Chaplygin's ball with a gyrostat: singular solutions

Section: Robots With Internal Flywheelsmentioning

confidence: 99%

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

Karavaev¹

2022

“…Let's consider a special case where the inertia tensor has constant components. If the gyrostatic momentum k = const, the system (2.5) has additionally an energy integral [2,18]…”

Section: Equations Of Motion and First Integralsmentioning

confidence: 99%

“…Sergei Chaplygin was the first to conduct in 1903 a study of the dynamics of motion of such a ball [1]. A sufficient number of papers have been devoted to various generalizations of the Chaplygin ball problem [2][3][4][5][6][7][8]. The analysis of the trajectory of the point of contact of the ball with the surface on which it rolls is presented in the paper [9].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the Chaplygin Ball with Variable Parameters

Borisov¹,

Mikishanina²

2020

This work is devoted to the study of the dynamics of the Chaplygin ball with variable moments of inertia, which occur due to the motion of pairs of internal material points, and internal rotors. The components of the inertia tensor and the gyrostatic momentum are periodic functions. In general, the problem is nonintegrable. In a special case, the relationship of the problem under consideration with the Liouville problem with changing parameters is shown. The case of the Chaplygin ball moving from rest is considered separately. Poincaré maps are constructed, strange attractors are found, and the stages of the origin of strange attractors are shown. Also, the trajectories of contact points are constructed to confirm the chaotic dynamics of the ball. A chart of dynamical regimes is constructed in a separate case for analyzing the nature of strange attractors.

“…The problem of controlling the spherical robot (spherical shell) using various mechanisms that set it in motion is one of the urgent problems of nonholonomic mechanics and robotics. These are rotary mechanisms [7][8][9][10][11][12], pendulum mechanisms [13][14][15][16][17], mechanisms with omniwheels [18][19][20] and some others [21,22]. In these works, the equations of motion of the studied mechanical systems are given and control actions for the realization of motion are obtained.…”

Section: Introductionmentioning

confidence: 99%

Control of a Spherical Robot with a Nonholonomic Omniwheel Hinge Inside

Mikishanina

2024

This study investigates the rolling along the horizontal plane of two coupled rigid bodies: a spherical shell and a dynamically asymmetric rigid body which rotates around the geometric center of the shell. The inner body is in contact with the shell by means of omniwheels. A complete system of equations of motion for an arbitrary number of omniwheels is constructed. The possibility of controlling the motion of this mechanical system along a given trajectory by controlling the angular velocities of omniwheels is investigated. The cases of two omniwheels and three omniwheels are studied in detail. It is shown that two omniwheels are not enough to control along any given curve. It is necessary to have three or more omniwheels. The quaternion approach is used to study the dynamics of the system.