Kinematical invariants and applications for surfaces in three dimensional Euclidean space
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In three dimensional Euclidean space we consider kinematical invariants of the surface which is generated by the motion of a planar curve, especially, the surface which is foliated by circles. At first we characterize the properties of single parameter plane with the theories of unit spherical curve in three dimensional Euclidean space. Then using these results we give the invariants and differential invariants, kinematical properties and some special examples of the surface foliated by circles. The methods established here can be used to the other kinds of the surface in three dimensional Euclidean space.
Abstract
In three dimensional Euclidean space we consider kinematical invariants of the surface which is generated by the motion of a planar curve, especially, the surface which is foliated by circles. At first we characterize the properties of single parameter plane with the theories of unit spherical curve in three dimensional Euclidean space. Then using these results we give the invariants and differential invariants, kinematical properties and some special examples of the surface foliated by circles. The methods established here can be used to the other kinds of the surface in three dimensional Euclidean space.
참고문헌 (12)
- H. H. Hacisalihoˇglu, "Holditch’s theorem for one-parameter closed motions", Mech. Mach. Theory, 32, pp.235~239 (1997)
- H. Liu, "Ruled surfaces with lightlike ruling in 3-Minkowski space", J. Geom. Phys, 59(1), pp.74~78 (2009)[DOI]
- H. Liu, "Characterizations of ruled surfaces with lightlike ruling in Minkowski 3-space", Results Math, 56(1-4), pp.357~368 (2009)[DOI]
- H. Liu, "Ruled invariants and associated ruled surfaces of a space curve", Appl. Math. Comput, 348, pp.479~486 (2019)[DOI]
- H. Liu, "Ruled invariants and total classification of nondevelopable ruled surfaces", J. Geom, 113(1), pp.13~ (2022)[DOI]
- H. Liu, "Invariants of non-developable ruled surfaces in Euclidean 3-space", Beitr. Algebra Geom, 55(1), pp.189~199 (2014)[DOI]
- H. Liu, "Pitch functions of ruled surfaces and B-scrolls in Minkowski 3-space", J. Geom. Phys, 62(1), pp.47~52 (2012)[DOI]
- H. R. M¨uller, "¨ Uber geschlossene Bewegungsvorg¨ange", Monatsh. Math, 55, pp.206~214 (1951)[DOI]
- H. Pottmann, "¨ Offnungsinvarianten der Bahnregelfl¨achen euklidischer Zwangl¨aufe", Beitr¨age Algebra Geom, (27), pp.97~111 (1988)
- B. Roth, "On the advantages of instantaneous invariants and geometric kinematics", Mech. Mach. Theory, 89, pp.5~13 (2015)
- D. Wang, "Kinematic diffferential geometry of a rigid body in spatial motion-I, II, III", Mech. Mach. Theory, 32, pp.419~432 (1997)
- Y. Yu, "Structure and characterization of ruled surfaces in Euclidean 3-space", Appl. Math. Comput, 233, pp.252~259 (2014)[DOI]