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  2. Double pendulum - Wikipedia

    en.wikipedia.org/wiki/Double_pendulum

    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]

  3. Generalized coordinates - Wikipedia

    en.wikipedia.org/wiki/Generalized_coordinates

    A double pendulum. The benefits of generalized coordinates become apparent with the analysis of a double pendulum. For the two masses m i (i = 1, 2), let r i = (x i, y i), i = 1, 2 define their two trajectories. These vectors satisfy the two constraint equations,

  4. Pendulum - Wikipedia

    en.wikipedia.org/wiki/Pendulum

    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. [18]

  5. Pendulum (mechanics) - Wikipedia

    en.wikipedia.org/wiki/Pendulum_(mechanics)

    A pendulum is a body suspended from a fixed support such that it freely swings back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back towards the equilibrium position.

  6. Complex harmonic motion - Wikipedia

    en.wikipedia.org/wiki/Complex_harmonic_motion

    Moreover, a double pendulum may exert motion without the restriction of only a two-dimensional (usually vertical) plane. In other words, the complex pendulum can move to anywhere within the sphere, which has the radius of the total length of the two pendulums. However, for a small angle, the double pendulum can act similarly to the simple ...

  7. Dance eases depression symptoms in Parkinson's patients, new ...

    www.aol.com/news/dance-eases-depression-symptoms...

    A new study found that Parkinson's disease patients who took dance classes experienced fewer symptoms of depression, with dance having "a positive effect on the mood circuits in the brain."

  8. Border leaders say their communities are regaining ‘normalcy ...

    www.aol.com/news/border-leaders-communities...

    Leaders at the southern border tell Fox News Digital that illegal immigrant numbers are down, and their communities are regaining a sense of “normalcy" ahead of President-elect Trump’s ...

  9. Three-body problem - Wikipedia

    en.wikipedia.org/wiki/Three-body_problem

    The mathematical statement of the three-body problem can be given in terms of the Newtonian equations of motion for vector positions = (,,) of three gravitationally interacting bodies with masses :