Integration of the equations of motion of nonholonomic systems with a partial dissipation of energy

1976 ◽  
Vol 12 (8) ◽  
pp. 853-856
Author(s):  
N. V. Nikitina
Keyword(s):  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Partial Dissipation ◽  
Dissipation Of Energy

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

Motion Tracking Control Design for Wheeled Mobile Systems

2008 ◽  
Author(s):  
Elz˙bieta Jarze˛bowska
Keyword(s):  
Tracking Control ◽  
Motion Tracking ◽  
Controller Design ◽  
Control Strategies ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Point Of View ◽  
Mobile Systems ◽  
Task Constraints ◽  
Nonlinear Control Theory

The paper presents a model-based tracking control strategy design for wheeled mobile systems (WMS). The strategy enables tracking a variety of WMS motions that come from task specifications and control or design requirements put on them. From the point of view of mechanics and derivation of equations of motion, the WMS belongs to one class of first order nonholonomic systems. From the perspective of nonlinear control theory, the WMS differ and may not be approached by the same control strategies and algorithms, e.g. some of them may be controlled at the kinematic level and the other at the dynamic level only. The strategy we propose is based on a modeling control oriented framework. It serves a unification of the WMS modeling and a subsequent controller design with no regard whether a specific WMS is fully actuated, underactuated, or constrained by the task constraints.

On First-Order Decoupling of Equations of Motion for Constrained Dynamical Systems

1993 ◽  
Author(s):  
Timothy A. Loduha ◽  
Bahram Ravani
Keyword(s):  
Dynamical Systems ◽  
Equations Of Motion ◽  
Relaxation Method ◽  
Nonholonomic Systems ◽  
Dynamical Equations ◽  
Generalized Coordinates ◽  
First Order ◽  
Constraint Relaxation ◽  
Constrained Dynamical Systems ◽  
Generalized Coordinate

Abstract In this paper we present a method for obtaining first-order decoupled equations of motion for multi-rigid body systems. The inherent flexibility in choosing generalized velocity components as a function of generalized coordinates is used to influence the structure of the resulting dynamical equations. Initially, we describe how a congruency transformation can be formed that represents the transformation between generalized velocity components and generalized coordinate derivatives. It is shown that the proper choice for the congruency transformation will insure generation of first-order decoupled equations of motion for holonomic systems. In the case of nonholonomic systems, or more complex dynamical systems, where the appropriate congruency transformation may be difficult to obtain, we present a constraint relaxation method based on the use of orthogonal complements. The results are illustrated using several examples. Finally, we discuss numerical implementation of congruency transformations to achieve first-order decoupled equations for simulation purposes.

An example of minimum energy dissipation in viscous flow

1959 ◽  
Vol 251 (1267) ◽  
pp. 550-564 ◽  
Keyword(s):  
Maximum Rate ◽  
Equations Of Motion ◽  
Minimum Energy ◽  
Vertical Tube ◽  
Approximate Theory ◽  
Eccentricity Ratio ◽  
Dissipation Of Energy ◽  
Rapid Fall ◽  
The Times ◽  
Minimum Energy Dissipation

An approximate theory is developed to describe the behaviour of a heavy ball passing slowly down a vertical tube having a diameter only slightly exceeding the diameter of the ball, and filled with a viscous fluid. It is shown that according to this theory the equations of motion can be satisfied when the ball takes up any degree of eccentricity in the tube and that any given eccentricity requires a particular velocity of rotation about a horizontal axis. It is found that the eccentricity ratio corresponding to minimum dissipation of energy for given velocity of descent (i.e. to maximum rate of fall for a given weight of ball) is about 0.98, and that the velocity is then rather more than twice the velocity corresponding to zero eccentricity. Experiments are described in which it was shown that provided conditions were such that the ball descended very slowly, the minimum dissipation prediction was verified within the expected accuracy, but that for larger clearances and more rapid fall the predicted angular velocity and eccentricity were not achieved within the times for which observation was possible.

Unified Approach for Holonomic and Nonholonomic Systems Based on the Modified Hamilton’s Principle

2009 ◽  
Author(s):  
Keisuke Kamiya ◽  
Junya Morita ◽  
Yutaka Mizoguchi ◽  
Tatsuya Matsunaga
Keyword(s):  
Equations Of Motion ◽  
Time Derivative ◽  
Nonholonomic Systems ◽  
Hamilton’S Principle ◽  
Virtual Power ◽  
Unified Approach ◽  
Hamilton's Principle ◽  
Basic Principles ◽  
Principle Of Virtual Power ◽  
Holonomic And Nonholonomic Systems

As basic principles for deriving the equations of motion for dynamical systems, there are d’Alembert’s principle and the principle of virtual power. From the former Hamilton’s principle and Langage’s equations are derived, which are powerful tool for deriving the equation of motion of mechanical systems since they can give the equations of motion from the scalar energy quantities. When Hamilton’s principle is applied to nonholonomic systems, however, care has to be taken. In this paper, a unified approach for holonomic and nonholonomic systems is discussed based on the modified Hamilton’s principle. In the present approach, constraints for both of the holonomic and nonholonomic systems are expressed in terms of time derivative of the position, and their variations are treated similarly to the principle of virtual power, i.e. time and position are fixed in operation with respect to the variations. The approach is applied to a holonomic and a simple nonholonomic systems.

A Variationally Consistent Approach to Constrained Motion

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
John T. Foster
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
A Priori ◽  
Nonholonomic Systems ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Constrained Motion ◽  
Consistent Approach ◽  
Holonomic And Nonholonomic Systems ◽  
D'alembert's Principle

A variationally consistent approach to constrained rigid-body motion is presented that extends D'Alembert's principle in a way that has a form similar to Kane's equations. The method results in minimal equations of motion for both holonomic and nonholonomic systems without a priori consideration of preferential coordinates.

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