广义Hojman定理

研究利用Lie对称的生成元τ(t,q,q·)和ξ_s(t,q,q·)来构造广义H ojman守恒 量，并讨论三种特殊情况，研究表明：Hojman守恒量是该广义守恒量的特例，且在Lie对称 的生成元的形式为τ(t,q)和ξ_s(t,q)时，该广义Hojman守恒量可以导出Lu tzky守恒 量，此外，还给出一个排除平凡守恒量的条件.最后，给出两个简单例子，作为所获得结果 的说明. 关键词： 动力学系统 广义Hojman定理 Lie对称 守恒量

The generalized Hojman's theorem

A new conservation theorem is studied, the conserved quantity is only constructe d in terms of the infinitesimal generators τ(t,q,q·) and ξ_s( t,q,q· ) of Lie symmetry of the dynamical equations. Three special cases are discussed, where the Hojman conserved quantity can be deduced as a corollary of this gener al conservation theorem at τ(t,q,q·)=0, and the Lutzky conserved quantity can be derived by using this general conservation theorem at τ=τ(t,q) and ξ_s=ξ_s(t,q).Moreover, a condition is presented to exc lude trivial conse rved quantities. Finally, two examples to illustrate the application of the resu lts are given.