Euler-Savary’s formula on Minkowski geometry. (English) Zbl 1066.53039

Ikawa, T.

Balkan J. Geom. Appl. 8, No. 2, 31-36 (2003).

If in the Euclidean plane a curve \(c_R\) rolls without gliding along another curve \(c_B\), any point \(P\) attached to \(c_B\) runs on a path \(c_L\). The classical formula of Euler-Savary links the curvatures \(k_B\), \(k_R\) and \(k_L\) of the curves \(c_B\), \(c_R\) and \(c_L\). In this paper Euler-Savary’s formula is derived in case the underlying metric being Minkowskian instead of Euclidean.

Reviewer: Anton Gfrerrer (Graz)

MSC:

53A35	Non-Euclidean differential geometry
53B30	Local differential geometry of Lorentz metrics, indefinite metrics
53A17	Differential geometric aspects in kinematics

Keywords:

curvature; rolling curves; kinematics; Minkowski plane