Mathematics – Dynamical Systems
Scientific paper
Apr 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aps..apr.d1026g&link_type=abstract
American Physical Society, April Meeting, 2003, April 5-8, 2003 Philadelphia, Pennsylvania, MEETING ID: APR03, abstract #D1.026
Mathematics
Dynamical Systems
Scientific paper
This work determines how one can: [a] obtain symbolic Taylor-series (and thus approximate) solutions, to any order in the independent variable, for equations which describe a variety of dynamical systems, whether or not those systems have a Hamiltonian. The user-friendly program can also: [b] generate Euler-Lagrange equations, and [c] Hamilton's equations. Furthermore it can: [d] construct the generalized momenta and the Hamiltonian from the Lagrangian. As a working tool, the program interrelates [a] through [d]. The program is written in MACSYMA and will be modified to run on Freeware known as MAXIMA. Among the variety of cross-disciplinary applications are: (1) a simple harmonic oscillator in 3 dimensions [classical mechanics], (2) a charged particle in a constant magnetic field [electromagnetism], (3) the Lorenz equations [classical chaos]; also (4) an adaptive neural network, and (5) the orbital equations corresponding to a quantum system with a single component of angular momentum [autonomous systems of differential equations].
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