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kinematics; two-parametric motions; rolling of two isometric surfaces; differential geometry; Lie groups and Lie algebras
The paper deals with the local differential geometry of two-parametric motions in the Euclidean space. The first part of the paper contains contemporary formulation of classical results in this area together with the connection to the elliptical differential geometry. The remaining part contains applications. Necessary and sufficient conditions for splitting of a two-parametric motion into a product of two one-parametric motions, characterization of motions with constant invariants and some others. The case of rolling of two isometric surfaces is treated in detail.
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