Euler-Lagrange equation for general n-order character functional and unification of quantitative causal principle, principle of relativity and general Newton’s laws

Abstract

This paper gives a general n-order character functional, and uses the quantitative causal principle to derive the general variational principle; furthermore the Euler-Lagrange equation and conservative quantities for a general n-order character functional are derived, and the link between the principle of relativity and the quantitative causal principle is revealed. Newton's first, second, and third laws are then derived, but the third laws is also regarded as a new law: it is a theorem that force is zero in translational invariance, and its general physical meaning in classic mechanics is revealed. The results obtained have been successful applied to the galaxy gravitational potential correction, molecular potential, quark confinement potential, etc., and the results are consistent with the physical experiments.