不同积分变分原理的统一

依据定量因果原理的数学表示，统一地导出了Lagrange量中含坐标关于时间一阶、二阶导数 的积分型的Hamilton原理、Voss原理、Hlder原理和Maupertuis-Lagrange原理等，给出了 这些原理的本质联系和统一描述.得出f₀=0并不是通常的保持Euler-Lagrange方 程不 变的结果，而是满足定量因果原理的结果.还得出Lagrange量的所有的积分型变分原理等价 地对应于两类满足定量因果原理的不变形式.同时发现所有积分型变分原理的运动方程都是E uler-Lagrange 方程，但不同条件的变分原理所对应的不同群Ｇ作用下的守恒量是不同 的.从而可对过去众多零散的积分型变分原理有一个系统和深入的理解，并使这些变分原理 自然地成为定量因果原理的推论.关键词：变分原理因果原理运动方程对称性

Unification of different integral variational principles

In terms of a mathematical expression of the quantitative causal principle, this paper gives a unification of Hamilton, Voss, Hlder, Maupertuis-Lagrange varia tional principles of integral style of the second-order Lagrangians, and finds t he intrinsic relations among all the different integral variational principles. It is proved that f₀= 0 is just the result satisfying the quantitati ve ca usal principle． The Noether conservation charges of Hamilton, Voss, Hlder, Ma upertuis-Lagrange variational principles are shown up, and the intrinsic relatio ns among the Noether conservation charges of all the integral variational princ iples are discovered. Our investigations make the expressions of the past scrappy numerous variational principles be unified into a relative consistent system o f all the variational principles in terms of the quantitative causal principle, and show that all the variational principles become deductions of the quantitat ive causal principle.