GITA: A REDUCE program for the normalization of polynomial Hamiltonians

• Published in: Computer physics communications Vol. 90; no. 2; pp. 355 - 368
• Main Authors: Basios, V., Chekanov, N.A., Markovski, B.L., Rostovtsev, V.A., Vinitsky, S.I.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 1995; Elsevier Science
• Subjects: Algebraic equation; Canonical transformation; Computational techniques; Computer algebra; Exact sciences and technology; Hamiltonian; Homogeneous polynomial; Integral of motion; Mathematical methods in physics; Normal Birkhoff-Gustavson form; Physics; REDUCE; Normal Birkhoff-Gustavson form; Integral of motion; Algebraic equation; Homogeneous polynomial; Computer algebra; Hamiltonian; Canonical transformation; REDUCE; Canonical transformations; Computer program; Hamiltonians; Standardization; Polynomials
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/0010-4655(95)00080-Y

For a given polynomial Hamiltonian near an equilibrium point the program GITA calculates analytically the normal Birkhoff-Gustavson form in Cartesian as well as angle-action coordinates and the formal integral of the motion. These quantities are presented in the form of a truncated power series, the highest degree of which determines the degree of the approximation. The program performs the calculation of the modified normal Birkhoff-Gustavson form for the Hamiltonian restricted by the resonance condition. The program package is written in the computer algebra system REDUCE.