, giving rise to forces that resist motion in the same direction. If however, the pendulums are moving in opposite directions, these forces cancel each other out, causing the beam to remain nearly motionless. Thus, motion, in this example, tends to be perfectly asynchronous.
Huygens
Huygens
Huygens is a Dutch patronymic surname, meaning "son of Hugo". People with the name Huygens include:People* Constantijn Huygens , Dutch poet and composer...
only observed anti-phase synchronization of pendulum clocks. Bennett and co-workers reported both anti-phase and in-phase synchronization of their clocks as well as "death" states wherein one or both of the clocks stops. Synchronization of driven oscillators is also discussed in books written by I.I. Blekhman, and by Pikovsky and co-workers. A detailed analysis was provided by Fradkov and Andrievsky from Russia in 2007 regarding the conditions for in-phase or anti-phase synchronization of a 2-pendulum system.