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The Atwood machine (or Atwood's machine) was invented in 1784 by the English mathematician George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration. Atwood's machine is a common classroom demonstration used to illustrate principles of classical mechanics .
Motion of Swinging Atwood's Machine for M/m = 4.5. 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.
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.
Phase portrait of a two-well Duffing oscillator (a differential equation, rather than a map) showing chaotic behavior. The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior.
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 ...
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.
Celso Grebogi FRSE (born 1947) is a Brazilian theoretical physicist who works in the area of chaos theory.He is one among the pioneers in the nonlinear and complex systems and chaos theory.
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 ...