The motions of a spheroid on a horizontal plane with viscous friction

Steady motions of nonhomogeneous ellipsoid on horizontal plane

“…The regions of stability in the plane of parameters ) , (   , corresponding to conditions (12) in the case of homogeneous ellipsoid have been given earlier [1]. For nonhomogeneous case, let us assume that the small value of friction coefficient confines itself to considering in (12) in terms of the first order of smallness.…”

“…In the case when the parameters of the ellipsoid satisfy condition (15), values 1  and 2  have one sign, conditions are satisfied everywhere except for a small neighborhood of point 1/3 = …”

Spherical Robots: An Up-to-Date Overview of Designs and Features

“…At present, active research is underway on quite a number of related problems. 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.…”

Dynamics of a rolling and sliding disk in a plane. Asymptotic solutions, stability and numerical simulations

“…4 §4] contains more general results concerning asymptotic motions of a solid body with an arbitrary shape moving on the horizontal plane and include results of Moshchuk. The value μ = 0 corresponds to the case of an absolutely smooth surface and an appropriate limit μ → ∞ corresponds to the case of an absolutely rough surface, see, e.g., [21].…”