Differential equations of motion of mechanical systems with variable parameters

1974 ◽  
Vol 10 (6) ◽  
pp. 671-674
Author(s):  
V. A. Lazaryan ◽  
L. A. Manashkin ◽  
A. V. Yurchenko
Keyword(s):  
Differential Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Variable Parameters

Differential equations of three-dimensional vibrations for one-dimensional mechanical systems with variable parameters

1984 ◽  
Vol 20 (1) ◽  
pp. 100-106
Author(s):  
E. P. Blokhin ◽  
A. V. Yurchenko ◽  
N. P. Yangulov
Keyword(s):  
Differential Equations ◽  
Three Dimensional ◽  
Mechanical Systems ◽  
Variable Parameters ◽  
One Dimensional

Transient Analysis of Forced Vibrations of Complex Structural-Mechanical Systems

1962 ◽  
Vol 66 (619) ◽  
pp. 457-460 ◽  
Author(s):  
S. P. Chan ◽  
H. L. Cox ◽  
W. A. Benfield
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Finite Differences ◽  
Transient Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Forced Vibrations ◽  
Degree Of Freedom ◽  
Dynamic Forces ◽  
Complex Structural

This paper presents a numerical method, derived directly from the basic differential equations of motion and expressed in the form of recurrence-matrix of finite differences, that can be generally applied to all multi-degree-of-freedom structures subjected to dynamic forces or forced displacements on any masses at any instants of time. The movements of the system may be described by any form of generalised co-ordinates.

Higher-order differential variational principle and differential equations of motion for mechanical systems in event space

2014 ◽  
Vol 23 (10) ◽  
pp. 104501
Author(s):  
Xiang-Wu Zhang ◽  
Yuan-Yuan Li ◽  
Xiao-Xia Zhao ◽  
Wen-Feng Luo
Keyword(s):  
Variational Principle ◽  
Differential Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Higher Order ◽  
Event Space

New Formulations on Motion Equations in Analytical Dynamics

2016 ◽  
Vol 823 ◽  
pp. 49-54 ◽  
Author(s):  
Iuliu Negrean ◽  
Kalman Kacso ◽  
Claudiu Schonstein ◽  
Adina Duca ◽  
Florina Rusu ◽  
...  
Keyword(s):  
Differential Equations ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Higher Order ◽  
Analytical Dynamics ◽  
Lagrange Principle ◽  
Motion Equations ◽  
Differential Motion

Using the main author's researches on the energies of acceleration and higher order equations of motion, this paper is devoted to new formulations in analytical dynamics of mechanical multibody systems (MBS). Integral parts of these systems are the mechanical robot structures, serial, parallel or mobile on which an application will be presented in order to highlight the importance of the differential motion equations in dynamics behavior. When the components of multibody mechanical systems or in its entirety presents rapid movements or is in transitory motion, are developed higher order variations in respect to time of linear and angular accelerations. According to research of the main author, they are integrated into higher order energies and these in differential equations of motion in higher order, which will lead to variations in time of generalized forces which dominate these types of mechanical systems. The establishing of these differential equations of motion, it is based on a generalization of a principle of analytical differential mechanics, known as the D`Alembert – Lagrange Principle.

Application of Euler Parameters to the Dynamic Analysis of Three-Dimensional Constrained Mechanical Systems

1982 ◽  
Vol 104 (4) ◽  
pp. 785-791 ◽  
Author(s):  
P. E. Nikravesh ◽  
I. S. Chung
Keyword(s):  
Differential Equations ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Influence Coefficient ◽  
Variable Order ◽  
Total System ◽  
Euler Parameters ◽  
Generalized Coordinates ◽  
Dependent Variables

This paper presents a computer-based method for formulation and efficient solution of nonlinear, constrained differential equations of motion for spatial dynamic analysis of mechanical systems. Nonlinear holonomic constraint equations and differential equations of motion are written in terms of a maximal set of Cartesian generalized coordinates, three translational and four rotational coordinates for each rigid body in the system, where the rotational coordinates are the Euler parameters. Euler parameters, in contrast to Euler angles or any other set of three rotational generalized coordinates, have no critical singular cases. The maximal set of generalized coordinates facilitates the general formulation of constraints and forcing functions. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent variables, and constructs an influence coefficient matrix relating variations in dependent and indpendent variables. This information is employed to numerically construct a reduced system of differential equations of motion whose solution yields the total system dynamic response. A numerical integration algorithm with positive-error control, employing a predictor-corrector algorithm with variable order and step size, integrates for only the independent variables, yet effectively determines dependent variables.

scholarly journals INVESTIGATION OF THE DYNAMICS OF NONLINEAR MECHANICAL SYSTEMS WITH LONG POWER LINES THROUGH DIGITAL MODELING

2019 ◽  
Vol 16 (33) ◽  
pp. 668-680
Author(s):  
L. A. KONDRATENKO ◽  
L. I. MIRONOVA ◽  
V. G. DMITRIEV ◽  
O. V. EGOROVA ◽  
A. O. SHEMIAKOV
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Wave Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Hydraulic Drive ◽  
Operating Conditions ◽  
Dynamic Features ◽  
Good Convergence ◽  
Operating Modes

Many of the mechanisms used in industry contain input and output links connected by long lines of force. Increasing the efficiency and service life of mechanical systems with long lines is of great importance for the country's economy. For a more rational use of these devices, it is important to maintain these operating modes with maximum accuracy, usually including the required speed of the actuator and the voltage in the lines. Such parameters can spontaneously change depending on the operating conditions of the system. In the presence of various influences, similar tasks to determine the marked regimes and parameters indicating the need for their change can be solved only with the help of the corresponding theory and research methods. The article presents the problems and the method of studying two-tier mechanical systems with an infinite number of degrees of freedom on the basis of the equations of momentum and moment of momentum in differential form. Transformations with the use of well-known wave equations are proposed, which made it possible to explicitly take into account the oscillations of the speeds of motion and stresses in the force lines of mechanical systems when describing dynamic processes. The solution of systems of partial differential equations is given using the Laplace transform, which made it possible to obtain general equations of motion and, after some simplifications, proceed to ordinary differential equations that take into account the dynamic features of systems with distributed parameters. The modernized Runge-Kutta method obtained solutions and carried out numerical simulation of transient processes in the hydraulic drive, the results of which have good convergence with full-scale experiments.

Integrals of Linearized Differential Equations of Motion of Mechanical Systems; Part I: Linearized Differential Equations

1987 ◽  
Vol 54 (3) ◽  
pp. 656-660 ◽  
Author(s):  
T. R. Kane ◽  
S. Djerassi
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Partial Linearization

Part I of this paper deals with relationships between integrals of a set of nonlinear differential equations and integrals of equations obtained from such a set by a process of linearization. The terms “total linearization,” “reduction,” and “partial linearization” are introduced, a theorem is stated and proved in connection with each of these, and the use of each theorem is illustrated by means of an example. In Part II, the theorems are applied to differential equations of motion of mechanical systems.

A Method for Testing Numerical Integrations of Equations of Motion of Mechanical Systems

1988 ◽  
Vol 55 (3) ◽  
pp. 711-715 ◽  
Author(s):  
T. R. Kane ◽  
D. A. Levinson
Keyword(s):  
Angular Momentum ◽  
Differential Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Test Results ◽  
Conservation Of Energy ◽  
Testing Method ◽  
Conservation Principle ◽  
Numerical Integrations ◽  
Conservation Principles

It is common practice to use conservation principles, such as the principles of conservation of energy or angular momentum, to test results of numerical integrations of differential equations of motion of mechanical systems. This paper deals with a testing method that can be used even when no conservation principle is applicable.

A set of ordinary differential equations of motion for constrained mechanical systems

2014 ◽  
Vol 79 (3) ◽  
pp. 1911-1938 ◽  
Author(s):  
S. Natsiavas ◽  
E. Paraskevopoulos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Constrained Mechanical Systems
Sign in / Sign up

Export Citation Format

Share Document