内弹道拉格朗日问题摄动一级近似解

The First-order Approximate Solution of the Lagrangian Problem in Interior Ballistics with the Perturbation Method.

经典内弹道学把求解膛内弹后空间压力分布问题称为拉格朗日问题。本文取ε=ω/φ_1m为小参数,对这个问题进行了摄动求解。证明了拉格朗日假设下的密度、速度、压力分布的结果是本文方法的零级近似解,从而看出对于ε较大的火炮,拉格朗日近似误差较大。

ε =ω/(φ_1m) being taken as a small parameter,the pressure distri-bution problem,called as Lagrangian Problem in the classical interior ballis-tics, is solved with the perturbation method in this paper. The density,velocityand pressure distribution obtained under the Lagrangian Assumption are thezero-order approximate results given in the paper. Thus it is shown that the er-ror of the Lagrangian Approximate is obvious for the guns with the large ε val-ue.