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  2. Pendulum (mechanics) - Wikipedia

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

    The animations below depict the motion of a simple (frictionless) pendulum with increasing amounts of initial displacement of the bob, or equivalently increasing initial velocity. The small graph above each pendulum is the corresponding phase plane diagram; the horizontal axis is displacement and the vertical axis is velocity. With a large ...

  3. Rayleigh–Lorentz pendulum - Wikipedia

    en.wikipedia.org/wiki/Rayleigh–Lorentz_pendulum

    Rayleigh–Lorentz pendulum (or Lorentz pendulum) is a simple pendulum, but subjected to a slowly varying frequency due to an external action (frequency is varied by varying the pendulum length), named after Lord Rayleigh and Hendrik Lorentz. [1] This problem formed the basis for the concept of adiabatic invariants in mechanics. On account of ...

  4. Holonomic constraints - Wikipedia

    en.wikipedia.org/wiki/Holonomic_constraints

    A simple pendulum. As shown on the right, a simple pendulum is a system composed of a weight and a string. The string is attached at the top end to a pivot and at the bottom end to a weight. Being inextensible, the string’s length is a constant.

  5. Pendulum - Wikipedia

    en.wikipedia.org/wiki/Pendulum

    "Simple gravity pendulum" model assumes no friction or air resistance. A pendulum is a device made of a weight suspended from a pivot so that it can swing freely. [1] 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 toward the equilibrium position.

  6. Inelastic collision - Wikipedia

    en.wikipedia.org/wiki/Inelastic_collision

    Simple ballistic pendulum problems obey the conservation of kinetic energy only when the block swings to its largest angle. In nuclear physics, an inelastic collision is one in which the incoming particle causes the nucleus it strikes to become excited or to break up.

  7. Separatrix (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Separatrix_(mathematics)

    These curves correspond to the pendulum swinging periodically from side to side. If < then the curve is open, and this corresponds to the pendulum forever swinging through complete circles. In this system the separatrix is the curve that corresponds to =. It separates — hence the name — the phase space into two distinct areas, each with a ...

  8. Generalized coordinates - Wikipedia

    en.wikipedia.org/wiki/Generalized_coordinates

    The relationship between the use of generalized coordinates and Cartesian coordinates to characterize the movement of a mechanical system can be illustrated by considering the constrained dynamics of a simple pendulum. [12] [13] A simple pendulum consists of a mass M hanging from a pivot point so that it is constrained to move on a circle of ...

  9. Inverted pendulum - Wikipedia

    en.wikipedia.org/wiki/Inverted_pendulum

    The inverted pendulum is related to rocket or missile guidance, where the center of gravity is located behind the center of drag causing aerodynamic instability. [2] The understanding of a similar problem can be shown by simple robotics in the form of a balancing cart.