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Surface-Depended growth kinematics
  • Sezen Öncül,
  • Zehra Özdemir,
  • İsmail Gök
Sezen Öncül
Ankara Üniversitesi Fen Bilimleri Enstitüsü
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Zehra Özdemir
Amasya University
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İsmail Gök
Ankara Universitesi
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Abstract

In this paper, we investigate the surface-dependent growth model in Euclidean 3-space. The surface-dependent model is developed to model the kinematics of surface growth for objects that can be generated by the curves on the surface, such as parasites and plants. This paper includes two main purposes for this model. The first one is to parametrize this model by using the quaternions and homothetic motions.Furthermore, we express the matrix representations of the surface-dependent growth model. The second one is to construct the surface-dependent growth model by using the growth velocity components related to the Darboux frame at each point of the generating curve. Moreover, to support the theory studied in the paper various illustrated examples are presented.

Peer review status:ACCEPTED

01 Apr 2020Submitted to Mathematical Methods in the Applied Sciences
03 Apr 2020Submission Checks Completed
03 Apr 2020Assigned to Editor
03 Apr 2020Reviewer(s) Assigned
23 May 2020Review(s) Completed, Editorial Evaluation Pending
24 May 2020Editorial Decision: Revise Minor
28 May 20201st Revision Received
29 May 2020Submission Checks Completed
29 May 2020Assigned to Editor
29 May 2020Editorial Decision: Accept