Kinematics of moving generalized curves in a n -dimensional Euclidean space is formulated in terms of intrinsic geometries. The evolution equations of the orthonormal frame and higher curvatures are obtained. The integrability conditions for the evolutions are given. Finally, applications in 2 R are given and plotted.

Kinematic of moving generalized space curves in R n is formulated in terms of intrinsic geometries. The model for the dynamics is specified by acceleration fields. The acceleration is assumed to be local in the sense that it is a functional of the heir curvatures and their derivatives. By solving the nonlinear partial differential equations which governing the motion of the curves, we get on there curvatures and integrating the Seret-Frenet equations we display family of curves in plane and space.