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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]
Pendulum. Inverted pendulum; Double pendulum; Foucault pendulum; Spherical pendulum; Kinematics; Equation of motion; Dynamics (mechanics) Classical mechanics; Isolated physical system. Lagrangian mechanics; Hamiltonian mechanics; Routhian mechanics; Hamilton-Jacobi theory; Appell's equation of motion; Udwadia–Kalaba equation; Celestial ...
An example of a generalized coordinate would be to describe the position of a pendulum using the angle of the pendulum relative to vertical, rather than by the x and y position of the pendulum. Although there may be many possible choices for generalized coordinates for a physical system, they are generally selected to simplify calculations ...
The swinging Atwood's machine is a system with two degrees of freedom. We may derive its equations of motion using either Hamiltonian mechanics or Lagrangian mechanics. Let the swinging mass be and the non-swinging mass be . The kinetic energy of the system, , is:
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
The simplest kind of an orbit is a fixed point, or an equilibrium. If a mechanical system is in a stable equilibrium state then a small push will result in a localized motion, for example, small oscillations as in the case of a pendulum. In a system with damping, a stable equilibrium state is moreover asymptotically stable. On the other hand ...
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.
In physics and mathematics, in the area of dynamical systems, an elastic pendulum [1] [2] (also called spring pendulum [3] [4] or swinging spring) is a physical system where a piece of mass is connected to a spring so that the resulting motion contains elements of both a simple pendulum and a one-dimensional spring-mass system. [2]