Gliding motions of a rigid body: the curious dynamics of Littlewood's rolling hoop

Bronars, Antonia; O’Reilly, Oliver M.

doi:10.1098/rspa.2019.0440

Cited by 9 publications

(4 citation statements)

References 24 publications

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“…Finally, the present formulation can provide a solid basis to develop a numerical scheme for systems with unilateral constraints. In fact, it will be quite helpful in efforts to examine special situations arising in contact problems, where conditions of contact are fulfilled temporarily or change instantly [33][34][35]. In such cases, where the unilateral constraints can be treated as bilateral up to their violation, the constraints can not be put in an integrable form and should therefore be treated as nonholonomic.…”

Section: Synopsis and Extensionsmentioning

confidence: 99%

Numerical integration of multibody dynamic systems involving nonholonomic equality constraints

2021

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This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton's second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.

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Section: Synopsis and Extensionsmentioning

confidence: 99%

Numerical integration of multibody dynamic systems involving nonholonomic equality constraints

2021

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“…It is also possible for an intermediate phase to occur in which the friction provided by the rolling surface is insufficient to maintain the pure rolling constraint. In this case, the hoop could undergo slipping, skidding, or gliding motions [10], [28]. In this work, we will assume that such effects are negligible.…”

Section: A Rolling Phasementioning

confidence: 99%

Optimal Trajectory Tracking for a Magnetically Driven Microswimmer

Buzhardt

Tallapragada

2020

2020 American Control Conference (ACC)

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In this paper, we present a novel rolling, jumping robot. The robot consists of a driven pendulum mounted to a wheel in a compact, lightweight, 3D printed design. We show that by using the driven pendulum to change it's weight distribution, the robot is able to obtain significant rolling speed, achieve jumps of up to 2.5 body lengths vertically, and also clear horizontal distances of over 6 body lengths while jumping. The robot's dynamic model is derived and simulation results indicate that it is consistent with the motion and jumping observed on the robot. The ability to both roll and jump effectively using a minimalistic design makes this robot unique and could inspire the use of similar mechanisms on robots intended for applications in which agile locomotion on unstructured terrain is necessary, such as disaster response or planetary exploration.

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“…The motion of the cylinder, despite its seemingly simple nature, exhibits a complex range of behaviors. Extensive analysis has revealed self-induced jumping motions and transitions between rolling and slipping [7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Jump effect of an eccentric cylinder rolling on an inclined plane

Aldo Arroyo,

Aparicio Alcalde

2024

J. Phys. A: Math. Theor.

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This work addresses the intriguing phenomenon of the jump effectexhibited by an eccentric cylinder rolling on an inclined plane.Our main objective is to determine the region of the parameterspace where the cylinder can undergo a jump after pure rollingmotion. In previous works, it was assumed that slipping alwaysprecedes a jump, leading to the belief that slip is necessary. Incontrast, our study challenges this prevailing notion bydemonstrating the existence of situations where a jump can occurafter pure rolling motion. We present a detailed theoreticaldescription of the jump effect, investigating the dependence ofthe jump behavior on the initial conditions, the forces involved,and the parameter values. Through rigorous analysis, we determinethe restricted region in the parameter space that allows for jumpsto occur without slipping. Our findings contribute to the ongoingdebate surrounding the jump effect in eccentric cylinder dynamics.

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Gliding motions of a rigid body: the curious dynamics of Littlewood's rolling hoop

Cited by 9 publications

References 24 publications

Numerical integration of multibody dynamic systems involving nonholonomic equality constraints

Numerical integration of multibody dynamic systems involving nonholonomic equality constraints

Optimal Trajectory Tracking for a Magnetically Driven Microswimmer

Jump effect of an eccentric cylinder rolling on an inclined plane

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