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Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics. The ideal Atwood machine consists of two objects of mass m 1 and m 2, connected by an inextensible massless string over an ideal massless pulley. [1] Both masses experience uniform acceleration. When m 1 = m 2, the machine is in neutral ...
The swinging Atwood's machine (SAM) is a mechanism that resembles a simple Atwood's machine except that one of the masses is allowed to swing in a two-dimensional plane, producing a dynamical system that is chaotic for some system parameters and initial conditions.
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 equation describing the relative motion is known as the swing equation, which is a non-linear second order differential equation that describes the swing of the rotor of synchronous machine. The power exchange between the mechanical rotor and the electrical grid due to the rotor swing (acceleration and deceleration) is called Inertial ...
George Atwood FRS (c. October 1745 – 11 July 1807) was an English mathematician who invented the Atwood machine for illustrating the effects of Newton's laws of motion. He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor , the leading master of ...
Tinkerbell attractor with a=0.9, b=-0.6013, c=2, d=0.5. Used starting values of = and =.. The Tinkerbell map is a discrete-time dynamical system given by: + = + + + = + + Some commonly used values of a, b, c, and d are
Can someone please expand the section for 'Equation for an Ideal Pulley'? We just went over the Atwood machine in a Lab and also just learned about angular mom./acc./vel. and moment of Inertia and I found this part to be a bit vague. It'd be nice to have how to account for the pulley in the experiment/machine demonstrated.
Analyzing the circuit using Kirchhoff's circuit laws, the dynamics of Chua's circuit can be accurately modeled by means of a system of three nonlinear ordinary differential equations in the variables x(t), y(t), and z(t), which represent the voltages across the capacitors C1 and C2 and the electric current in the inductor L1 respectively. [5]