VERSAL NORMAL-FORM OF THE HAMILTONIAN FUNCTION OF THE RESTRICTED PROBLEM OF 3 BODIES NEAR L(4)

[摘要] When one studies matrices depending on parameters, the transformation into Jordan canonical form can become singular, when multiple eigenvalues occur. The versal normal form for a matrix was introduced by Amol'd (1971) in order to overcome this difficulty. Unfortunately, no method was given on how to construct this transformation. For a special class of matrices we describe a simple procedure to accomplish this task. We use the one-to-one resonance at the Lagrangian triangular equilibrium point in the restricted problem of three bodies as an example to demonstrate our method. We then extend the idea of versal normal form to higher-order terms in the Hamiltonian function. After performing this normalization, we are able to analyze the behavior of the periodic orbits near the equilibrium point.

[发布日期] 1994-07-20

[关键词] HAMILTONIAN MECHANICS;LAGRANGIAN EQUILIBRIUM POINT;ONE-TO-ONE RESONANCE;VERSAL NORMAL FORM