Generalized Methods of Analytical Dynamics

2009 ◽  
pp. 207-287
Keyword(s):  
Analytical Dynamics

SINGULARITY, SWITCHABILITY AND BIFURCATIONS IN A 2-DOF, PERIODICALLY FORCED, FRICTIONAL OSCILLATOR

2013 ◽  
Vol 23 (03) ◽  
pp. 1330009 ◽  
Author(s):  
ALBERT C. J. LUO ◽  
MOZHDEH S. FARAJI MOSADMAN
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Degrees Of Freedom ◽  
Eigenvalue Analysis ◽  
Analytical Dynamics ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper, the analytical dynamics for singularity, switchability, and bifurcations of a 2-DOF friction-induced oscillator is investigated. The analytical conditions of the domain flow switchability at the boundaries and edges are developed from the theory of discontinuous dynamical systems, and the switchability conditions of boundary flows from domain and edge flows are presented. From the singularity and switchability of flow to the boundary, grazing, sliding and edge bifurcations are obtained. For a better understanding of the motion complexity of such a frictional oscillator, switching sets and mappings are introduced, and mapping structures for periodic motions are adopted. Using an eigenvalue analysis, the stability and bifurcation analysis of periodic motions in the friction-induced system is carried out. Analytical predictions and parameter maps of periodic motions are performed. Illustrations of periodic motions and the analytical conditions are completed. The analytical conditions and methodology can be applied to the multi-degrees-of-freedom frictional oscillators in the same fashion.

Is analytical dynamics a theoretical or an experimental science?

2005 ◽  
Vol 63 (5-7) ◽  
pp. 692-698
Author(s):  
Firdaus E. Udwadia ◽  
Robert E. Kalaba ◽  
Yueyue Fan
Keyword(s):  
Analytical Dynamics ◽  
Experimental Science

Analytical Dynamics of Unrooted Multibody-Systems With Symmetries

1998 ◽  
Author(s):  
Felix M. J. Pfister ◽  
Sunil K. Agrawal
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Analytical Dynamics ◽  
Geometric Properties

Abstract The objectives of this paper are to (i) exploit the structure of Euler-Liouville equations for multibody systems and separate the external and internal aspects of motion, (ii) specialize these equations to systems with special mass and geometric properties such as holonomoids and orthotropoids, (iii) apply the results to special orthotropoids, the spheroidal linkages of Wohlhart, and write their equations of motion in a simple and elegant manner.

scholarly journals Formal Foundation of Analytical Dynamics Based on the Contact Structure

1970 ◽  
Vol 37 ◽  
pp. 107-119
Author(s):  
Minoru Kurita
Keyword(s):  
Dynamical Systems ◽  
Contact Structure ◽  
The Other ◽  
Analytical Dynamics ◽  
Finsler Spaces ◽  
Systematic Treatment ◽  
Bundle Structure

A systematic treatment of analytical dynamics was given by E. Cartan in [1], where the 1-form plays the fundamental role. We give here a further investigation. One of our main purposes is to clarify relations between dynamical systems and Finsler spaces and the other is to formulate an intrinsic bundle structure of the systems. This paper is closely related to my previous papers [4] [5].

New Formulations on Acceleration Energies in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 43-48
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Fast Moving ◽  
Mechanical Systems ◽  
Higher Order ◽  
Dynamic Study ◽  
Final Part ◽  
Transient Phase ◽  
Dynamic Aspect ◽  
Analytical Dynamics ◽  
Time Variations

This paper presents new formulations on the higher order motion energies that are applied in the dynamic study of multibody mechanical systems in keeping with the researches of the main author. The analysis performed in this paper highlights the importance of motion energies of higher order in the study of dynamic behavior of fast moving mechanical systems, as well as in transient phase of motion. In these situations, are developed higher order time variations of the linear and angular accelerations. As a result, in the final part of this paper is presented an application that emphasizes this essential dynamic aspect regarding the higher order acceleration energies.

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