Rolling of a body on a plane or a sphere: a geometric point of view

Moghadasi, Seyed Reza

doi:10.1017/s0004972700034468

Cited by 3 publications

(2 citation statements)

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“…Note that in general this motion cannot be recovered from these two curves, but in the non-slipping motions these curves describe the motion uniquely. One can find physical description of such motions and their equivalent mathematical explanations in [16]. Here, we only review some results which we use in this paper.…”

Section: Description Of Rolling Surfacesmentioning

confidence: 99%

Controllability of Rolling Bodies With Regular Surfaces

Moghadasi¹

2016

Journal of the Korean Mathematical Society

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Abstract. A pair of bodies rolling on each other is an interesting example of nonholonomic systems in control theory. There is a geometric condition equivalent to the rolling constraint which enables us to generalize the rolling motions for any two-dimensional Riemannian manifolds. This system has a five-dimensional phase space. In order to study the controllability of the rolling surfaces, we lift the system to a six-dimensional space and show that the lifted system is controllable unless the two surfaces have isometric universal covering spaces. In the non-controllable case there are some three-dimensional orbits each of which corresponds to an isometry of the universal covering spaces.

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Section: Description Of Rolling Surfacesmentioning

confidence: 99%

Controllability of Rolling Bodies With Regular Surfaces

Moghadasi¹

2016

Journal of the Korean Mathematical Society

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“…This includes investigation and development of models of contact interaction of a spherical body with the plane (surface) [8][9][10][11][12][13][14][15][16][17][18][19], explanation of the dynamics of motion of inhomogeneous spherical bodies, in particular, those with internal mechanisms changing the position of the center of mass and the angular momentum of the system [4,[20][21][22][23][24][25]. The problems of planning the motion of spherical robots along a trajectory [26][27][28][29][30][31][32][33][34][35][36] are no less popular.…”

Section: Introductionmentioning

confidence: 99%