Considering a nonlinear dynamic oscillator a high Lyapunov exponent indicates a high degree of randomness useful in many applications including cryptography Most existing oscillators yield very low Lyapunov exponents The proposed work presents a general strategy to derive an n D hyperchaotic map with a high Lyapunov exponent A 2D case study was analyzed using some well known nonlinear
Get PriceMay 18 2022James Meiss 2024 Scholarpedia 2 8 1943 A dynamical system of first order ordinary differential equations is an degree of freedom Hamiltonian system when it is nonautonomous it has Here is the Hamiltonian a smooth scalar function of the extended phase space variables and time the matrix is the Poisson matrix and
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Get Pricethe pendulum about an axis through then the moment of inertia I about a parallel axis at a distance l from is given by I=IG MI2 =Mk2 MI2 where k is the radius of gyration of the pendulum about the axis through Using Equation 2 in Equation 1 we get T =2 M k 2 M l2
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Get PriceA rigid body with distributed mass able to freely pivot about a horizontal axis which does not coincide with the center of gravity is called a compound pendulum The compound pendulum is an interesting example of a pendulum that undergoes simple harmonic Kater s pendulum It is a compound pendulum constructed on the principle that centre of
Get Pricecauses the pendulum to move faster Put the values in a spread sheet and you ll see the effect If the rotational inertial mass of the upper bob dominates the lower bob will increase the rate until it becomes the dominate mass because of its distance squared from the pivot point It is much easier to use a smaller mass higher up and
Get PriceTo me a compound pendulum can be considered as a general pendulum as compared to a simple pendulum The angular frequency of both pendulums can be expressed as where is the distance from the pivot to the center of mass and is the moment of inertia For a simple pendulum becomes when the bob has most of the mass in this setup
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Get PriceKater s pendulum stopwatch meter scale and knife edges Theory Kater s pendulum shown in Fig 1 is a physical pendulum composed of a metal rod m in length upon which are mounted a sliding metal weight W 1 a sliding wooden weight W 2 a small sliding metal cylinder w and two sliding knife edges K 1 and K 2 that face each other
Get PriceLets make a cartesian plane with origin in the base of the pendulum We can see the [math]x [/math] coordinate will be [math]x = lsintheta [/math] while [math]y = lcostheta [/math] The velocity in each coordinate will be the derivatives of the coordinates then [math]V x = dfra [/math] Continue Reading 5 Mark Barton
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