Search results
Results from the WOW.Com Content Network
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]
Degenerate Double Rotor map: De Jong fractal map [14] discrete: real: 2: 4: Delayed-Logistic system [15] discrete: real: 2: 1: Discretized circular Van der Pol system [16] discrete: real: 2: 1: Euler method approximation to 'circular' Van der Pol-like ODE. Discretized Van der Pol system [17] discrete: real: 2: 2: Euler method approximation to ...
Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics.
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 ...
Orbit diagram for the Hénon map with b=0.3.Higher density (darker) indicates increased probability of the variable x acquiring that value for the given value of a.Notice the satellite regions of chaos and periodicity around a=1.075-- these can arise depending upon initial conditions for x and y.
Gingerbreadman map for subset , [,]: the color of each point is related to the relative orbit period.To view the gingerbread man, you must rotate the image 135 degrees clockwise.
To see how this number arises, consider the real one-parameter map =.Here a is the bifurcation parameter, x is the variable. The values of a for which the period doubles (e.g. the largest value for a with no period-2 orbit, or the largest a with no period-4 orbit), are a 1, a 2 etc.
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 ...