scholarly journals Simulation of an Exoskeleton with a Hybrid Linear Gravity Compensator

2020 ◽  
Vol 24 (3) ◽  
pp. 66-78
Author(s):  
A. E. Karlov ◽  
A. A. Postolny ◽  
A. V. Fedorov ◽  
S. F. Jatsun
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Differential Equations ◽  
Kinematic Model ◽  
Hybrid Approach ◽  
Second Order ◽  
System Parameters ◽  
Second Order Differential Equations ◽  
Gravity Compensator ◽  
Linear Gravity

Purpose of research. Development of a mathematical model of an exoskeleton equipped with a hybrid linear gravity compensator (HLGC), dynamic analysis on the example of a typical exoskeleton application scenario (in the process of lifting a load), obtaining time patterns of changes in system parameters, including electric drive torques allowing assessment of power plan power consumption and energy efficiency. The article deals with the challenging issue of improving the efficiency of the exoskeletal suit by means of HLGC. The use of a hybrid approach makes it possible to increase the efficiency of assisting the exoskeletal suit when performing various technological operations, for example, when lifting a load, when tilting and holding. Methods. When developing a mathematical model, an original approach was used to form the motion trajectory of the exoskeleton sectors during operation, based on the use of seventh-order polynomials. The paper uses a mathematical model represented by a system of second-order differential equations that connects the moments acting on the operator and the exoskeleton, the angular accelerations of the operator's back and the exoskeleton. Results. During numerical simulation, time diagrams of changes in system parameters, angles of rotation of exoskeleton hinges, moments that occur in a hybrid LGC, as well as graphs of current consumption of engines when performing lift and tilt with a load are obtained. Conclusion. In the course of the research, a kinematic model of an exoskeleton suit equipped with a GLGC was developed, second-order differential equations describing the dynamic behavior of the electromechanical system were written, and numerical simulation was performed to estimate the forces and energy consumption in the exoskeleton hinges and the drive of the hybrid linear gravity compensator.

scholarly journals Dynamics of the mathematical model of phase-locked systems with delay

2021 ◽  
Vol 23 (1) ◽  
pp. 28-42
Author(s):  
Sergei S. Mamonov ◽  
Irina V. Ionova ◽  
Anastasiya O. Kharlamova
Keyword(s):  
Mathematical Model ◽  
Comparative Analysis ◽  
Differential Equations ◽  
Limit Cycles ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Self Tuning ◽  
Phase Systems ◽  
Tuning Systems ◽  
The Mathematical Model

In the article, the conditions for the existence of limit cycles of the first kind are obtained for self-tuning systems with delay, which, in turn, determine the conditions for the occurrence of hidden synchronization modes in such systems. The principle of the proof is based on constructing a positively invariant toroidal set using two cylindrical surfaces, whose boundaries are determined by the limit cycles of a system of the second-order differential equations. Using the results obtained in the article for limit cycles, the possibility of using the curvature of the cycle for a comparative analysis of the proximity of the cycles of phase and non-phase systems, as well as for determining the mode of hidden synchronization, is shown.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1159
Author(s):  
Shyam Sundar Santra ◽  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Fluid Dynamics ◽  
Neural Networks ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Qualitative Behavior ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Delay Differential

In continuous applications in electrodynamics, neural networks, quantum mechanics, electromagnetism, and the field of time symmetric, fluid dynamics, neutral differential equations appear when modeling many problems and phenomena. Therefore, it is interesting to study the qualitative behavior of solutions of such equations. In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. Finally, we show an example to validate the main results, and an open problem is included.

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