Long Write
نویسندگان
چکیده
A set of Maplev R.3 software routines, for plotting 2D/3D projections of Poincar e surfaces-of-section of Hamiltonian dynamical systems, is presented. The package consists of a plotting-command plus a set of facility-commands for a quick setup of the Hamilton equations of motion, initial conditions for numerical experiments, and for the zooming of plots. Memory required to execute with typical data: 8 Megabytes. Nature of mathematical problem Computation and plotting of 2D/3D projections of Poincar e surfaces-of-section of Hamiltonian systems. Methods of solution A 4 th order Runge-Kutta method with optional stepsize and number of iterations is used. However, it is possible to indicate any user-method to be used in the integration scheme. Restrictions concerning the complexity of the problem Besides the inherent restrictions of the Runge-Kutta method, this rst version of the package does not makes use of adaptative stepsize control. Typical running time It depends strongly on the surface-of-section to be plotted. With a Pentium-90 PC (32 Mb. RAM), fast plots usually take from a few seconds to a few minutes. On the other extreme, in an example considered in this paper, a surface-of-section with 10,000 points and an energy threshold 10 ?8 took 35 minutes. Unusual features of the program This package provides easy-to-use software tools for plottings 2D/3D projections of Poincar e surfaces-of-section of Hamiltonians systems. The speed at which the returned plots are calculated is adjustable, in connection with their accuracy. This feature permits alternatively searching for, say, \\rst order" phenomena at remarkable high speed, or, say, \high order" detailed 2D/3D projections displaying \is-lands" and the inner structure of a surface-of-section, as desired. The 2D intersection plane over which the surface-of-section is plotted can be any one of the coordinate planes of the phase space, and can be shifted in the positive and negative directions. The package also provides routines for setting large sets of initial conditions for numerical experiments in seconds. The implementation in a symbolic computing environment allows for combined symbolic/numerical studies.
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