Mathematics – Differential Geometry
Scientific paper
2009-12-31
Mathematics
Differential Geometry
Scientific paper
10.1007/s00006-010-0255-3
In \cite{Mul} one-parameter planar motion was first introduced and the relations between absolute, relative, sliding velocities (and accelerations) in the Euclidean plane $\mathbb{E}^2$ were obtained. Moreover, the relations between the Complex velocities one-parameter motion in the Complex plane were provided by \cite{Mul}. One-parameter planar homothetic motion was defined in the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion is defined in the Hyperbolic plane. Some characteristic properties about the velocity vectors, the acceleration vectors and the pole curves are given. Moreover, in the case of homothetic scale $h$ identically equal to 1, the results given in \cite{Yuc} are obtained as a special case. In addition, three hyperbolic planes, of which two are moving and the other one is fixed, are taken into consideration and a canonical relative system for one-parameter planar hyperbolic homothetic motion is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, is obtained with the help of this relative system.
Akyigit Mahmut
Ersoy Soley
No associations
LandOfFree
One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-104594