Dmitry Zenkov

Works (16)

Updated: April 5th, 2024 03:20

2023 journal article

Discrete Hamiltonian Variational Mechanics and Hamel's Integrators

JOURNAL OF NONLINEAR SCIENCE, 33(2).

By: S. Gao*, D. Shi * & D. Zenkov n

author keywords: Exact integrators; Hamel's equations; Nonholonomic systems; Momentum; Symmetry
topics (OpenAlex): Numerical methods for differential equations; Control and Stability of Dynamical Systems; Dynamics and Control of Mechanical Systems
Source: Web Of Science
Added: January 30, 2023

2023 article

Discrete Hamiltonian Variational Mechanics and Hamel's Integrators (vol 33, 26, 2023)

Gao, S., Shi, D., & Zenkov, D. V. (2023, April). JOURNAL OF NONLINEAR SCIENCE, Vol. 33.

By: S. Gao*, D. Shi * & D. Zenkov n

topics (OpenAlex): Control and Stability of Dynamical Systems; Numerical methods for differential equations
Source: Web Of Science
Added: March 20, 2023

2020 journal article

A Variational Integrator for the Chaplygin-Timoshenko Sleigh

JOURNAL OF NONLINEAR SCIENCE, 30(4), 1381–1419.

By: Z. An*, S. Gao*, D. Shi * & D. Zenkov n

author keywords: Hamel's equations; Field theories; Nonholonomic systems; Discrete mechanics; Geometric integration
topics (OpenAlex): Numerical methods for differential equations; Dynamics and Control of Mechanical Systems; Modeling and Simulation Systems
Source: Web Of Science
Added: July 6, 2020

2020 journal article

Hamel's Formalism for Classical Field Theories

JOURNAL OF NONLINEAR SCIENCE, 30(4), 1307–1353.

By: D. Shi *, D. Zenkov n & A. Bloch *

author keywords: Hamel's equations; Nonholonomic systems; Momentum; Symmetry
topics (OpenAlex): Dynamics and Control of Mechanical Systems; Control and Dynamics of Mobile Robots; Control and Stability of Dynamical Systems
Source: Web Of Science
Added: July 6, 2020

2017 journal article

Hamel's Formalism for Infinite-Dimensional Mechanical Systems

JOURNAL OF NONLINEAR SCIENCE, 27(1), 241–283.

By: D. Shi *, Y. Berchenko-Kogan*, D. Zenkov n & A. Bloch*

author keywords: Hamel equations; Nonholonomic constraints; Momentum; Symmetry
topics (OpenAlex): Control and Dynamics of Mobile Robots; Robotic Path Planning Algorithms; Dynamics and Control of Mechanical Systems
Source: Web Of Science
Added: August 6, 2018

2016 journal article

ON HAMEL'S EQUATIONS

THEORETICAL AND APPLIED MECHANICS, 43(2), 191–220.

By: D. Zenkov n

author keywords: infinite-dimensional mechanics; nonholonomic constraints; variational integrators
topics (OpenAlex): Numerical methods for differential equations; Dynamics and Control of Mechanical Systems
TL;DR: This paper reviews recent results on the extension of Hame’s formalism to infinite-dimensional mechanical systems and to variational integrators and considers applications to the dynamics and numerical integration of systems with velocity constraints. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2015 article

The Helmholtz Conditions and the Method of Controlled Lagrangians

INVERSE PROBLEM OF THE CALCULUS OF VARIATIONS: LOCAL AND GLOBAL THEORY, pp. 1–29.

By: A. Bloch*, D. Krupka & D. Zenkov n

topics (OpenAlex): Control and Stability of Dynamical Systems; Dynamics and Control of Mechanical Systems; Modeling and Simulation Systems
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Source: Web Of Science
Added: August 6, 2018

2015 book

The inverse problem of the calculus of variations: Local and global theory

Dmitry Zenkov

topics (OpenAlex): Mathematical and Theoretical Analysis
Source: NC State University Libraries
Added: August 6, 2018

2014 journal article

The geometry and integrability of the Suslov problem

JOURNAL OF MATHEMATICAL PHYSICS, 55(11).

By: O. Fernandez *, A. Bloch* & D. Zenkov n

topics (OpenAlex): Control and Dynamics of Mobile Robots; Advanced Differential Geometry Research; Robotic Path Planning Algorithms
Source: Web Of Science
Added: August 6, 2018

2012 journal article

A Fiber Bundle Approach to the Transpositional Relations in Nonholonomic Mechanics

JOURNAL OF NONLINEAR SCIENCE, 22(4), 431–461.

By: J. Maruskin*, A. Bloch*, J. Marsden* & D. Zenkov n

author keywords: Geometric mechanics; Constrained dynamics; Variational principles
topics (OpenAlex): Control and Dynamics of Mobile Robots; Dynamics and Control of Mechanical Systems; Advanced Differential Geometry Research
Source: Web Of Science
Added: August 6, 2018

2012 conference paper

Hamel's formalism and variational integrators on a sphere

2012 ieee 51st annual conference on decision and control (cdc), 7504–7510.

By: D. Zenkov n, M. Leok * & A. Bloch*

topics (OpenAlex): Dynamics and Control of Mechanical Systems; Numerical methods for differential equations; Modeling and Simulation Systems
TL;DR: Hamel's formalism utilizes redundant coordinates in order to eliminate multiple charts on the configuration space as well as nonphysical artificial singularities induced by local coordinates, while keeping the minimal possible degree of redundancy and avoiding integration of differential-algebraic equations. (via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018

2011 journal article

Nonholonomic Hamilton-Jacobi theory via Chaplygin Hamiltonization

JOURNAL OF GEOMETRY AND PHYSICS, 61(8), 1263–1291.

By: T. Ohsawa *, O. Fernandez *, A. Bloch * & D. Zenkov n

author keywords: Nonholonomic mechanics; Hamilton-Jacobi theory; Reduction; Hamiltonization
topics (OpenAlex): Control and Dynamics of Mobile Robots; Advanced Differential Geometry Research
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Quasivelocities and symmetries in non-holonomic systems

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 24(2), 187–222.

By: A. Bloch*, J. Marsden* & D. Zenkov n

author keywords: Hamel equations; momentum; symmetry
topics (OpenAlex): Control and Dynamics of Mobile Robots; Quantum chaos and dynamical systems; Nonlinear Waves and Solitons
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15. Life on Land (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

2007 journal article

Matching and stabilization of discrete mechanical systems

PAMM, 7(1), 1030603–1030604.

By: A. Bloch*, M. Leok *, J. Marsden* & D. Zenkov n

topics (OpenAlex): Control and Stability of Dynamical Systems; Modeling and Simulation Systems; Dynamics and Control of Mechanical Systems
Source: Crossref
Added: August 28, 2020

2005 journal article

Discrete nonholonomic LL systems on Lie groups

NONLINEARITY, 18(5), 2211–2241.

By: Y. Fedorov* & D. Zenkov n

topics (OpenAlex): Control and Dynamics of Mobile Robots; Dynamics and Control of Mechanical Systems; Fluid Dynamics Simulations and Interactions
Source: Web Of Science
Added: August 6, 2018

2003 journal article

Invariant measures of nonholonomic flows with internal degrees of freedom

NONLINEARITY, 16(5), 1793–1807.

By: D. Zenkov n & A. Bloch *

topics (OpenAlex): Control and Dynamics of Mobile Robots; Advanced Differential Equations and Dynamical Systems; Advanced Differential Geometry Research
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UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions (OpenAlex)
Source: Web Of Science
Added: August 6, 2018

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