Motion of curves specified by acceleration field in R^n

Abstract

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.

Spacelike curves and evolution equations in de Sitter 3-space

“…Theorem 3.3 Let r(s, t) be an inelastic spacelike curve in S 3 1 and consider Frenet matrix Ω that satisfies Eqs. (10) and (21). Then, we have the integrability condition:…”

“…The analysis is extended to more general types of motion and other integrable systems [6,7]. For more details, one can see [8][9][10][11][12][13][14][15][16].…”

Geometry and evolution of Hasimoto surface in Minkowski 3-space

“…Numerous spaces, including the Euclidean space [ 16 ], Minkowski space [ 17 ], Galilean space [ 18 ], and pseudo-Galilean space [ 5 ], have been used to study the equations of motion of curves and surfaces. Within the scope of our work, we investigate the evolution equations of Hasimoto surface by employing the quasi-frame of spacelike curve with timelike binormal.…”

“…The flowing curve of the sine Gordon equation was analyzed by Rick Mukherjee and Radha Balakrishnan [ 19 ]. In [ 5 , 16 ], the authors investigated the motion of plane curves, hypersurface motion, and the motion of space curves in various spaces. By using the fundamental existence and uniqueness hypothesis of space curves, the authors in [ 13 ] developed Hasimoto surface via integration for Frenet-Serret equations.…”