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

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.

### 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
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