相关论文: Trajectory tracing in figure skating

The Chaplygin sleigh is a classic example of a nonholonomically constrained mechanical system. The sleigh's motion always converges to a straight line whose slope is entirely determined by the initial configuration and velocity of the…

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…

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…

We derive and analyze a three dimensional model of a figure skater. We model the skater as a three-dimensional body moving in space subject to a non-holonomic constraint enforcing movement along the skate's direction and holonomic…

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…

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…

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…

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…

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…

This paper presents a data-driven optimal control policy for a micro flapping wing unmanned aerial vehicle. First, a set of optimal trajectories are computed off-line based on a geometric formulation of dynamics that captures the nonlinear…

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…

For a moving bicycle, the power can be modelled as a response to the propulsion of the centre of mass of the bicycle-cyclist system. On a velodrome, an accurate modelling of power requires a distinction between the trajectory of the wheels…

Trajectories are optimized for a two-dimensional simplified skateboarding system to allow it to perform a fundamental skateboarding trick called an "ollie". A methodology for generating trick trajectories by controlling the position of a…

We provide an ice friction model for vehicle dynamics of a two-man bobsled which can be used for driver evaluation and in a driver-in-the-loop simulator. Longitudinal friction is modeled by combining experimental results with finite element…

A large number of curling shots using a wide range of rotational and translational velocities on two different ice surfaces have been recorded and analyzed. The observed curling rock trajectories are described in terms of a…

The steering control of an autonomous unicycle is considered. The underlying dynamical model of a single rolling wheel is discussed regarding the steady state motions and their stability. The unicycle model is introduced as the simplest…

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…

In this paper, we develop the Chaplygin reducing multiplier method; using this method, we obtain a conformally Hamiltonian representation for three nonholonomic systems, namely, for the nonholonomic oscillator, for the Heisenberg system,…

The paper considers a motion control problem for kinematic models of nonholonomic wheeled systems. The class of maneuverable wheeled systems is defined consisting of systems that can follow any sufficiently smooth non-stop trajectory on the…

Two different controlling methods are proposed to stabilize unstable continuous-sliding states of a dry-friction oscillator. Both methods are based on a delayed-feedback mechanism well-known for stabilizing periodic orbits in deterministic…