Udwadia–Kalaba Equation for Constrained Mechanical Systems: Formulation and Applications
Autor: | Ye-Hwa Chen, Han Zhao, Xiao-Min Zhao, Fang-Fang Dong |
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Rok vydání: | 2018 |
Předmět: |
Nonholonomic system
0209 industrial biotechnology Holonomic lcsh:Mechanical engineering and machinery Mechanical Engineering lcsh:Ocean engineering Gauss Equations of motion 02 engineering and technology Moore–Penrose inverse Industrial and Manufacturing Engineering Projection (linear algebra) Mechanical system Constraint 020303 mechanical engineering & transports 020901 industrial engineering & automation 0203 mechanical engineering Analytical mechanics lcsh:TC1501-1800 Applied mathematics lcsh:TJ1-1570 Udwadia–Kalaba Equation Representation (mathematics) Mathematics |
Zdroj: | Chinese Journal of Mechanical Engineering, Vol 31, Iss 1, Pp 1-14 (2018) |
ISSN: | 2192-8258 1000-9345 |
Popis: | There are many achievements in the field of analytical mechanics, such as Lagrange Equation, Hamilton’s Principle, Kane’s Equation. Compared to Newton–Euler mechanics, analytical mechanics have a wider range of applications and the formulation procedures are more mathematical. However, all existing methods of analytical mechanics were proposed based on some auxiliary variables. In this review, a novel analytical mechanics approach without the aid of Lagrange’s multiplier, projection, or any quasi or auxiliary variables is introduced for the central problem of mechanical systems. Since this approach was firstly proposed by Udwadia and Kalaba, it was called Udwadia–Kalaba Equation. It is a representation for the explicit expression of the equations of motion for constrained mechanical systems. It can be derived via the Gauss’s principle, d’Alembert’s principle or extended d’Alembert’s principle. It is applicable to both holonomic and nonholonomic equality constraints, as long as they are linear with respect to the accelerations or reducible to be that form. As a result, the Udwadia–Kalaba Equation can be applied to a very broad class of mechanical systems. This review starts with introducing the background by a brief review of the history of mechanics. After that, the formulation procedure of Udwadia–Kalaba Equation is given. Furthermore, the comparisons of Udwadia–Kalaba Equation with Newton–Euler Equation, Lagrange Equation and Kane’s Equation are made, respectively. At last, three different types of examples are given for demonstrations. |
Databáze: | OpenAIRE |
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