Dynamic Equilibrium Configurations of Multibody Systems

2014 ◽  
Vol 619 ◽  
pp. 8-12
Author(s):  
Ju Seok Kang
Keyword(s):  
Iteration Method ◽  
Multibody Systems ◽  
Equilibrium Configuration ◽  
Dynamic Equilibrium ◽  
Mechanical Systems ◽  
Railway Vehicle ◽  
Algebraic Form ◽  
Constrained Mechanical Systems ◽  
Speed Governor ◽  
Equilibrium Configurations

It is difficult to calculate dynamic equilibrium configuration in the mechanical systems, especially with the constraint conditions. In this paper, a method to calculate the dynamic equilibrium positions in the constrained mechanical systems is proposed. The accelerations of independent coordinates are derived in the algebraic form so that the numerical solution is easily obtained by the iteration method. The proposed method has been applied to calculate the dynamic equilibrium configuration for speed governor and the wheelset of railway vehicle.

On the Use of the Canonical Equations of Motion for the Dynamic Analysis of Constrained Multibody Systems

1992 ◽  
Author(s):  
E. Bayo ◽  
J. M. Jimenez
Keyword(s):  
Dynamic Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Numerical Algorithms ◽  
Constrained Multibody Systems ◽  
Constrained Mechanical Systems ◽  
First Order ◽  
Canonical Variables ◽  
Lagrange’S Multipliers

Abstract We investigate in this paper the different approaches that can be derived from the use of the Hamiltonian or canonical equations of motion for constrained mechanical systems with the intention of responding to the question of whether the use of these equations leads to more efficient and stable numerical algorithms than those coming from acceleration based formalisms. In this process, we propose a new penalty based canonical description of the equations of motion of constrained mechanical systems. This technique leads to a reduced set of first order ordinary differential equations in terms of the canonical variables with no Lagrange’s multipliers involved in the equations. This method shows a clear advantage over the previously proposed acceleration based formulation, in terms of numerical efficiency. In addition, we examine the use of the canonical equations based on independent coordinates, and conclude that in this second case the use of the acceleration based formulation is more advantageous than the canonical counterpart.

Tolerance Analysis of Dynamic Equilibria in Multibody Systems Having Prescribed Rotational Motion

2007 ◽  
Author(s):  
Dong Hwan Choi ◽  
Hong Hee Yoo ◽  
Jonathan A. Wickert
Keyword(s):  
Monte Carlo ◽  
Rotational Motion ◽  
Multibody Systems ◽  
Dynamic Equilibrium ◽  
Tolerance Analysis ◽  
Computational Method ◽  
Speed Governor ◽  
Gyroscope Sensor ◽  
Power Generation Systems ◽  
Dynamic Equilibria

A general formulation for the tolerance analysis of dynamic equilibria in multibody systems having prescribed rotational motion is developed. In a state of dynamic equilibrium, a subset of generalized coordinates assume constant values, while the remaining coordinates vary and respond in time. Applications in which multibody systems exhibit dynamic equilibria include robots, spacecraft, propulsion and power generation systems, and some sensor devices. In the derived approach, manufacturing tolerances are mathematically modeled by probabilistic and statistical variables, through an analytical approach and through Monte Carlo simulation. An efficient computational method based upon direct differentiation is developed to calculate the first order sensitivity of the equilibria with respect to the design and manufacturing variables. To verify the accuracy and effectiveness of the present method, the present analytical method and the companion Monte Carlo approach are applied in examples to a rotating pendulum, a mechanical speed governor, and a model of a rate gyroscope sensor.

A Comparative Study on Some Different Formulations of the Dynamic Equations of Constrained Mechanical Systems

1987 ◽  
Vol 109 (4) ◽  
pp. 466-474 ◽  
Author(s):  
J. Unda ◽  
J. Garci´a de Jalo´n ◽  
F. Losantos ◽  
R. Enparantza
Keyword(s):  
Comparative Study ◽  
Relative Efficiency ◽  
Multibody Systems ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Dynamic Equations ◽  
Natural Coordinates ◽  
Constrained Mechanical Systems ◽  
Computer Codes

This paper presents a comparative theoretical and numerical study on the efficiency of several numerical methods for the dynamic analysis of constrained mechanical systems, also called in the literature multibody systems. This comparative study has been performed between methods based on the use of “reference point” coordinates and those based on the use of “natural” coordinates. This study embraces different possibilities to formulate the differential equations of motion. The relative efficiency of the resulting algorithms has been analyzed theoretically in terms of the number of multiplications needed to evaluate the mechanism accelerations. This efficiency has also been studied implementing the methods into computer codes and testing them with different examples. Conclusions on the relative efficiency of the methods are finally presented.

scholarly journals Dynamic Equilibria in Statistical and Nonlinear Physics of Uniform Stress Rotating Space Elevators (USRSE)

2019 ◽  
Vol 11 (6) ◽  
pp. 56
Author(s):  
Leonardo Golubovic ◽  
Steven Knudsen
Keyword(s):  
Carbon Nanotubes ◽  
Materials Science ◽  
Dynamic Equilibrium ◽  
Outer Space ◽  
Point Of View ◽  
Uniform Stress ◽  
The Earth ◽  
Equilibrium Configurations ◽  
Space Elevators ◽  
Dynamic Equilibria

The discovery of ultra-strong materials such as carbon nanotubes and diamond nano-thread structures has recently motivated an enhanced interest for the physics of Space Elevators connecting the Earth with outer space. A new concept has recently emerged in space elevator physics: Rotating Space Elevators (RSE) [Golubović, L. & Knudsen, S. (2009). Classical and statistical mechanics of celestial scale spinning strings: Rotating space elevators. Europhysics Letters 86(3), 34001.]. Objects sliding along rotating RSE string (sliding climbers) do not require internal engines or propulsion to be transported from the Earth's surface into outer space. Here we address the physics of a special RSE family, Uniform Stress Rotating Space Elevators (USRSE), characterized by constant tensile stress along the string. From the point of view of materials science, this condition provides the best control of string’s global integrity. We introduce an advanced analytic approach to obtain the dynamic equilibrium configurations of USRSE strings. We use our results to discuss the applications of USRSE for spacecraft launching.

scholarly journals Numerical solution for consistent initial conditions of constrained mechanical systems

2003 ◽  
Vol 25 (3) ◽  
pp. 170-185
Author(s):  
Dinh Van Phong
Keyword(s):  
Numerical Solution ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Differential Algebraic Equations ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Flexible Approach ◽  
Constrained Mechanical Systems ◽  
Consistent Initial Values

The article deals with the problem of consistent initial values of the system of equations of motion which has the form of the system of differential-algebraic equations. Direct treating the equations of mechanical systems with particular properties enables to study the system of DAE in a more flexible approach. Algorithms and examples are shown in order to illustrate the considered technique.

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