American Journal of Mechanical Engineering
ISSN (Print): 2328-4102 ISSN (Online): 2328-4110 Website: http://www.sciepub.com/journal/ajme Editor-in-chief: Kambiz Ebrahimi, Dr. SRINIVASA VENKATESHAPPA CHIKKOL
Open Access
Journal Browser
Go
American Journal of Mechanical Engineering. 2014, 2(7), 178-183
DOI: 10.12691/ajme-2-7-1
Open AccessArticle

Theoretical Basics of Geometric Mechanics and Differential Geometry

Tomáš Lipták1, , Alexander Gmiterko1, Michal Kelemen1, Ivan Virgala1, Erik Prada1 and František Menda2

1Department of Mechatronics, Faculty of Mechanical Engineering, Technical University of Košice, Košice, Slovakia

2Department of Applied mechanics and mechanical engineering, Faculty of Mechanical Engineering, Technical University of Košice, Košice, Slovakia

Pub. Date: September 30, 2014

Cite this paper:
Tomáš Lipták, Alexander Gmiterko, Michal Kelemen, Ivan Virgala, Erik Prada and František Menda. Theoretical Basics of Geometric Mechanics and Differential Geometry. American Journal of Mechanical Engineering. 2014; 2(7):178-183. doi: 10.12691/ajme-2-7-1

Abstract

In this article are described the theoretical basics of geometric mechanics and differential geometry. In the introductory part of article, basic notions are explained that frequently occurring in the concept of geometric mechanics. It contains the basic building blocks that are used to create the configuration spaces. Further were described groups applied to the kinematic description of structure and to control in area of robotics and the fiber bundle that represents the configuration space for mechanical systems. The last part deals with the actions, such as the left and right action, lifted action and adjoint action.

Keywords:
configuration configuration space left and right action lifted action adjoint action

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Elie A. Shammas, Generalized Motion Planning for Underactuated Mechanical Systems, The dissertation thesis,Carnegie Mellon University, Pittsburgh, March 20, 2006.
 
[2]  Ross L. Hatton, Howie Choset, An Introduction to Geometric Mechanics and Differential Geometry, December 6, 2011.
 
[3]  James Patrick Ostrowski, The Mechanics and Control of Undulatory Robotic Locomotion, The dissertation thesis, California Institute of Technology Pasadena, September 19, 1995.
 
[4]  Silvia Ebetiuc, Staab Haraldw, “Applying Differential Geometry to Kinematic Modeling in mobile Robotics”, 2005 WSEAS Int. Conf. on Dynamical systems and control, Italy, November 2-4, 2005,106-112.
 
[5]  Ross L. Hatton, Howie Choset, “Connection Vector Fields for Underactuated Systems”, Proceedings of the 2nd Biennial IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics Scottsdale, USA, October 19-22, 2008, 451-456.
 
[6]  Elie Shammas, Klaus Achmidt, Howie Choset, “Natural Gait Generation Techniques for Multi-bodied Isolated Mechanical Systems”, Proceedings of the 2005 IEEE International Conference on Robotics and Automation Barcelona, Spain, April 2005, 3664-3669.
 
[7]  Ross L. Hatton, Howie Choset, “Optimizing Coordinate Choice for Locomoting Systems”, 2010 IEEE International Conference on Robotics and Automation Anchorage Convention District, USA, May 3-8, 2010, 4493-4498.