拉格朗日微分一式变换的多参数李变换法
A multi-parameter Lie transform method applied to the transform of the Lagrangian differential one-form
摘要：
本文将文献[AnnPhys，151 1（1983）]中的单参数Lie变换微扰理论推广到多参数情形，给出了由原来的Lagrange微分1-形式转化而来的新的Lagrange微分1-形式的形式解，以适应多尺度微扰。在新方法中，生成元及其阶数的选择是以逐阶减少新拉格朗日微分1-形式中的快变量为目的的。在应用方面，将多参数李变换方法应用于低频静电扰动下的陀螺动力学模型的推导。与传统模型相比，新模型完全取消了拉格朗日1-形式中的有限拉莫尔半径项，而不使用任何规范函数。
英文摘要：
In this paper, to fit the multi-scale perturbations, the single-parameter Lie transform perturbation theory given in [Ann Phys, 151 1 (1983)] is generalized to a multi-parameter case, which provides a formal solution of the new Lagrangian differential 1-form transformed from the old one. In the new method, the generators and their orders are appropriately chosen under the purpose of reducing the fast variables from the new Lagrangian differential 1-form order by order. As for the application, this multi-parameter Lie transform method is applied to deriving the gyrokinetic model with the presentation of low-frequency electrostatic perturbations. Compared with the conventional model, the Finite Larmor Radius terms in the Lagrangian 1-form of the new model are perfectly cancelled, without using any gauge function.
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