scholarly journals PROBLEM OF THE COSMIC GRAVITY MEASUREMENT

2021 ◽  
Vol 82 (2) ◽  
pp. 46-49
Author(s):  
Vasil Сhaban ◽  
Keyword(s):  
Computer Simulation ◽  
Differential Equations ◽  
Physical Interpretation ◽  
Equations Of Motion ◽  
Gravity Measurement ◽  
Force Component ◽  
Universal Gravitation ◽  
Finite Velocity ◽  
Celestial Bodies ◽  
First Time

Based on Newton's adapted law of universal gravitation in the case of moving masses, taking into account the finite velocity of gravity, differential equations of motion of celestial bodies are obtained. The transient process of the precession of the planet's perihelion was simulated for the first time. A new physical interpretation of the celestial phenomenon due to the discovered new component of force in addition to the Newtonian and Lorentz (gravitomagnetic) is given. The problem of measuring a new force has been formed. The results of computer simulation of the precessing perihelion of the planet considering a new force component are discussed.

scholarly journals Differential equations of motion of a material point in the perpendicular plane to the plane of the gravitating disk

2021 ◽  
Vol 24 (3) ◽  
pp. 1307
Author(s):  
Zhenisgul Rakhmetullina ◽  
Indira Uvaliyeva ◽  
Farida Amenova
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Nonlinear Equations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Material Point ◽  
Point System ◽  
Disk Material ◽  
Analytical Review ◽  
Celestial Bodies

This paper presents an analytical solution of the differential equations of motion of a material point in the plane perpendicular to the plane of the gravitating disk. The differential equations of the problem under study and the applied Gilden's method are described in the works of A. Poincaré. Differential equations refer to nonlinear equations. The analysis of methods for solving nonlinear differential equations was carried out. The methodology of applying the Gilden method to the solution of the differential equations under consideration can be applied in studies of the problem of the motion of celestial bodies in the “disk-material point” system in perpendicular planes. To identify the various properties of the gravitating disk, an analytical review of the state of the problem of the motion of a material point in the field of a gravitating disk is carried out. Summing up the presented review on the problem under study, a conclusion is made. The substantive formulation of the problem is described, which is formulated as follows: the study of the influence of disk-shaped bodies on the motion of a material point and methods for their solution.

scholarly journals Law of universal gravitation with finite velocity of gravity and mathematical model of motion of a finite number of material points

2020 ◽  
pp. 120-123
Author(s):  
Vasyl Slyusarchuk
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Finite Number ◽  
Ordinary Differential Equations ◽  
Classical Model ◽  
Universal Gravitation ◽  
Finite Velocity ◽  
Deviating Argument ◽  
The Law ◽  
Material Points

The law of universal gravitation is intro- duced taking into account the finiteness of the gravi- tational velocity. Based on this law, a mathematical model of the motion of a finite number of material points is constructed, a separate case of which is the classical model of the motion of points, which is de- scribed by a system of ordinary differential equations. The constructed model is a system of nonlinear dif- ferential equations with deviating argument and func- tional equations. It more accurately describes the dy- namics of a finite number of material points than the corresponding classical model. A mathematical model of the motion of two material points is also considered.

scholarly journals Introductory Address

1979 ◽  
Vol 81 ◽  
pp. 1-4
Author(s):  
Yusuke Hagihara
Keyword(s):  
Differential Equations ◽  
Celestial Mechanics ◽  
Physical Theory ◽  
Initial Conditions ◽  
Stellar Systems ◽  
Universal Gravitation ◽  
Time Space ◽  
All Solutions ◽  
Celestial Bodies ◽  
The Masses

The aim of celestial mechanics is to derive all solutions of the differential equations of the three- and n-body problems and to reveal the interrelation among all such solutions with various values of the masses and initial conditions, not only to predict the positions of celestial bodies at any instant but to think over the cosmogony of stellar systems and to ascertain the law of universal gravitation in view of the time-space picture of physical theory.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

Dynamics of Rolling-Element Bearings—Part I: Cylindrical Roller Bearing Analysis

1979 ◽  
Vol 101 (3) ◽  
pp. 293-302 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Normal Force ◽  
Equations Of Motion ◽  
Roller Bearing ◽  
Rolling Element Bearings ◽  
Analytical Formulation ◽  
Rolling Element ◽  
Cylindrical Roller Bearing ◽  
Cylindrical Roller ◽  
Bearing Analysis

An analytical formulation for the roller motion in a cylindrical roller bearing is presented in terms of the classical differential equations of motion. Roller-race interaction is analyzed in detail and the resulting normal force and moment vectors are determined. Elastohydrodynamic traction models are considered in determining the roller-race tractive forces and moments. Formulation for the roller end and race flange interaction during skewing of the roller is also considered. Roller-cage interactions are assumed to be either hydrodynamic or fully metallic. Simple relationships are used to determine the churning and drag losses.

scholarly journals Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Justine Yasappan ◽  
Ángela Jiménez-Casas ◽  
Mario Castro
Keyword(s):  
Asymptotic Behavior ◽  
Viscoelastic Fluid ◽  
Closed Loop ◽  
Theoretical Study ◽  
Equations Of Motion ◽  
Asymptotic Properties ◽  
Inertial Manifold ◽  
Thermal Gradients ◽  
External Temperature ◽  
First Time

Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian) fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient.

Mulit-Pulse Orbits and Chaotic Motion of Composite Laminated Plates

2008 ◽  
Author(s):  
Xiangying Guo ◽  
Wei Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Differential Equations ◽  
Thin Plate ◽  
Equations Of Motion ◽  
Laminated Plates ◽  
Phase Method ◽  
Rectangular Thin Plate ◽  
Partial Differential ◽  
Chaotic Motions

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

2010 ◽  
Vol 25 (02) ◽  
pp. 135-141
Author(s):  
H. A. ELEGLA ◽  
N. I. FARAHAT
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Singular System ◽  
Constrained Systems ◽  
Classical Structure ◽  
Path Integral Quantization ◽  
Total Differential

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

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