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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 ...
The difficulty of this problem arises from the functional fixedness of the box, which originally contained thumb-tacks. It is a container in the problem situation but must be used as a shelf in the solution situation. Other examples for this type of mental restructuring are: an electromagnet must be used as part of a pendulum
A classic example along these lines is the inverted pendulum. [42] Other examples are vibrations of a string with periodically varying tension [41] stability of railroad rails as trains drive over them; seasonally forced population dynamics; the phenomenon of parametric resonance in forced oscillators; motion of ions in a quadrupole ion trap [43]
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.
Since the system is invariant under time reversal and translation, it is equivalent to say that the pendulum starts at the origin and is fired outwards: [1] r ( 0 ) = 0 {\displaystyle r(0)=0} The region close to the pivot is singular, since r {\displaystyle r} is close to zero and the equations of motion require dividing by r {\displaystyle r} .
Spherical pendulum: angles and velocities. In physics, a spherical pendulum is a higher dimensional analogue of the pendulum. It consists of a mass m moving without friction on the surface of a sphere. The only forces acting on the mass are the reaction from the sphere and gravity.
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details
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]