Lagrangian Systems with a Finite Number of Degrees of Freedom

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.

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On the Dynamic Isotropy of Mechanisms With Two Degrees of Freedom

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2005-85023 ◽

2005 ◽

Author(s):

Raffaele Di Gregorio ◽

Alessandro Cammarata ◽

Rosario Sinatra

Keyword(s):

Finite Number ◽

Degrees Of Freedom ◽

Point Of View ◽

Closed Curves ◽

Special Cases ◽

Dynamic Performances ◽

Definition Of ◽

Geometric Locus

The comparison of mechanisms with different topology or with different geometry, but with the same topology, is a necessary operation during the design of a machine sized for a given task. Therefore, tools that evaluate the dynamic performances of a mechanism are welcomed. This paper deals with the dynamic isotropy of 2-dof mechanisms starting from the definition introduced in a previous paper. In particular, starting from the condition that identifies the dynamically isotropic configurations, it shows that, provided some special cases are not considered, 2-dof mechanisms have at most a finite number of isotropic configurations. Moreover, it shows that, provided the dynamically isotropic configurations are excluded, the geometric locus of the configuration space that collects the points associated to configurations with the same dynamic isotropy is constituted by closed curves. This results will allow the classification of 2-dof mechanisms from the dynamic-isotropy point of view, and the definition of some methodologies for the characterization of the dynamic isotropy of these mechanisms. Finally, examples of applications of the obtained results will be given.

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Full Control of Virtual Objects Manipulation Based on the Images of Real Ones

International Journal of Virtual Reality ◽

10.20870/ijvr.2011.10.3.2820 ◽

2011 ◽

Vol 10 (3) ◽

pp. 51-60

Author(s):

Brahim Nini

Keyword(s):

Finite Number ◽

Degrees Of Freedom ◽

Moving Object ◽

Real Object ◽

Virtual Object ◽

Analytical Geometry ◽

Six Degrees Of Freedom ◽

Virtual Objects ◽

Simulation Process ◽

Full Control

This work deals with the virtual manipulation of a real object through its images. The results presented in this paper give a movie-based solution to the simulation process. We show how the simulation of infinite virtual views of a moving object can be reached using a finite number of object's taken images stored in an organized way. The basis of this solution is an analytical geometry-based method that links explicit applied user's actions, resulting in an object's views change, and images that match the best such views. This paper presents an overall solution for these three intertwined parts of the virtual manipulation that involves six degrees of freedom. Hence, a user is able to freely manipulate a virtual object in a scene in whatever manner s/he likes. In this case, the actions are transformed into rotations and/or translations which lead to some changes in object's appearance, both covered by two viewing features: zoom and/or rotations

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Structures with a Finite Number of Dynamic Degrees of Freedom

Studies in Applied Mechanics - Strength of Structural Elements ◽

10.1016/b978-0-444-98763-1.50017-2 ◽

1991 ◽

pp. 231-245

Keyword(s):

Finite Number ◽

Degrees Of Freedom

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Oscillations of a statically indeterminate system with a finite number of degrees of freedom (the experience with the application of mathematical packages in the technical university course of mechanics)

MATEC Web of Conferences ◽

10.1051/matecconf/201821117008 ◽

2018 ◽

Vol 211 ◽

pp. 17008

Author(s):

Alexander Kuznechikov ◽

Dmitry Levitskiy ◽

Sergey Zotov

Keyword(s):

Finite Number ◽

Degrees Of Freedom ◽

Bending Moment ◽

Beam Length ◽

Single Moments ◽

Concentrated Masses ◽

Technical University ◽

University Course ◽

Graphic Methods

Symbolic mathematics packages give the opportunity to execute the difficult symbolic transformations with use of computer, abandoning graphic methods. The resilient weightless beam fixed by resilient links and carrying two concentrated masses is considered. Instead of building the bending moment diagram and the later use of Vereshchagin's method for disclosure of static indeterminacy, the equation of distribution of the bending and single moments along the beam length is written, and Mohr's integral is calculated.

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