# Normal Form, Lie-Poisson Structure and Reduction for the Henon-Heiles System

Author: Kasperczuk, S.

Source: Celestial Mechanics and Dynamical Astronomy, Volume 63, Numbers 3-4, 1995 , pp. 245-253(9)

Publisher: Springer

OR

Price: \$47.00 plus tax (Refund Policy)

Abstract:

The reduced Henon-Heiles system is investigated as a Hamiltonian dynamical system obtained by applying the normalization of the Hamiltonian $$H={1 \over 2}(p_1^2+p_2^2+q_1^2+q_2^2)+{1 \over 3}\mu q_1^3-q_1q_2^2$$ to fourth-degree terms. The related equations of motion are bi-Hamiltonian and possess the Lie-Poisson structure. Each Lie-Poisson structure possesses an associated Casimir function. When reduced to level sets of these functions, the equations of motion take various symplectic forms. The various reductions give different coordinate representations of the solutions. These coordinate representations are used to seek the simplest representation of the solutions.

Document Type: Regular Paper

Affiliations: Institute of Physics, Pedagogical University, Plac Słowiański 6, PL 65069 Zielona Góra, Poland

Publication date: 1995-01-01

Related content

#### Key

Free content
New content
Open access content
Subscribed content
Free trial content

A | A | A | A