Lorentziyen 3-Uzayda Spacelike Yüzeylerin Kontak Yuvarlanmasinin İleri Kinematiği

Yıl 2018, Cilt: 39 Sayı: 4, 882 - 899, 24.12.2018

Mehmet Aydınalp Mustafa Kazaz Hasan Hüseyin Uğurlu

https://doi.org/10.17776/csj.389649

Öz

Bu makalede, 3-boyutlu Lorentziyen uzayda bir
spacelike yüzeyin bir diğer spacelike yüzey üzerinde yüzeylerin kontak
spacelike yörünge eğrileri boyunca kaymaksızın dönme-yuvarlanma hareketinin
ileri kinematiğini inceledik. Holonomik olmayan bir sistemde ortaya çıkan
dönme-yuvarlanma hareketinin anlık kinematiğini kurmak için bir Darboux çatı
metodu kullanılmıştır. Ardından, kontravaryant vektörler, yuvarlanma hızı ve
geometrik değişmezlere göre hareketli spacelike yüzeyin dönme-yuvarlanma
hareketinin yeni kinematik formülasyonları elde edilmiştir. Keyfi bir noktanın
öteleme hızı formülasyonu ve hareketli spacelike yüzey üzerindeki açısal hız
formülasyonunun denklemi elde edilmiştir.
Geometrik değişmezlerle ifade edilen denklem, her mertebeden
türevlenebilirdir ve keyfi spacelike parametrik yüzeye ve spacelike kontak
yörünge eğrisine kolayca uygulanabilir. Dönme-yuvarlanma kinematiğinin bağıl
eğrilikleri ve burulmasının etkisi açık olarak gösterilmektedir.

Anahtar Kelimeler

Lorentziyen 3-Uzay, Darboux Çatısı, İleri Kinematik, Kontak Yuvarlanma, Has yuvarlanma, Dönme-yuvarlanma

The Forward Kinematics of Rolling Contact of Spacelike Surfaces in Lorentzian 3-Space

Öz

In this
paper, we investigate the forward kinematics of spin-rolling motion without
sliding of one spacelike surface on another spacelike surface along the
spacelike contact trajectory curves of the surfaces in Lorentzian 3-space. A
Darboux frame method is adopted to develop instantaneous kinematics of
spin-rolling motion, which occurs in a nonholonomic system. Then new kinematic
formulations of spin-rolling motion of spacelike moving surface with respect to
contravariant vectors, rolling velocity, and geometric invariants are obtained.
The translational velocity formulation of an arbitrary point and the equation
of the angular velocity formulation on the spacelike moving surface are
derived. The equation, which is represented with geometric invariants, can be
easily applied to arbitrary spacelike parametric surface and spacelike contact
trajectory curve and can be differentiated to any order. The influence of the
relative curvatures and torsion on spin-rolling kinematics is clearly
presented.

2010 AMS Subject Classification: 70B10, 53A17, 53A25, 53A35.

Anahtar Kelimeler

Darboux Frame, Forward Kinematics, Lorentzian 3-Space, Rolling Contact, Pure-rolling, Spin-rolling

Kaynakça

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