scholarly journals Impulse control of a two-link manipulation robot

2021 ◽  
Vol 57 ◽  
pp. 77-90
Author(s):  
Yu.F. Dolgii ◽  
I.A. Chupin
Keyword(s):  
Computer Simulation ◽  
Configuration Space ◽  
Impulse Control ◽  
Nonlinear Differential Equations ◽  
Classical Mechanics ◽  
First Integrals ◽  
Initial Moment ◽  
Analytical Integration ◽  
Impulse Controls ◽  
Manipulation Robot

A nonlinear problem of controlling the movements of a two-link manipulation robot is considered. The free mechanical system has two first integrals in involution. Methods of classical mechanics are used for analytical integration of the system of nonlinear differential equations. A trajectory connecting the initial and final positions of the two-link manipulation robot in the configuration space is found. Impulse controls at the initial moment of time impart the necessary energy to the robot to enter this trajectory. Impulse controls are also used to damp the speeds of the robot at the end position. In a computer simulation of the proposed procedure for moving the robot, generalized impulse controls are approximated by rectangular impulses.

scholarly journals IMPULSE CONTROL OF THE MANIPULATION ROBOT

2019 ◽  
Vol 5 (2) ◽  
pp. 13 ◽  
Author(s):  
Yurii F. Dolgii ◽  
Alexander N. Sesekin ◽  
Ilya G. Chupin
Keyword(s):  
Computer Simulation ◽  
Kinetic Energy ◽  
Impulse Control ◽  
First Integrals ◽  
Lagrangian Mechanics ◽  
Solvability Conditions ◽  
Control Goal ◽  
Analytical Formulas ◽  
Impulse Controls ◽  
Manipulation Robot

A nonlinear control problem for a manipulation robot is considered. The solvability conditions for the problem are obtained in the class of special impulse controls. To achieve the control goal, the kinetic energy of the manipulation robot is used. When finding analytical formulas for controls, the classical first integrals of Lagrangian mechanics were used. The effectiveness of the proposed algorithm is illustrated by computer simulation.

scholarly journals Non-Smooth Geodesic Flows and Classical Mechanics

1969 ◽  
Vol 12 (2) ◽  
pp. 209-212 ◽  
Author(s):  
J. E. Marsden
Keyword(s):  
Phase Space ◽  
Kinetic Energy ◽  
Hamiltonian Systems ◽  
Configuration Space ◽  
Smooth Function ◽  
Cotangent Bundle ◽  
Classical Mechanics ◽  
Riemannian Metric ◽  
Geodesic Flows ◽  
Image Position

As is well known, there is an intimate connection between geodesic flows and Hamiltonian systems. In fact, if g is a Riemannian, or pseudo-Riemannian metric on a manifold M (we think of M as q-space or the configuration space), we may define a smooth function Tg on the cotangent bundle T*M (q-p-space, or the phase space). This function is the kinetic energy of q, and locally is given by

An Observation on Least Action Principle in Classical Mechanics Oriented on the Evaluation of Relativistic Error Concerning the Measurements of Light Propagating in a Liquid

2011 ◽  
Vol 1 (3) ◽  
pp. 14-24 ◽  
Author(s):  
Alessandro Massaro ◽  
Piero Adriano Massaro
Keyword(s):  
Euler Equations ◽  
Classical Mechanics ◽  
First Integrals ◽  
Action Principle ◽  
Classical Approach ◽  
Limit Case ◽  
Least Action Principle ◽  
Calculus Of Variation ◽  
Least Action ◽  
Approximate First Integrals

The authors prove that the standard least action principle implies a more general form of the same principle by which they can state generalized motion equation including the classical Euler equation as a particular case. This form is based on an observation regarding the last action principle about the limit case in the classical approach using symmetry violations. Furthermore the well known first integrals of the classical Euler equations become only approximate first integrals. The authors also prove a generalization of the fundamental lemma of the calculus of variation and we consider the application in electromagnetism.

Respiratory sinus arrhythmia: laws derived from computer simulation

1960 ◽  
Vol 15 (5) ◽  
pp. 863-874 ◽  
Author(s):  
Manfred Clynes
Keyword(s):  
Heart Rate ◽  
Computer Simulation ◽  
Differential Equations ◽  
Respiratory Sinus Arrhythmia ◽  
Nonlinear Differential Equations ◽  
Analogue Computer ◽  
Sinus Arrhythmia ◽  
Respiratory Effects ◽  
Rate Effects ◽  
Mathematical Relations

Dynamic mathematical relations describing respiratory sinus arrhythmia were derived through analogue computer simulation. If a signal proportional to thorax circumference is fed into the analogue computer, it calculates with differential equations the complex heart rate changes in real time and records them along with those of the real heart. Close correspondence of the predicted and actual changes of heart rate for a wide variety of modes of breathing, and for different individuals, proves the validity of the nonlinear differential equations describing the phenomenon. The respiratory effects are shown to be caused by two separate reflexes each producing biphasic heart rate transients in the same directions. The observed effects are the result of superposition of those transients. Previous paradoxical results in attempting to relate heart rate to respiration on a steady-state, nondynamic basis are thus explained. The laws indicate that stretch receptors and not hemodynamic or central nervous factors initiate the changes in heart rate. The analysis also allows heart rate effects of exercise and emotional stresses to be more precisely perceived, as clearly separated from respiratory effects. Submitted on June 16, 1959

scholarly journals Instability of Surface Quasigeostrophic Spatially Periodic Flows

2019 ◽  
Vol 77 (1) ◽  
pp. 239-255 ◽  
Author(s):  
M. V. Kalashnik ◽  
M. V. Kurgansky ◽  
S. V. Kostrykin
Keyword(s):  
Continued Fraction ◽  
Nonlinear Oscillations ◽  
Nonlinear Differential Equations ◽  
Classical Mechanics ◽  
Growth Increment ◽  
Periodic Flows ◽  
Galerkin Approximations ◽  
Spatially Periodic ◽  
Zero Potential ◽  
The Galerkin Method

Abstract The surface quasigeostrophic (SQG) model is developed to describe the dynamics of flows with zero potential vorticity in the presence of one or two horizontal boundaries (Earth surface and tropopause). Within the framework of this model, the problems of linear and nonlinear stability of zonal spatially periodic flows are considered. To study the linear stability of flows with one boundary, two approaches are used. In the first approach, the solution is sought by decomposing into a trigonometric series, and the growth rate of the perturbations is found from the characteristic equation containing an infinite continued fraction. In the second approach, few-mode Galerkin approximations of the solution are constructed. It is shown that both approaches lead to the same dependence of the growth increment on the wavenumber of perturbations. The existence of instability with a preferred horizontal scale on the order of the wavelength of the main flow follows from this dependence. A similar result is obtained within the framework of the SQG model with two horizontal boundaries. The Galerkin method with three basis trigonometric functions is also used to study the nonlinear dynamics of perturbations, described by a system of three nonlinear differential equations similar to that describing the motion of a symmetric top in classical mechanics. An analysis of the solutions of this system shows that the exponential growth of disturbances at the linear stage is replaced by a stage of stable nonlinear oscillations (vacillations). The results of numerical integration of full nonlinear SQG equations confirm this analysis.

ON TWO HIERARCHIES OF SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS, FIRST INTEGRALS, NAMBU MECHANICS, AND PAINLEVÉ PROPERTY

2010 ◽  
Vol 07 (03) ◽  
pp. 405-409
Author(s):  
WILLI-HANS STEEB
Keyword(s):  
Differential Equations ◽  
Chaotic Behavior ◽  
Nonlinear Differential Equations ◽  
Autonomous Systems ◽  
First Integrals ◽  
Harmonic Oscillators ◽  
Painlevé Test ◽  
Yang Mills ◽  
Nambu Mechanics ◽  
Painlevé Property

We study a hierarchy of nonlinear autonomous systems of first ordinary differential equations. We show that it is completely integrable using the Painlevé test and finding the first integrals. We also show that it can be derived from the first integrals using Nambu mechanics. A corresponding dynamical system with chaotic behavior is also derived. A modified system with harmonic oscillators as first integrals is also considered. A connection with the Yang–Mills equation and the self-dual Yang–Mills equation is also discussed.

An Observation on Least Action Principle in Classical Mechanics Oriented on the Evaluation of Relativistic Error Concerning the Measurements of Light Propagating in a Liquid

2013 ◽  
pp. 166-176
Author(s):  
Alessandro Massaro ◽  
Piero Adriano Massaro
Keyword(s):  
Euler Equations ◽  
Classical Mechanics ◽  
First Integrals ◽  
Action Principle ◽  
Classical Approach ◽  
Limit Case ◽  
Least Action Principle ◽  
Calculus Of Variation ◽  
Least Action ◽  
Approximate First Integrals

The authors prove that the standard least action principle implies a more general form of the same principle by which they can state generalized motion equation including the classical Euler equation as a particular case. This form is based on an observation regarding the last action principle about the limit case in the classical approach using symmetry violations. Furthermore the well known first integrals of the classical Euler equations become only approximate first integrals. The authors also prove a generalization of the fundamental lemma of the calculus of variation and we consider the application in electromagnetism.

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