A Variational Integrator for the Chaplygin–Timoshenko Sleigh

Zhipeng An; Shan Gao; Donghua Shi; Dmitry V. Zenkov

doi:10.1007/s00332-020-09611-2

A Variational Integrator for the Chaplygin–Timoshenko Sleigh

Zhipeng An
, Shan Gao
, Donghua Shi^*
, Dmitry V. Zenkov

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology
North Carolina State University

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

The paper introduces a mechanically inspired nonholonomic integrator for numerical simulation of the dynamics of a constrained geometrically exact beam that is a field-theoretic analogue of the Chaplygin sleigh. The integrator features an exact constraint preservation, an excellent numerical energy conservation throughout a large number of iterations, while avoiding the use of unnecessary Lagrange multipliers. Simulations of the dynamics of the constrained beam reveal typical for nonholonomic system’s behavior, such as motion reversals and locomotion generation.

Original language	English
Pages (from-to)	1381-1419
Number of pages	39
Journal	Journal of Nonlinear Science
Volume	30
Issue number	4
DOIs	https://doi.org/10.1007/s00332-020-09611-2
Publication status	Published - 1 Aug 2020

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SDG 7 Affordable and Clean Energy

Keywords

Discrete mechanics
Field theories
Geometric integration
Hamel’s equations
Nonholonomic systems

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10.1007/s00332-020-09611-2

Cite this

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abstract = "The paper introduces a mechanically inspired nonholonomic integrator for numerical simulation of the dynamics of a constrained geometrically exact beam that is a field-theoretic analogue of the Chaplygin sleigh. The integrator features an exact constraint preservation, an excellent numerical energy conservation throughout a large number of iterations, while avoiding the use of unnecessary Lagrange multipliers. Simulations of the dynamics of the constrained beam reveal typical for nonholonomic system{\textquoteright}s behavior, such as motion reversals and locomotion generation.",

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author = "Zhipeng An and Shan Gao and Donghua Shi and Zenkov, \{Dmitry V.\}",

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AU - Gao, Shan

AU - Shi, Donghua

AU - Zenkov, Dmitry V.

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Y1 - 2020/8/1

N2 - The paper introduces a mechanically inspired nonholonomic integrator for numerical simulation of the dynamics of a constrained geometrically exact beam that is a field-theoretic analogue of the Chaplygin sleigh. The integrator features an exact constraint preservation, an excellent numerical energy conservation throughout a large number of iterations, while avoiding the use of unnecessary Lagrange multipliers. Simulations of the dynamics of the constrained beam reveal typical for nonholonomic system’s behavior, such as motion reversals and locomotion generation.

AB - The paper introduces a mechanically inspired nonholonomic integrator for numerical simulation of the dynamics of a constrained geometrically exact beam that is a field-theoretic analogue of the Chaplygin sleigh. The integrator features an exact constraint preservation, an excellent numerical energy conservation throughout a large number of iterations, while avoiding the use of unnecessary Lagrange multipliers. Simulations of the dynamics of the constrained beam reveal typical for nonholonomic system’s behavior, such as motion reversals and locomotion generation.

KW - Discrete mechanics

KW - Field theories

KW - Geometric integration

KW - Hamel’s equations

KW - Nonholonomic systems

UR - https://www.scopus.com/pages/publications/85078407644

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ER -

A Variational Integrator for the Chaplygin–Timoshenko Sleigh

Abstract

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Keywords

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