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A double pendulum consists of two pendulums attached end to end.. In physics and mathematics, in the area of dynamical systems, a double pendulum, also known as a chaotic pendulum, is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. [1]
This space-dependence is called a normal mode. Usually, for problems with continuous dependence on (x, y, z) there is no single or finite number of normal modes, but there are infinitely many normal modes. If the problem is bounded (i.e. it is defined on a finite section of space) there are countably many normal modes (usually numbered n = 1, 2 ...
These normal modes have (slightly) different frequencies because the second involves the (weak) spring while the first does not. The initial state of the two-pendulum system is a combination of both normal modes. Over time, these normal modes drift out of phase, and this is seen as a transfer of motion from the first pendulum to the second.
The concept of a dynamical system has its origins in Newtonian mechanics.There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is an implicit relation that gives the state of the system for only a short time into the future.
Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics.
Years later, Keeler claims Cleary sent her chilling messages on Facebook admitting to the sexual assault. "So I raped you,” Cleary allegedly wrote, per the affidavit.
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(Reuters) -U.S. President-elect Donald Trump said in an interview aired on Sunday he will not try to replace Federal Reserve Chair Jerome Powell upon taking office in January. Trump added that he ...