In this paper,some criteria which judge the origin of the Liénard system to be a local center or a global center are given.

This paper gives a theorem for the local center of generalized Lienard system; the relative theorems in the references can be deduced from our corollaries.

In this paper, for the origin of the generalized Lienard systems to be the global centerand the local center we give the necessary and sufficient conditions and sufficient conditionsrespectively.

The curvature center of the Gaussian beam located by using dynamic speckle;

The paper explains three types of evolute of cone curve,and introduces curvature center on top of cone curve and drawing way with compasses and ruler of curvature circle.

In this paper the general spiral trajectory curvature center of curvature and torsion formula,revealed the relationship between the general line of curvature,torsion and its curvature center of curvature of the track.

The paper points out the intrinsic relation between developable normal surfaces and parallel curves,where the uniqueness,the transitivity of parallel curves and the relationship between their center of curvature are set and proven.

In this paper we discuss the generalized Liénard system and give several sufficient conditions to guarantee the origin is the local center.

The conditions of a local center for a Liénard system d~2xdt~2+f(x)dxdt+g(x)=0 are discussed.