Three Lorentzian planes moving with respect to one another and pole points

On the Moving Coordinate System and Euler-Savary Formula in Affine Cayley-Klein Planes

“…db dp a a d p db (29) The equation 29 () P within the time scale t with respect to fixed plane  . Hence,  is the angular velocity of moving plane with respect to the fixed plane  is given below:…”

“…Furthermore, the canonical relative system for one-parameter planar motions were studied in [1], [27] and [28] in the planes 2 , 2 and 2 by using the notions of moving coordinate system, respectively. Three Lorentzian planes moving with respect to one another and pole points are studied in [29].…”

A Geometric Aspect of the Two-Parameter Planar Lorentzian Motions

“…A. A. Ergin also studied three Lorentzian planes and investigated relative, sliding, and absolute velocities [4]. Let A and be moving Lorentzian planes and be fixed Lorentzian plane and { ; b 1 , b 2 }, { ; l 1 , l 2 }, and { ; l 1 , l 2 } be their coordinate systems, respectively.…”

“…Assume that Φ and Φ are rotation angles of one-parameter planar Lorentzian motions A/ and A/ . In [4], the pole points of the Lorentzian motions A/ and A/ are examined. Let = ( , ) be a moving point on the plane A.…”

“…Furthermore, A. A. Ergin investigated Lorentzian moving planes and pole points [4]. One-parameter planar motions are given in affine Cayley Klein planes (CK-planes) by generalizing of the motions in Euclidean, Galilean, and Lorentzian planes in [5].…”