scholarly journals Discrete-continuous computational model of the coupled dynamic system: pantograph – overhead contact line

2016 ◽  
Vol 2016 (5) ◽  
pp. 71-83 ◽  
Author(s):  
Danuta Bryja ◽  
Dawid Prokopowicz
Keyword(s):  
Computer Simulation ◽  
Dynamic System ◽  
Computational Model ◽  
Contact Line ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Dynamic Interaction ◽  
Catenary System ◽  
Cable Vibrations

The paper presents the computational model of the pantograph – overhead contact line (OCL), which uses the theory of cable vibrations and Lagrange – Ritz approximation method to derive equations of motion of the overhead contact line subjected to moving pantographs. The pantograph is modelled as a dynamic system of two degrees of freedom describing the motion of two masses replacing a collector head and an articulating frame. The overhead contact line is defined as a catenary system with continuously distributed mass. It consists of a multi-span cable characterized by a curvilinear route (catenary wire) and a straight cable (contact wire) connected with a catenary wire by elastic droppers. The main objective of the paper is to present principal ideas of the computational model, with a particular emphasis on formulating the equation of motion of a pre-tensioned multi-span cable with non-negligible static sag. Much attention is paid to the description of dynamic interaction between the pantograph and overhead contact line. The model allows computer simulation of catenary vibrations induced by two pantographs passing over the contact line, as well as a simulation of dynamic increments of the contact force.

Automatic Generation of Equations of Motion of Mechanical Systems

2014 ◽  
Vol 611 ◽  
pp. 40-45
Author(s):  
Darina Hroncová ◽  
Jozef Filas
Keyword(s):  
Computer Simulation ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Automatic Generation ◽  
Lagrange Equations ◽  
Kinematic Chains ◽  
Transformation Matrices

The paper describes an algorithm for automatic compilation of equations of motion. Lagrange equations of the second kind and the transformation matrices of basic movements are used by this algorithm. This approach is useful for computer simulation of open kinematic chains with any number of degrees of freedom as well as any combination of bonds.

An Efficient Algorithm for Nonlinear Analysis of Vehicle/Track Interaction Problems

2016 ◽  
Vol 16 (08) ◽  
pp. 1550040 ◽  
Author(s):  
J. Sadeghi ◽  
A. Khajehdezfuly ◽  
M. Esmaeili ◽  
D. Poorveis
Keyword(s):  
Time Domain ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Dynamic Interaction ◽  
Integration Scheme ◽  
Equilibrium Equations ◽  
Track System ◽  
Newton Raphson ◽  
Interaction Problem

In this paper, a new algorithm for solving the vehicle/track dynamic interaction problem is developed, aimed at reducing the computational cost. The algorithm called Advanced Solver Algorithm (ASA) uses the full Newton–Raphson incremental-iterative method in conjunction with the Newmark integration scheme to solve the equilibrium equations of the coupled vehicle/track system in time domain. Considering the track as a beam resting on a viscoelastic foundation and each vehicle as a wagon with ten degrees of freedom, the governing differential equations of motion of the vehicle/track system were derived. The wheel/rail contact was considered as a nonlinear Hertz spring and consequently the vehicle/track nonlinear dynamic interaction problem was solved. A comparison between the results of the ASA and those of the most advanced algorithm available was made to evaluate the efficiency of the ASA. It is confirmed that using the ASA can result in 40–70 % of reduction in computational cost.

Aerodynamic and flight dynamic interaction in spin

2019 ◽  
Vol 91 (3) ◽  
pp. 437-447
Author(s):  
Ewa Marcinkiewicz ◽  
Zdobyslaw Jan Goraj ◽  
Marcin Figat
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Integrated Approach ◽  
Dynamic Interaction ◽  
Euler Method ◽  
Computational Method ◽  
Control Surface ◽  
Sideslip Angle ◽  
Flight Tests ◽  
Content Type

PurposeThe purpose of this paper is to describe an integrated approach to spin analysis based on 6-DOF (degrees of freedom) fully nonlinear equations of motion and a three-dimensional multigrid Euler method used to specify a flow model. Another purpose of this study is to investigate military trainer performance during a developed phase of a deliberately executed spin, and to predict an aircraft tendency while entering a spin and its response to control surface deflections needed for recovery.Design/methodology/approachTo assess spin properties, the calculations of aerodynamic characteristics were performed through an angle-of-attack range of −30 degrees to +50 degrees and a sideslip-angle range of −30 degrees to +30 degrees. Then, dynamic equations of motion of a rigid aircraft together with aerodynamic loads being premised on stability derivatives concept were numerically integrated. Finally, the examination of light turboprop dynamic behaviour in post-stalling conditions was carried out.FindingsThe computational method used to evaluate spin was positively verified by comparing it with the experimental outcome. Moreover, the Euler code-based approach to lay down aerodynamics could be considered as reliable to provide high angles-of-attack characteristics. Conclusions incorporate the results of a comparative analysis focusing especially on comprehensive assessment of output data quality in relation to flight tests.Originality/valueThe conducted calculations take into account aerodynamic and flight dynamic interaction of an aerobatic-category turboprop in spin conditions. A number of manoeuvres considering different aircraft configurations were simulated. The computational outcomes were subsequently compared to the results of in-flight tests and the collected data were thoroughly analysed to draw final conclusions.

Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms With Mutual Dependence Between Rigid Body and Elastic Motions: Part II—System Equations

1990 ◽  
Vol 112 (2) ◽  
pp. 215-224 ◽  
Author(s):  
S. Nagarajan ◽  
D. A. Turcic
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Elastic Response ◽  
Mutual Dependence ◽  
Generalized Coordinates ◽  
Lagrange’S Equation ◽  
Elastic Mechanism

The first step in the derivation of the equations of motion for general elastic mechanism systems was described in Part I of this work. The equations were derived at the elemental level using Lagrange’s equation and the generalized coordinates were both the rigid body degrees of freedom, and the elastic degrees of freedom of element ‘e’. Each rigid body degree of freedom gave rise to a scalar equation of motion, and the elastic degrees of freedom of element e gave rise to a vector equation of motion. Since both the rigid body degrees of freedom and elastic degrees of freedom are considered as generalized coordinates, the equations derived take into account the mutual dependence between the rigid body and elastic motions. This is important for mechanisms that are built using lightweight and flexible members and which operate at high speeds. A schematic diagram of how the equations of motion are obtained in this work is shown in Fig. 1 in Part I. The transformation step in the figure refers to the rotational transformation of the nodal elastic displacements (which were measured in the element coordinate system), so that they are measured in terms of the reference coordinate system. This transformation is necessary in order to ensure compatibility of the displacement, velocity and acceleration of the degrees of freedom that are common to two or more links during the assembly of the equations of motion. This final set of equations after assembly are obtained in closed form, and, given external torques and forces, can be solved for the rigid body and elastic response simultaneously taking into account the mutual dependence between the two responses.

scholarly journals Design Blocks in Simulink to Detection Singularity in the Workspace of Gough-Stewart Robot Manipulator

2019 ◽  
Vol 27 (1) ◽  
pp. 1-15
Author(s):  
Hassan Mohammed Alwan ◽  
Riyadh Ahmed Sarhan
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Lagrange Method ◽  
Six Degrees Of Freedom ◽  
Moving Platforms ◽  
Current Input ◽  
Fixed Base

This work deals with Gough-Stewart robot manipulator, which has six degrees of freedom, six actuators, fixed base, and moving platforms. Here, the Jacobian matrix derived to detect the singular point in the workspace for manipulator at determinant of Jacobian matrix equal to zero, then derived the equation of motion from the dynamic analysis by Lagrange method to verify the singular points with Jacobian where the forces increase rapidly at this point. Finally, design blocks in Simulink include the Jacobian matrix and the equations of motion to detection the singularities at any time for current input parameters (X, Y, Z, α, β, γ), where the determinant of the Jacobian equal to zero at maximum forces.

scholarly journals STABILITY AND CONTROLABILITY ANALYSIS ON LINEARIZED DYNAMIC SYSTEM EQUATION OF MOTION OF LSU 05-NG USING KALMAN RANK CONDITION METHOD

2020 ◽  
Vol 18 (2) ◽  
pp. 81
Author(s):  
Angga Septiyana
Keyword(s):  
Dynamic System ◽  
State Space ◽  
Equations Of Motion ◽  
Moment Equation ◽  
Equation Of Motion ◽  
Stability Control ◽  
Rank Condition ◽  
System Equation ◽  
Kalman Rank Condition ◽  
Scientific Platform

This paper discusses the stability, control and observation of the dynamic system of the Lapan Surveillance UAV 05-NG (LSU 05-NG) aircraft equation. This analysis is important to determine the performance of aircraft when carrying out missions such as photography, surveillance, observation and as a scientific platform to test communication based on satellite. Before analyzing the dynamic system, first arranged equations of motion of the plane which includes the force equation, moment equation and kinematics equation. The equation of motion of the aircraft obtained by the equation of motion of the longitudinal and lateral directional dimensions. Each of these equations of motion will be linearized to obtain state space conditions. In this state space, A, B and C is linear matrices will be obtained in the time domain. The results of the analysis of matrices A, B and C show that the dynamic system in the LSU 05-NG motion equation is a stable system on the longitudinal dimension but on the lateral dimension directional on the unstable spiral mode. As for the analysis of the control of both the longitudinal and lateral directional dimensions, the results show that the system is controlled.

An Efficient O(N) Algorithm for Computer Simulation of Rigid Body Molecular Dynamics

2007 ◽  
Author(s):  
Shanzhong Duan ◽  
Andrew Ries
Keyword(s):  
Molecular Dynamics ◽  
Computer Simulation ◽  
Degrees Of Freedom ◽  
Molecular System ◽  
Equations Of Motion ◽  
Interaction Forces ◽  
High Frequencies ◽  
Coordinate Method ◽  
Computational Costs ◽  
Solution Of Equations

Molecular dynamics is effective for a nano-scale phenomenon analysis. There are two major computational costs associated with computer simulation of atomistic molecular dynamics. They are calculation of the interaction forces and formation/solution of equations of motion. In this paper, an O(N) (order N) procedure is presented for calculation of the interaction forces and formation/solution of equations of motion. For computational costs associated with potentials or interaction forces, an internal coordinate method is used. Use of the internal coordinate method makes application of multi-rigid body molecular dynamics to an atomistic molecular system become possible. The algorithm based on the method makes the calculation considerably more practical for large-scale problems encountered in molecular dynamics such as conformation dynamics of polymers. For computational costs associated with formation/solution of equations of motion, Kane method and the internal coordinate method are used for recursive formation and solution of equations of motion of an atomistic molecular system. However, in computer simulation of atomistic molecular dynamics, the inclusion of lightly excited all degrees of freedom of an atom, such as inter-atomic oscillations and rotation about double bonds with high frequencies, introduces limitations to the simulation. The high frequencies of these degrees of freedom force the use of very small integration step sizes, which severely limit the time scales for the atomic molecular simulation over long periods of time. To improve this, holonomic constraints such as strictly constant bond lengths and bond angles are introduced to freeze these high frequency degrees of freedom since they have insignificant effect on long time scale processes in conformational dynamics. In this way, the procedure developed in multibody dynamics can be utilized to achieve higher computing efficiency and an O(N) computational performance can be realized for formation/solution of equations of motion.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

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