scholarly journals Taming the Beast: Diffusion Method in Nonlocal Gravity

Universe ◽  
2018 ◽  
Vol 4 (9) ◽  
pp. 95 ◽  
Author(s):  
Gianluca Calcagni
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Form Factors ◽  
Specific Form ◽  
Diffusion Method ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Gravitational Theories

We present a method to solve the nonlinear dynamical equations of motion in gravitational theories with fundamental nonlocalities of a certain type. For these specific form factors, which appear in some renormalizable theories, the number of field degrees of freedom and of initial conditions is finite.

Influence of Bistable Plunge Stiffness On Nonlinear Airfoil Flutter

2021 ◽  
Author(s):  
Renan F. Corrêa ◽  
Flávio D. Marques
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Vibration ◽  
Nonlinear Behavior ◽  
Limit Cycle Oscillation ◽  
Restoring Force ◽  
Aeroelastic System ◽  
Technical Literature ◽  
Practical Applications

Abstract Aeroelastic systems have nonlinearities that provide a wide variety of complex dynamic behaviors. Nonlinear effects can be avoided in practical applications, as in instability suppression or desired, for instance, in the energy harvesting design. In the technical literature, there are surveys on nonlinear aeroelastic systems and the different manners they manifest. More recently, the bistable spring effect has been studied as an acceptable nonlinear behavior applied to mechanical vibration problems. The application of the bistable spring effect to aeroelastic problems is still not explored thoroughly. This paper contributes to analyzing the nonlinear dynamics of a typical airfoil section mounted on bistable spring support at plunging motion. The equations of motion are based on the typical aeroelastic section model with three degrees-of-freedom. Moreover, a hardening nonlinearity in pitch is also considered. A preliminary analysis of the bistable spring geometry’s influence in its restoring force and the elastic potential energy is performed. The response of the system is investigated for a set of geometrical configurations. It is possible to identify post-flutter motion regions, the so-called intrawell, and interwell. Results reveal that the transition between intrawell to interwell regions occurs smoothly, depending on the initial conditions. The bistable effect on the aeroelastic system can be advantageous in energy extraction problems due to the jump in oscillation amplitudes. Furthermore, the hardening effect in pitching motion reduces the limit cycle oscillation amplitudes and also delays the occurrence of the snap-through.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

Phase transitions in the adsorbed molecular chains

Open Physics ◽  
2005 ◽  
Vol 3 (1) ◽  
Author(s):  
Victor Lykah ◽  
Evgen Syrkin
Keyword(s):  
Effective Potential ◽  
Degrees Of Freedom ◽  
Nearest Neighbor ◽  
Structural Data ◽  
Dynamical Analysis ◽  
Second Phase ◽  
Integral Of Motion ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Wave Limit

AbstractRotational excitations of molecular adsorbed layers are studied theoretically. Nonlinear dynamical equations are obtained with accounting of quadrupolar interactions between molecules and freezing of translational degrees of freedom. The equilibrium positions of the molecules are found to be experimentally observed structures with alternating rotational ordering of planar rotors along the direction to the nearest neighbor (for linear or square structures) under low temperature. Dynamical analysis gives an integral of motion (energy) of the chain that in the long-wave limit leads consequently to the existence of four phases. The first one corresponds to oscillations near equilibrium ordered states. The second phase corresponds to low-energy rotational excitations along ‘valleys’ (easy directions in the effective potential) that do not destroy strong correlations between molecules while structural data can show rotational disorder (melting). The third phase corresponds to an energy that is enough to travel between ‘valleys’; only some ‘islands’ in the angle space are forbidden. Complete destruction of correlation when the energy is over the peaks of the effective potential corresponds to the fourth phase. Therefore rotational melting is a complex phenomenon that has several stages.

Approximate Floquet Analysis of Parametrically Excited Multi-Degree-of-Freedom Systems With Application to Wind Turbines

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Gizem D. Acar ◽  
Brian F. Feeny
Keyword(s):  
Eigenvalue Problem ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
System Response ◽  
Periodic Part ◽  
Mdof Systems ◽  
Floquet Modes ◽  
Problem Frequency ◽  
Exponential Part

General responses of multi-degrees-of-freedom (MDOF) systems with parametric stiffness are studied. A Floquet-type solution, which is a product between an exponential part and a periodic part, is assumed, and applying harmonic balance, an eigenvalue problem is found. Solving the eigenvalue problem, frequency content of the solution and response to arbitrary initial conditions are determined. Using the eigenvalues and the eigenvectors, the system response is written in terms of “Floquet modes,” which are nonsynchronous, contrary to linear modes. Studying the eigenvalues (i.e., characteristic exponents), stability of the solution is investigated. The approach is applied to MDOF systems, including an example of a three-blade wind turbine, where the equations of motion have parametric stiffness terms due to gravity. The analytical solutions are also compared to numerical simulations for verification.

Dynamics of a Basketball Rolling Around the Rim

2005 ◽  
Vol 128 (2) ◽  
pp. 359-364
Author(s):  
C. Q. Liu ◽  
Fang Li ◽  
R. L. Huston
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Dynamical Equations ◽  
First Order ◽  
Coaching Strategies ◽  
Ball Motion

Governing dynamical equations of motion for a basketball rolling on the rim of a basket are developed and presented. These equations form a system of five first-order, ordinary differential equations. Given suitable initial conditions, these equations are readily integrated numerically. The results of these integrations predict the success (into the basket) or failure (off the outside of the rim) of the basketball shot. A series of examples are presented. The examples show that minor changes in the initial conditions can produce major changes in the subsequent ball motion. Shooting and coaching strategies are recommended.

Assessing the influence of the road-tire friction coefficient on the yaw and roll stability of articulated vehicles

2018 ◽  
Vol 233 (12) ◽  
pp. 2987-2999 ◽  
Author(s):  
André de Souza Mendes ◽  
Agenor de Toledo Fleury ◽  
Marko Ackermann ◽  
Fabrizio Leonardi ◽  
Roberto Bortolussi
Keyword(s):  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Lateral Force ◽  
Longitudinal Force ◽  
Convergence Region ◽  
The Road ◽  
Articulated Vehicles ◽  
Tire Friction

This article addresses the yaw stability of articulated vehicles by assessing the influence of the road-tire friction coefficient on the convergence region of a particular equilibrium condition. In addition, the boundaries of this region are compared to the boundaries of the non-jackknife and non-rollover regions to distinguish the instability phenomenon, jackknife or roll-over, responsible for this delimitation. The vehicle configuration considered in this analysis is composed by one tractor unit and one towed unit connected through an articulation point, for instance, a tractor-semitrailer combination. A nonlinear articulated bicycle model with four degrees of freedom is used together with a nonlinear lateral force tire model. To estimate the convergence region, the phase trajectory method is used. The equations of motion of the mathematical model are numerically integrated for different initial conditions in the phase plane, and the state orbits are monitored in order to verify the convergence point and the occurrence of instability events. In all cases, the longitudinal force on each tire, such as traction and braking, is not considered. The results show the existence of convergence regions delimited only by jackknife events, for low values of the friction coefficient, and only by rollover events, for high values of the friction coefficient. Moreover, the transition between these two conditions as the friction coefficient is changed is graphically presented. The main contributions of this article are the identification of the abrupt reduction of the convergence region as the value of the friction coefficient increases and the distinction of the instability events, jackknife or rollover, that define the boundaries of the convergence region.

The evolution of the gaseous envelope around a newborn protostar

2019 ◽  
Vol 28 (08) ◽  
pp. 1950103
Author(s):  
Mohammad Mahdi Memarian ◽  
Motahareh Mohammadpour
Keyword(s):  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Adomian Decomposition ◽  
Accretion Rates ◽  
Spherical Cloud ◽  
Isothermal Processes ◽  
Increasing Functions ◽  
The Magnetic Field

In this paper, we investigate the influence of nonisothermal processes on the evolution of the cloud's envelope around a newborn protostar. For this purpose, we study the evolution of a spherical cloud harboring a central hydrostatic newborn protostar. This model includes thermal effects due to heating of the cosmic rays and cooling of the gas and gas–dust energy transfer. We have ignored the effects of the magnetic field and rotation. The semianalytical Adomian decomposition method (ADM) is used to solve the system of nonlinear dynamical equations for different initial conditions. In this paper, the ADM allows us to follow the time evolution of the cloud's envelope and its mass accretion rate onto the newborn protostar. We find that the mass accretion rates of the envelope are increasing functions of time and highly depend on the choice of initial conditions. Moreover, we find that the nonisothermal processes affect the evolution of the mass accretion rates compared with the isothermal processes for different initial conditions.

scholarly journals Analytical Model of the Two-Mass Above Resonance System of the Eccentric-Pendulum Type Vibration Table

2020 ◽  
Vol 25 (4) ◽  
pp. 116-129
Author(s):  
O.S. Lanets ◽  
V.T. Dmytriv ◽  
V.M. Borovets ◽  
I.A. Derevenko ◽  
I.M. Horodetskyy
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Oscillation Mode ◽  
Oscillatory System ◽  
Forced Oscillations ◽  
System Of Differential Equations ◽  
Lagrange Equations

AbstractThe article deals with atwo-mass above resonant oscillatory system of an eccentric-pendulum type vibrating table. Based on the model of a vibrating oscillatory system with three masses, the system of differential equations of motion of oscillating masses with five degrees of freedom is compiled using generalized Lagrange equations of the second kind. For given values of mechanical parameters of the oscillatory system and initial conditions, the autonomous system of differential equations of motion of oscillating masses is solved by the numerical Rosenbrock method. The results of analytical modelling are verified by experimental studies. The two-mass vibration system with eccentric-pendulum drive in resonant oscillation mode is characterized by an instantaneous start and stop of the drive without prolonged transient modes. Parasitic oscillations of the working body, as a body with distributed mass, are minimal at the frequency of forced oscillations.

Kinematics and dynamics of a parallel manipulator with a new architecture

Robotica ◽  
2000 ◽  
Vol 18 (5) ◽  
pp. 535-543 ◽  
Author(s):  
A. Fattah ◽  
G. Kasaei
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Orthogonal Complement ◽  
Flight Simulator ◽  
Kinematics And Dynamics ◽  
Dynamical Equations ◽  
Euler’S Equations ◽  
Euler's Equations ◽  
Moving Platform

In this paper, the kinematics and dynamics of a parallel manipulator with a new architecture supposed to be used as a moving mechanism in a flight simulator project is studied. This manipulator with three independent degrees of freedom consists of a moving platform connected to a based platform by means of three legs. Kinematic solutions for this manipulator at position, velocity and acceleration levels are obtained. Moreover, the dynamical equations of motion of the manipulator are determined using Newton-Euler's equations and applying the natural orthogonal complement (NOC) method. Using kinematics and dynamics and also performing simulation for different manoeuvres of moving platform, the motion and the actuator forces of the legs are obtained.

scholarly journals A fully nonlinear, dynamically consistent numerical model for solid-body ship motion. I. Ship motion with fixed heading

2010 ◽  
Vol 467 (2128) ◽  
pp. 911-927 ◽  
Author(s):  
Ray-Qing Lin ◽  
Weijia Kuang
Keyword(s):  
Numerical Model ◽  
Solid Body ◽  
Initial Conditions ◽  
A Priori ◽  
Hydrodynamic Pressure ◽  
Ship Motion ◽  
Body Motion ◽  
Dynamical Equations ◽  
Fully Nonlinear ◽  
Nonlinear Dynamical

In this paper, we describe the details of our numerical model for simulating ship solid-body motion in a given environment. In this model, the fully nonlinear dynamical equations governing the time-varying solid-body ship motion under the forces arising from ship–wave interactions are solved with given initial conditions. The net force and moment (torque) on the ship body are directly calculated via integration of the hydrodynamic pressure over the wetted surface and the buoyancy effect from the underwater volume of the actual ship hull with a hybrid finite-difference/finite-element method. Neither empirical nor free parametrization is introduced in this model, i.e. no a priori experimental data are needed for modelling. This model is benchmarked with many experiments of various ship hulls for heave, roll and pitch motion. In addition to the benchmark cases, numerical experiments are also carried out for strongly nonlinear ship motion with a fixed heading. These new cases demonstrate clearly the importance of nonlinearities in ship motion modelling.

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