Related papers: Chaotic Dynamics of the Chaplygin sleigh with a pa…
We consider the motion of rigid bodies in a potential fluid subject to certain nonholonomic constraints and show that it is described by Euler--Poincar\'e--Suslov equations. In the 2-dimensional case, when the constraint is realized by a…
We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a…
This paper is concerned with the Chaplygin sleigh with timevarying mass distribution (parametric excitation). The focus is on the case where excitation is induced by a material point that executes periodic oscillations in a direction…
For a Chaplygin sleigh moving in the presence of weak friction, we present and investigate two mechanisms of arising acceleration due to oscillations of an internal mass. In certain parameter regions, the mechanism induced by small…
Biomimetic underwater robots use lateral periodic oscillatory motion to propel forward, which is seen in most fishes known as body caudal fin (BCF) propulsion. The lateral oscillatory motion makes slender-bodied fish-like robots roll…
The article considers Chaplygin sleigh on a plane in potential well, assuming that an external potential force is supplied at the mass center. Two particular cases are studied in some detail, namely, a one-dimensional potential valley and a…
In this paper we present an energy shaping control law for set-point regulation of the Chaplygin sleigh. It is well known that nonholonomic mechanical systems cannot be asymptotically stabilised using smooth control laws as they do no…
We consider nonholonomic systems whose configuration space is the central extension of a Lie group and have left invariant kinetic energy and constraints. We study the structure of the associated Euler-Poincare-Suslov equations and show…
In this work, we model the movement of a figure skater gliding on ice by the Chaplygin sleigh, a classic pedagogical example of a nonholonomic mechanical system. The Chaplygin sleigh is controlled by a movable added mass, modeling the…
In this paper, the dynamics of nonholonomic systems on Lie groups with a left-invariant kinetic energy and left-invariant constraints are considered. Equations of motion form a closed system of differential equations on the corresponding…
Chaplygin proved the integrability by quadratures of a round sphere, rolling without slipping on a horizontal plane, with center of mass at the center of the sphere, but with arbitrary moments of inertia. Although the system is integrable…
Rubber rolling (no-slip and no-twist) of a convex body on the plane under the influence of gravity is a SE(2) Chaplygin system, that reduces to the sphere of Poisson vectors. I comment upon an observation by A.V Borisov and I.S. Mamaev…
Many multi-agent systems in nature are comprised of agents that interact with, and respond to, the dynamics of their environment. In this paper, we approach the study of such agent-environment interactions through the study of passively…
We investigate the behavior of dynamical systems with nonholonomic constraints when coupled to a thermal bath, focusing on the paradigmatic case of the Chaplygin sleigh. A straightforward Langevin-type approach obtained by naively adding…
This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical…
A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it…
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled…
This paper addresses the problem of the Chaplygin ball rolling on a horizontal plane which rotates with constant angular velocity. In this case, the equations of motion admit area integrals, an integral of squared angular momentum and the…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
In this paper I consider the self-excited rotation of an elliptical cylinder towed in a viscous fluid as a canonical model of nonlinear fluid structure interactions with possible applications in the design of sensors and energy extraction…