The generalized Hojman’s theorem
Hongbin Zhang, Chen Li-Qun, Liu Rong-Wan, Shulong Gu, (1)安徽省巢湖学院物理系，巢湖 238000; (2)上海大学上海市应用数学和力学研究所，上海 200072; (3)上海大学上海市应用数学和力学研究所，上海 200072;安徽省巢湖学院物理系，巢湖 238000; (4)上海大学上海市应用数学和力学研究所，上海 200072;广东省韶关大学物理系，韶关 512005 · Acta Physica Sinica · 2005
A new conservation theorem is studied, the conserved quantity is only constructe d in terms of the infinitesimal generators τ(t,q,q·) and ξs( 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 ξs=ξs(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.