Any Hamiltonian System Is Locally Equivalent to a Free Particle

• 作者: Edwin Román-Hernández Elizabeth Galindo-Linares Esperanza Navarro-Morale Gilberto Silva-Ortigoza Magdalena Marciano-Melchor Ramón Silva-Ortigoza Román Suárez-Xique
• 来源期刊: 力学国际期刊(英文)
• 学科: 数学
• 关键词: HAMILTONIAN System CANONICAL Transformation
• 年，卷（期）: 2012,（5）
• 页码范围: 246-252
• 页数: 7页
• 分类号: O1

摘要

In this work we use the Hamilton-Jacobi theory to show that locally all the Hamiltonian systems with n degrees of freedom are equivalent. That is, there is a canonical transformation connecting two arbitrary Hamiltonian systems with the same number of degrees of freedom. This result in particular implies that locally all the Hamiltonian systems are equivalent to that of a free particle. We illustrate our result with two particular examples;first we show that the one-dimensional free particle is locally equivalent to the one-dimensional harmonic oscillator and second that the two-dimensional free particle is locally equivalent to the two-dimensional Kepler problem.