![]() We define a function, poincare, which produces a Poincaré section for given values of A, γ, and ω, in which the first ndrop periods are assumed to be initial transient and so are not plotted, while the subsequent ndrop eriods are plotted. Clearly for a periodic orbit the Poincaré section is a single point, when the period has doubled it consists of two points, and so on. Phase space points of the particle at every period of the driving force, i.e. Phase space trajectory for all times, which gives a continuous curve, the Poincaré section is just the discrete set of Introduction to Linear Algebra with Mathematica Glossaryįinally, we present animation of periodic change the velocity versusĭisplacement of the chaotic attractor of the Duffing oscillator forĪ useful way of analyzing chaotic motion is to look at what is called the Poincaré section. Return to Part III of the course APMA0340 Return to the main page for the second course APMA0340 Return to the main page for the first course APMA0330 Return to Mathematica tutorial for the second course APMA0340 Return to Mathematica tutorial for the first course APMA0330 Return to computing page for the second course APMA0340 Return to computing page for the first course APMA0330 Laplace equation in spherical coordinates.Numerical solutions of Laplace equation.Laplace equation in infinite semi-stripe.Boundary Value Problems for heat equation.Part VI: Partial Differential Equations.Part III: Non-linear Systems of Ordinary Differential Equations.Part II: Linear Systems of Ordinary Differential Equations. ![]()
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