GEOMETRICAL PARTICLE MODELS ON 3D LIGHTLIKE CURVES

2006 ◽  
Vol 21 (40) ◽  
pp. 3039-3048 ◽  
Author(s):  
RONGPEI HUANG ◽  
CAISHENG LIAO
Keyword(s):  
Conservation Laws ◽  
Mechanical Systems ◽  
Motion Equation ◽  
Cartan Curvature ◽  
Special Case

The (2+1)-dimensional mechanical systems associated with lightlike curves are considered. We studied the action whose Lagrangian depends quadratically on the Cartan curvature (torsion). Some conservation laws are given and the motion equation for a special case is completely solved by using geometrical methods.

scholarly journals Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1077
Author(s):  
Yarema A. Prykarpatskyy
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Structure ◽  
Necessary Condition ◽  
Type Representation ◽  
Infinite Hierarchy ◽  
Polynomial Coefficients ◽  
Kdv Type Equations ◽  
Special Case

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

scholarly journals Quadratic integrals of a multi-scalar cosmological model

2020 ◽  
Vol 35 (10) ◽  
pp. 2050068 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Scalar Field ◽  
Cosmological Model ◽  
Conservation Laws ◽  
Analytical Solutions ◽  
Physical System ◽  
Noether Symmetries ◽  
Spatial Curvature ◽  
Special Case ◽  
Friedmann Robertson Walker ◽  
Field Integral

In the context of Friedmann–Robertson–Walker (FRW) spacetime with zero spatial curvature, we consider a multi-scalar tensor cosmology model under the pretext of obtaining quadratic conservation laws. We propose two new interaction potentials of the scalar field. Integral to this task is the existence of dynamical Noether symmetries which are Lie–Bäcklund transformations of the physical system. Finally, analytical solutions of the field are found corresponding to each new model. In one of the models, we find that the scale factor mimics [Formula: see text]-cosmology in a special case.

scholarly journals Lagrangians for Damped Linear Multi-Degree-of-Freedom Systems

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Hancheol Cho
Keyword(s):  
Inverse Problem ◽  
Conservation Laws ◽  
Degree Of Freedom ◽  
Linear Vibration ◽  
Gyroscopic System ◽  
Simple Manner ◽  
Vibration Theory ◽  
Stiffness Matrices ◽  
Two Degree Of Freedom ◽  
Special Case

This paper deals with finding Lagrangians for damped, linear multi-degree-of-freedom systems. New results for such systems are obtained using extensions of the results for single and two degree-of-freedom systems. The solution to the inverse problem for an n-degree-of-freedom linear gyroscopic system is obtained as a special case. Multi-degree-of-freedom systems that commonly arise in linear vibration theory with symmetric mass, damping, and stiffness matrices are similarly handled in a simple manner. Conservation laws for these damped multi-degree-of-freedom systems are found using the Lagrangians obtained and several examples are provided.

SYMMETRY ANALYSIS FOR A SEVENTH-ORDER GENERALIZED KdV EQUATION AND ITS FRACTIONAL VERSION IN FLUID MECHANICS

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050044 ◽  
Author(s):  
GANGWEI WANG ◽  
YIXING LIU ◽  
YANBIN WU ◽  
XING SU
Keyword(s):  
Fluid Mechanics ◽  
Conservation Laws ◽  
Kdv Equation ◽  
Differential Invariants ◽  
Potential Equation ◽  
Generalized Kdv Equation ◽  
Seventh Order ◽  
Special Case ◽  
Symmetry Method ◽  
Similarity Reductions

KdV types of equations play an important role in many fields. In this paper, we study a seventh-order generalized KdV equation and its fractional version in fluid mechanics using symmetry. From symmetry, the corresponding vectors, symmetry reduction and conservation laws are derived. Potential equation is also analyzed with regard to the symmetry method. Based on the symmetry, similarity reductions and conservation laws are also presented. Subsequently, the fractional version of the seventh-order KdV equation is discussed. Finally, differential invariants are constructed for the special case.

Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part I: Mechanics of Contact and Friction

1994 ◽  
Vol 47 (7) ◽  
pp. 209-226 ◽  
Author(s):  
R. A. Ibrahim
Keyword(s):  
Friction Force ◽  
Normal Load ◽  
Mechanical Systems ◽  
Static Friction ◽  
Friction Laws ◽  
Sliding Surfaces ◽  
Metal Metal ◽  
Satisfactory Method ◽  
Friction Induced Vibration ◽  
Special Case

Friction force between sliding surfaces arises due to varied and complex mechanisms and can be responsible for undesirable dynamic characteristics in many mechanical systems. Controversies over the theory of friction have been reported in the literature. Friction laws are phenomenological in charcacter since they are based on observable and measurable quantities. The mechanics of contact and friction in metal-metal and elastomer-metal contact surfaces are reviewed. Unfortunately, there is no satisfactory method capable of determining or measuring the area of contact between sliding bodies. Both dry friction and lubricated friction are considered. The modeling of the friction force in mechanical systems depends on several factors. These include the material properties and geometry of the sliding surfaces, surface roughness, surface chemistry, sliding speed, temperature, and normal load. Other factors include the effect of normal and tangential vibrations on the static friction. Here the static friction is considered as a special case of kinetic friction. This background is essential for dynamicists studying friction-induced vibration, chatter, squeal and chaos topics which will be presented in the second part.

scholarly journals Nonlinearly Self-Adjoint, Conservation Laws and Solutions for a Forced BBM Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Maria Luz Gandarias ◽  
Chaudry Masood Khalique
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
General Theorem ◽  
Partial Differential ◽  
Symmetry Generators ◽  
Special Case ◽  
Bbm Equation

We study a forced Benjamin-Bona-Mahony (BBM) equation. We prove that the equation is not weak self-adjoint; however, it is nonlinearly self-adjoint. By using a general theorem on conservation laws due to Nail Ibragimov and the symmetry generators, we find conservation laws for these partial differential equations without classical Lagrangians. We also present some exact solutions for a special case of the equation.

Bi-Mobile Leg Mechanism Dynamic Model

2015 ◽  
Vol 811 ◽  
pp. 273-278
Author(s):  
Adriana Comanescu ◽  
Dinu Comanescu ◽  
Ileana Dugaesescu ◽  
Liviu Marian Ungureanu
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Model ◽  
Dynamic Models ◽  
Mechanical Systems ◽  
Motion Equation ◽  
Active Group ◽  
Mobile Platform ◽  
Robot Arms ◽  
Classic Theory

The paper brings into attention the dynamic analysis of a bi-mobile mechanism selected from the literature and used for the leg of a mobile platform. Two solutions of bi-mobile mechanical systems applied in such purpose are found. In the classic theory of mechanisms the dynamic models for the mono-mobile mechanisms are known. Through the motion equation these put into evidence the variation of the reduced moment or reduced force applied to the input link for an entire cycle in the permanent regime functioning of the mechanism. In the case of the leg bi-mobile mechanism the approached dynamic model is based on the bi-mobile RTRTR active group firstly applied for a real technique solution in robotics. The mechanism may be also used for robot arms.

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