scholarly journals Noncommutative Lagrange Mechanics

2008 ◽  
Author(s):  
Denis Kochan
Keyword(s):  
Lagrange Mechanics

scholarly journals Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics

Open Physics ◽  
2011 ◽  
Vol 9 (5) ◽  
Author(s):  
Dumitru Baleanu ◽  
Sergiu Vacaru
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Geometric Mechanics ◽  
Fractional Dynamics ◽  
Constant Matrix ◽  
Curve Flows ◽  
Physical Interactions ◽  
Nonholonomic Manifolds ◽  
Lagrange Mechanics ◽  
Fractional Gravity

AbstractWe present a study of fractional configurations in gravity theories and Lagrange mechanics. The approach is based on a Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists of a proof that, for corresponding classes of nonholonomic distributions, a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.

New classical Hamilton-Lagrange mechanics for open systems

1979 ◽  
Vol 20 (6) ◽  
pp. 2370-2380 ◽  
Author(s):  
Robert Cawley
Keyword(s):  
Open Systems ◽  
Lagrange Mechanics

scholarly journals Spherical Pendulum Small Oscillations for Slewing Crane Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alexander V. Perig ◽  
Alexander N. Stadnik ◽  
Alexander I. Deriglazov
Keyword(s):  
Reference Frame ◽  
Natural Frequencies ◽  
Computational Results ◽  
Numerical Estimation ◽  
Spherical Pendulum ◽  
Lagrange Equations ◽  
Uniform Rotation ◽  
Small Oscillations ◽  
Mechanical Interpretation ◽  
Lagrange Mechanics

The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies’ problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown.

SUBALGEBRAS OF THE LIE ALGEBRA R6 AND THEIR APPLICATIONS

2007 ◽  
Vol 21 (22) ◽  
pp. 3809-3824 ◽  
Author(s):  
YU-FENG ZHANG ◽  
EN-GUI FAN
Keyword(s):  
Lie Algebra ◽  
Hamiltonian Systems ◽  
Hamiltonian Structure ◽  
Hamiltonian Structures ◽  
Soliton Theory ◽  
Soliton Equations ◽  
Integrable Couplings ◽  
Potential Component ◽  
Lagrange Mechanics ◽  
Important Significance

As we all know, the Hamiltonian systems are the same describing forms as Newton mechanics and Lagrange mechanics. Therefore, researching for a new Hamiltonian structure of the soliton equations has important significance. In the paper, firstly, with the help of the Lie algebra R6, a few types of subalgebras are constructed, from which the corresponding equivalent tensor systems are given. For their applications, two integrable couplings hierarchies along with the multi-potential component functions generated from the soliton theory and the Virasoro symmetric algebra are obtained. Secondly, the Hamiltonian structures of the above integrable couplings are worked out, which may become another describing expression for the Newton and Lagrange mechanics. In particular, one of the integrable couplings presented above reduces to the famous AKNS hierarchy of soliton equations.

Time-Integral Variational Principles for Nonlinear Nonholonomic Systems

1997 ◽  
Vol 64 (4) ◽  
pp. 985-991 ◽  
Author(s):  
J. G. Papastavridis
Keyword(s):  
Multibody Dynamics ◽  
Variational Principles ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Comprehensive Treatment ◽  
Time Integral ◽  
Velocity Constraints ◽  
Definition Of ◽  
Formal Application ◽  
Lagrange Mechanics

This is a comprehensive treatment of the time-integral variational “principles” of mechanics for systems subject to general nonlinear and possibly nonholonomic velocity constraints (i.e., equations of the form f(t, q, q˙) = 0, where t = time and q/q˙ = Lagrangean coordinates/velocities), in general nonlinear nonholonomic coordinates. The discussion is based on the Maurer-Appell-Chetaev-Hamel definition of virtual displacements and subsequent formulation of the corresponding nonlinear transitivity (or transpositional) equations. Also, a detailed analysis of the latter supplies a hitherto missing clear geometrical interpretation of the well-known discrepancies between the equations of motion obtained by formal application of the calculus of variations (mathematics) and those obtained from the principle of d’Alembert-Lagrange (mechanics); i.e., admissible adjacent paths (mathematics) are locally nonvirtual; and adjacent paths built from locally virtual displacements (mechanics) are not admissible. (These discrepancies, although revealed about a century ago, for systems under Pfaffian constraints (Hertz (1894), Ho¨lder (1896), Hamel (1904), Maurer (1905), and others) seem to be relatively unknown and/or misunderstood among today’s engineers.) The discussion includes all relevant nonlinear nonholonomic variational principles, in both unconstrained and constrained forms of their integrands, and the corresponding nonlinear nonholonomic equations of motion. Such time-integral formulations are useful both conceptually and computationally (e.g., multibody dynamics).

Lagrange Mechanics

2016 ◽  
pp. 1-99
Author(s):  
Wolfgang Nolting
Keyword(s):  
Lagrange Mechanics

On the Fractional Hamilton and Lagrange Mechanics

2012 ◽  
Vol 51 (9) ◽  
pp. 2909-2916 ◽  
Author(s):  
Alireza Khalili Golmankhaneh ◽  
Ali Moslemi Yengejeh ◽  
Dumitru Baleanu
Keyword(s):  
Lagrange Mechanics

scholarly journals Cálculo variacional e aplicações

2020 ◽  
Vol 42 ◽  
pp. 50
Author(s):  
Jardel Carpes Meurer ◽  
Lucas Tavares Cardoso ◽  
Glauber Rodrigues de Quadros
Keyword(s):  
Sufficient Conditions ◽  
Variational Calculus ◽  
Necessary And Sufficient Conditions ◽  
Stationary Points ◽  
Second Variation ◽  
Rigorous Treatment ◽  
Necessary And Sufficient ◽  
First And Second Variation ◽  
Lagrange Mechanics

This paper consists of a brief review and introduction to the main concepts of Classic Variational Calculus. Starting from thedefinitions of the concepts of first and second variation of a functional, we present a mathematically rigorous treatment for theVariational Calculus, establishing necessary and sufficient conditions for obtaining extrema. In this context, the notion of conjugatepoints is introduced, which is fundamental for the classification of weak extrema. Some simple and enlightening examples are dealtwith throughout the paper. Strong extrema are characterized and sufficient conditions for their occurrence are given. The paperconcludes with a brief application to Lagrange mechanics, showing the existence of actions whose stationary points are saddlepoints instead of minima.

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