@article{907.53008,
	title = {{Equiform bundle motions in $E_3$ with spherical trajectories. I.}},
	author = {Anton Gfrerrer and Johann Lang},
	journal = {Beitr. Algebra Geom.},
	number = {2},
	pages = {307-316},
	volume = {39},
	year = {1998},
	biburl = {http://www.bibsonomy.org/bibtex/2921a6c7fe9bae86c2006ac6d67ea2484/dmartins},
	description = {robotica-bib},
	abstract = {In 1906 and 1908 Bricard and Borel published two long papers in which
	they determined Euclidean motions with spherical trajectories [{\it
	R. Bricard}, J. l'Ecole Polytechnique, II. Ser. 11, 1-93 (1906; JFM
	37.0705.04); {\it E. Borel}, Mem. Sav. Etrangers, Paris 33, 1-128
	(1908; JFM 39.0749.02)]. Based on these papers the authors determine
	equiform bundle motions which have spherical trajectories. They introduce
	a 10-dimensional parameter space $P(W)$ in which a 6-dimensional
	surface $B_6$ represents the condition that a point remains on a
	sphere during an equiform motion. Furthermore, an embedding of the
	motion group into a 10-dimensional projective space $P(V)$ is used
	to give an interpretation of the sphere condition as an orthogonality
	relation between the points of $P(V)$ and $P(W)$. It is shown that
	the images of sphere conditions given by any motion are on a linear
	intersection of $B_6$. Because of this fact, linear subspaces of
	$P(W)$ and their intersection with $B_6$ are studied. The case that
	a line is contained in $B_6$ results in either one point having a
	circle as trajectory or the points of a circle or a line of the moving
	system are constrained to move on spheres or in planes. The case
	of the intersection of a 2-dimensional linear space with $B_6$ yields
	a one parameter motion which moves the points of a bundle plane on
	spherical trajectories. \par [For Part II, see the following review
	Zbl 907.53009]. },
	reviewer = {M.Husty (Leoben)}, language = {English}, classmath = {*53A17 Kinematics (differential geometry)},
	keywords = {bundle equiform motion; of principle spherical trajectories; transference }
}