scholarly journals Lagrangian mechanics, Gauss’ principle, quadratic programming, and generalized inverses: new equations for non-holonomically constrained discrete mechanical systems

1994 ◽  
Vol 52 (2) ◽  
pp. 229-241 ◽  
Author(s):  
Robert E. Kalaba ◽  
Firdaus E. Udwadia
Keyword(s):  
Quadratic Programming ◽  
Mechanical Systems ◽  
Generalized Inverses ◽  
Lagrangian Mechanics ◽  
Discrete Mechanical Systems ◽  
Gauss Principle

Dynamics of Mechanical Systems Solved by Quadratic Programming

1994 ◽  
Author(s):  
Deshi Wang ◽  
Xin Chen ◽  
Xindu Chen ◽  
Jun Yu ◽  
Ji Zhou
Keyword(s):  
Quadratic Programming ◽  
Software Package ◽  
Dynamic Models ◽  
Mechanical Systems ◽  
Complex Motion ◽  
Cad Systems ◽  
Gauss Principle ◽  
Quadratic Programming Problems ◽  
Dynamical Control ◽  
Analytical Dynamic

Abstract A new method for dynamics of mechanical systems has been established and the new use of the optimum software has been shown in this paper. Gauss’ principle in the theory of mechanics has been employed to transform the dynamical control and simulation into the quadratic programming problems, which makes it possible that the optimum software developed in CAD systems is applied to obtain the dynamics of mechanical systems. Such a method is significant for systems which contain complex motion and constraints, since there is no longer necessity of reducing the analytical dynamic models, which are tedious and even impossible to obtain. Morever, it gives a new way of applying the optimum software package. The dynamics of a robot with sliding and revolving joints has been demonstrated in detail.

scholarly journals Matching and stabilization of discrete mechanical systems

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1030603-1030604 ◽  
Author(s):  
Anthony M. Bloch ◽  
Melvin Leok ◽  
Jerrold E. Marsden ◽  
Dmitry V. Zenkov
Keyword(s):  
Mechanical Systems ◽  
Discrete Mechanical Systems

Mechanical Systems With Nonideal Constraints: Explicit Equations Without the Use of Generalized Inverses

2004 ◽  
Vol 71 (5) ◽  
pp. 615-621 ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Robert E. Kalaba ◽  
Phailaung Phohomsiri
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Generalized Inverses ◽  
Explicit Equations Of Motion

In this paper we obtain the explicit equations of motion for mechanical systems under nonideal constraints without the use of generalized inverses. The new set of equations is shown to be equivalent to that obtained using generalized inverses. Examples demonstrating the use of the general equations are provided.

Explicit Equations of Motion for Mechanical Systems With Nonideal Constraints

2000 ◽  
Vol 68 (3) ◽  
pp. 462-467 ◽  
Author(s):  
F. E. Udwadia ◽  
R. E. Kalaba
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Lagrangian Mechanics ◽  
Constrained Motion ◽  
Constraint Forces ◽  
Constrained Mechanical Systems ◽  
Lagrangian Formulations ◽  
Explicit Equations Of Motion ◽  
D'alembert's Principle

Since its inception about 200 years ago, Lagrangian mechanics has been based upon the Principle of D’Alembert. There are, however, many physical situations where this confining principle is not suitable, and the constraint forces do work. To date, such situations are excluded from general Lagrangian formulations. This paper releases Lagrangian mechanics from this confinement, by generalizing D’Alembert’s principle, and presents the explicit equations of motion for constrained mechanical systems in which the constraints are nonideal. These equations lead to a simple and new fundamental view of Lagrangian mechanics. They provide a geometrical understanding of constrained motion, and they highlight the simplicity with which Nature seems to operate.

The Computer Aided Passive Reduction of Vibration to Desired Vibration Amplitude

2013 ◽  
Vol 430 ◽  
pp. 342-350 ◽  
Author(s):  
Andrzej Dymarek ◽  
Tomasz Dzitkowski
Keyword(s):  
Vibration Amplitude ◽  
Vibration Reduction ◽  
Synthesis Method ◽  
Mechanical Systems ◽  
Synthesis Methods ◽  
Discrete Mechanical Systems ◽  
Computer Aided

The paper presents the problem of vibration reduction in designed discrete mechanical systems. The passive vibration reduction based on the synthesis method by using the Synteza application. The presented application has been developed by performing the algorithmization of formulated and formalized synthesis methods provided by the authors.

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