# Two-parametric motions in ${E}_{3}$

Aplikace matematiky (1987)

- Volume: 32, Issue: 2, page 96-119
- ISSN: 0862-7940

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topKarger, Adolf. "Two-parametric motions in $E_3$." Aplikace matematiky 32.2 (1987): 96-119. <http://eudml.org/doc/15483>.

@article{Karger1987,

abstract = {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.},

author = {Karger, Adolf},

journal = {Aplikace matematiky},

keywords = {kinematics; two-parametric motions; rolling of two isometric surfaces; differential geometry; Lie groups and Lie algebras; kinematics; two-parametric motions; rolling of two isometric surfaces},

language = {eng},

number = {2},

pages = {96-119},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Two-parametric motions in $E_3$},

url = {http://eudml.org/doc/15483},

volume = {32},

year = {1987},

}

TY - JOUR

AU - Karger, Adolf

TI - Two-parametric motions in $E_3$

JO - Aplikace matematiky

PY - 1987

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 32

IS - 2

SP - 96

EP - 119

AB - 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.

LA - eng

KW - kinematics; two-parametric motions; rolling of two isometric surfaces; differential geometry; Lie groups and Lie algebras; kinematics; two-parametric motions; rolling of two isometric surfaces

UR - http://eudml.org/doc/15483

ER -

## References

top- W. Blaschke, Nicht-Euklidische Geometrie und Mechanik, Hamb. Math. Einzelschriften 34. Heft, (1942). (1942) Zbl0027.13304MR0009861
- O. Bottema, Instantaneous kinematics for spatial two-parameter motion, Proceedings of Koninkl. Nedérl. Akad. van Wettenschappen - Amsterdam, Series B, 74, No. 1, (1971). (1971) Zbl0208.24302MR0281104
- O. Kowalski, The invariant classification of 3-dim. linear subspaces of infinitesimal isometrics of ${E}_{3}$, Comm. Math. Univ. Car. 8 (1967), No. 4, 635-649. (1967) MR0228629
- O. Kowalski, Orbits of transformation groups on certain Grasmann manifiolds, Czech. Math. Journ. 18 (93) (1968), 144-177 and 240-273. (1968) MR0231939
- H. R. Müller, Sphärische Kinematik, Berlin 1962. (1962) MR0145715
- A. Schoenflies M. Grübler, Kinematik, Encyklopädie der Mathematischen Wissenschaften, Band 4 (I), Heft 2, 3, Leipzig 1902. (1902)

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